The "quantum leap" to which the title of this book refers is to betaken both literally and figuratively. In its literal sense, thequantum leap is the tiny but explosive jump that a particle ofmatter undergoes in moving from one place to another. The "newphysics"—quantum physics—indicates that all particles compos-ing the physical universe must move in this fashion or cease toexist. Since you and I are composed of atomic and subatomicmatter, we too must "take the quantum leap."

In the figurative sense, taking the quantum leap meanstaking a risk, going off into an unchartered territory with noguide to follow. Such a venture is an uncertain affair at best. Italso means risking something that no one else would dare risk.But both you and I are willing to take such risks. I have riskedwriting this book and you, a nonphysicist, have risked picking itup to read. My colleagues warned me that such an undertakingwas impossible. "No one could understand quantum physics with-out a firm mathematical background," they told me.

For the scientists who discovered the underlying reality ofquantum mechanics, the quantum leap was also an uncertain andrisky affair. The uncertainty was literal. A quantum leap for anatomic particle is not a guaranteed business. There is no way toknow with absolute certainty the movements of such tinyparticles of matter. This in fact led to a new law of physics calledthe Principle of Indeterminism. But such new laws were risky,and the risk was to the scientists' sanity and self-respect. The newphysics uncovered a bizarre and magical underworld. It showedphysicists a new meaning for the word order. This new order, thebasis for the new physics, was not found in the particles ofmatter. Rather, it was found in the minds of the physicists.

Which meant that physicists had to give up their precon-ceived ideas about the physical world. Today, nearly eighty yearsafter the discovery of the quantum nature of matter, they are stillforced to reconsider all they had previously thought was sacro-sanct. The quantum world still holds surprises.

This book presents both the history and the concepts of thenew physics, called quantum mechanics. The most abstractconcepts, those least grounded in common experience, are pre-sented imaginatively. In this way, what was literal is presentedfiguratively. The thread of history and imaginative concepts runs

throughout the narrative. Thus I hope to reach even the mostmathematically unskilled among my readers.

Let me give an example. Quantum physicists discovered thatevery act of observation made of an atom by a physicist dis-turbed the atom. How?

Imagine you have been invited to tea. Surprise: the tea isgiven by extremely tiny elves! You will have to squeeze into theirlittle elfin house. Welcome in anyway. Watch your head,though—the rooms aren't very high. Watch your step, too—elvesonly need tiny furniture to sit in. Be careful ... oh well, too late.You just stomped a tiny teacup out of existence.

Peering into the world of atoms and subatomic particles islike looking into such an elfin house, with one additional distrac-tion: every time you look in, you must open a door or shutter,and in doing so, you shake up the delicate little house so badlythat it appears in total disorder.

Moreover, not only are the elves tiny, they are very tempera-mental. Walk into their house with a chip on your shoulder orfeeling just plain lousy and the little people behave very badlytoward you. Smile and act nice and they are warm and sparkly.Even if you aren't aware of your feelings in the matter, they are.Thus when you leave their little home, you may have had a goodor bad time and not realized how much you were responsible foryour experience.

If you now add that all you can observe is the results of suchactions (i.e., opening and closing elf house doors, shaking up elfhouses, breaking cups, etc.), you soon begin to wonder if whatyou are looking at is really a normal elf house or somethingentirely different. To some considerable extent, observationswithin the world of atoms appear equally bizarre. The meagerestattempt to observe an atom is so disruptive to the atom that it isnot possible to even picture what an atom looks like. This has ledscientists to question what is meant by any convenient picture ofan atom. A few scientists hold to the belief that atoms only existwhen they are observed to exist as fuzzy little balls.

In their reluctant attempts to describe the world of tinyobjects like atoms and electrons (tiny particles contained withinan atom and carrying an electrical charge), physicists devisedquantum mechanics. The discovery of the new physics is thestory of their adventure into the magical world of matter andenergy. Their attempts were reluctant because each discoverymade led to new and paradoxical conclusions. There were threeparadoxes.

The first paradox was that things moved without following alaw of mechanical motion. Physicists had grown accustomed tocertain basic ideas concerning the way things move. There was aninvested "faith" in the Newtonian or classical mechanical pictureof matter in motion. This picture described motion as a continu-ous "blend" of changing positions. The object moved in a "flow"from one point to another.

Quantum mechanics failed to reinforce that picture. In fact,it indicated that motion could not take place in that way. Instead,things moved in a disjointed or discontinuous manner. They"jumped" from one place to another, seemingly without effort andwithout bothering to go between the two places.

The second paradox involved scientists' view of science as areasonable, orderly process of observing nature and describingthe observed objectively. This view was founded on theconviction that whatever one observed as being out there wasreally out there. The idea of objectivity being absent from scienceis abhorrent to any rational person, particularly a physicist.

Yet quantum mechanics indicated that what one used toobserve nature on an atomic scale "created" and determined whatone saw. It is like always seeing light through a set of coloredfilters. The color of the light depends on the filter used. Yet therewas no way to get rid of the filters. Physicists don't know whatthe filters are. Even the most basic idea of matter, the concept ofa "particle," turns out to be misunderstood if one assumes thatthe particle has properties totally independent of the observer.What one observes appears to depend upon what one chooses toobserve.

In itself, that is not paradoxical. But the total picture of theobserved, drawn from the sum of observations, appears to benonsensical. Consider another example.

In a well-known experiment called the double slit experi-ment ^ a stream of particles is directed toward a screen. A secondscreen, containing two long and parallel slits, is placed inbetween the stream's source and the original screen. In this wayeach particle must pass through one slit or the other in order toreach the final screen. Each time a particle strikes the final screenit leaves a tiny imprint or dark spot. Yet the amazing thing isthat if you close down one of the slits more particles make theirway to certain places on the final screen than if you leave bothslits open.

There is no way to understand this paradox if you regard thestream as simply made up of little particles. How does a single

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particle know if you have two slits or only one slit open? Sinceeach particle has a choice of two slits to pass through, each hastwice the opportunity of reaching any point on the final screen.This means that, with two slits open, the particles should reachthe empty spaces on the screen with a greater frequency. Yet thatis not what we observe. When two slits are opened, the particlesleave empty spaces on the final screen adjoined by darkenedregions where they do finally land.

Closing down one of the two slits denies the particles anychoice. Yet they manage to fill in the blank spaces between thedarkened regions as soon as one slit is shut.

Introduction

Why do the particles avoid certain places on the screen whenboth slits are opened? Are the particles "aware" of the two slits?No ordinary commonsense picture of a particle explains the weirdbehavior it demonstrates when confronted with two choices.Perhaps the two possible paths for each particle, either throughone slit or the other, interfere with each other and cancel them-selves out. Or perhaps the particles in the stream bump into eachother when they pass through the slits.

No, it doesn't work that way. The particles can be controlledso that no more than one at a time passes through the slits. Yeteach and every particle avoids the blank spaces on the screenwhen both slits are opened. Perhaps there is another way toexplain the experiment.

Yes, there is. The particles are not particles when they passthrough the slits—they are waves. And waves do interfere witheach other. In fact, when each particle is given a wavelength andwave interference is taken into account, the blank spaces on thescreen are completely explainable. That means there must havebeen an error in the first picture of the particles. They are not"particles" at all. They are waves.

No, that isn't correct either. When the waves arrive at thescreen, they do not land everywhere on the screen at once likeany ordinary wave should. Instead, the waves arrive as a series ofpointlike spots. Thus the "waves" are particles after all.

Particles or waves? Which is the true picture? It depends onwhich part of the experiment is being performed. With one slitopen, the stream is composed of particles. With two slits, it iscomposed of waves. The nature of the physical stream of"particles" depends on how we set up the experiment.

The interference paHern from an arrangemen-tanalogous to a double slit produced by electrons.

Introduction

Which brings us to the third paradox presented by the newphysics: despite the natural disorder apparent in this and otherexperiments, quantum mechanics indicates that there is an orderto the universe. It simply isn't the order we expected. Evendescribing the true order of the universe is difficult because itinvolves something more than the physical world. It involves us,our minds, and our thoughts. Just how physics and our minds areto be brought together is a controversial subject. The gradualrecognition that what we think may physically influence what weobserve has led to a revolution in thought and philosophy, not tomention physics.

Quantum mechanics appears to describe a universal order thatincludes us in a very special way. In fact, our minds may enterinto nature in a way we had not imagined possible. The thoughtthat atoms may not exist without observers of atoms is, to me, avery exciting thought. Could this fact concerning atoms alsoapply in other realms of science? Perhaps much of what is takento be real is mainly determined by thought. Perhaps the appear-ance of the physical world is magical because the orderlyprocesses of science fail to take the observer into account. Theorder of the universe may be the order of our own minds.

Part One

Welcome to theMachine

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The PassiveObserver

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"Who has seen the wind?" asks poet Christina Rossetti. "Neitheryou nor I," yet we certainly believe it is there. Similariy, no onehas ever seen a fundamental particle, and yet physicists have agreat deal of faith in its existence. But to hold to that faith, theyhave had to give up some very precious ideas concerning thephysical worid, the world of matter and energy. What emergedfrom their reluctant ventures into this tiny worid of atoms, mole-cules, and other fundamental pari:icles was quantum mechanics.What they discovered using quantum mechanics has turned outto be a new insight concerning the universe: the observer affectsthe observed.

The roots of quantum mechanics, the new physics of motion,are buried in the ancient soil of our earliest awareness of howthings moved. Even further back in time, before any awarenessof motion, there existed a tiny tendril from these roots, and thatwas the idea of the observer. And within that idea is the notion ofthe "passive" or nondisruptive observer. Humans are creatures ofthe eye. They believe what they see.

Before scientific observation could take place, one had tolearn to observe, to tell things apart, and this took a very longtime to do. The earliest human observations were quite passiveand nondiscriminatory. We first began to observe our ownseparate existence. Looking up and out, we next began to observethings that were not ourselves. Timidly we reached out andtouched, sometimes with painful consequences. The world "outthere" was not always friendly. Overcoming our fears, we beganto touch things again and take them apart, especially if thesethings didn't bite. These were active or experimental obser-vations.

More than likely, our first observations were of movingobjects, such as grass blowing in the wind or clouds driftingoverhead. At night we saw the stars . . . and wondered. Fromdaybreak we watched the sun make its journey through the sky,following a path much like that of the stars through the nightsky. Perhaps we picked up a rock and threw it.

Movement caught our eyes and told secrets of the naturalorder of things. Fire went up. Matter stayed close to the earth.Air floated above water, and water fell to earth where it toofloated upon the earth's surface.

When things were out of their natural places, they moved,seeking the places they had come from. Fire came from the stars,for example. When humans entered the scene, we disrupted thenatural flow or continuous movement of everything to its properplace. By passively observing, we would learn nature's secrets.By touching, we would disrupt and learn nothing.

But we could think about motion. We could imagine how itwas occurring. We could even make models of motion, imaginingthe movement of an arrow flying as a series of stationary arrows,each arrow following upon another, like a sequence of still framesin a motion picture reel.

These thoughts and first observations were the roots of themodern science of motion, the magical world of quantummechanics.

Daivn of Consciousness

It is not difficult to travel back in time to the earliest humanattempts at observation. Simply observe a newborn baby. As youwatch an infant's attempts to grasp a finger held before itseyes—and indeed grasp understanding—you are witnessing theearly human observer. The child is becoming aware of the subtledivision between itself and the outside world.

A process of thinking is going on. It is wordless. Einsteinoften said that he got his best ideas in pictures rather thanwords. In fact, Einstein did not speak at all until he was fouryears old.

Perhaps there is a process of synthesis or analysis going onin an infant's mind. The child may be attaching the sounds itsmother makes to the things it observes. In any case, a distinctionmust be occurring in the child's mind. That distinction—theseparation of the "out there" from the "in here"—is called thesubject-object distinction.

When the first hypothetical observer was first learning thisdistinction, he was becoming conscious. Consciousness meansawareness, and that first awareness had to be the concept of"I am." In sensing this "I," our first observer was learning thathe was not his thumb nor his foot. The "in here" experience was"I." The "out there" experience was "it."

Today we make this distinction with no trouble at all. Con-sider a simple example. Become aware of your thumb. You canfeel your thumb or, better, you can sense the presence of yourthumb. Next, become aware of your left heel. Again with just a

thought, you can feel your heel. In fact, you can sense any part ofyour body this way. You need not reach over physically and feelyour body parts with your hands. You are able to sense them allwith your mind.

Once you have done this you realize that you are not thething you feel. We could regard this experience as the movementof your consciousness or awareness from your mind to your bodypart. A certain division takes place. A distinction separates your"in here" from your thumb or your heel. That "in here" experi-ence is necessary before any real observation can take place.Observation deals entirely with the "out there" experience.

It is thought that perhaps three thousand or more yearsago, people were not able to distinguish the "out there" in aclear way from the "in here" or "I am" experience. They mayhave been only dimly aware of their capacity to make such adistinction. They had no "I" consciousness. Julian Jaynes offers aspeculation on the development of the "I" consciousness in hisbook, The Origin of Consciousness and the Breakdown of theBicameral Mind.^

Jaynes claims that, about three thousand years ago, our fore-parents suffered their first "nervous breakdown." They thenbecame aware of themselves as "I" people and ceased to beunaware automatons following the voices of "gods" in theirheads. According to Jaynes, the two halves of the bicameral brainwere functioning more or less separately. But when the break-down occurred, the voices stopped and human beings becameaware of themselves as independent entities.

From this rather rude awakening humans learned a newawareness of their surroundings. The period of the early Greeksstarted only about five hundred years after the generalbreakdown proposed by Jaynes. Internal "godlike voices" are nolonger ruling human consciousness, but there are probably stillsome remnants of the early rumblings in Greek heads. TheGreeks began to observe everything in sight with a passion.However, being afraid of the "out there" and not too sure of them-selves, they remained passive but quite accurate observers. Andtheir first question was: "Is all one, or is all change?"

All Is One; All Is Change

The first observations of the early Greeks had to do with God,the spirit, and matter.^ They considered two conflicting ways ofunderstanding the human condition: either all was one or all was

12 Welcome to the Machine

change. These were no idle thoughts to the Greeks. They werebased upon observation. Indeed, these thoughts were largelybased upon self-observation.

Let us consider the hypothesis that all is one. How can wetoday understand that idea? We start with the undeniable experi-ence we all feel—the experience of our own existence, the instantknowing that is for each of us consciousness of our being. This isthe "I" experience, perhaps the only experience that each of us"knows" for sure. As you hold this book in your hands, take amoment to reflect that you are doing so. That instant ofreflection is the "all is one" experience that the Greeks werethinking about. To them, this experience was ultimate and funda-mental.

But what about everything else? Everything else was anillusion, a trip to Disneyland or the movies. After all, we ceinnotever be certain that everything and everyone out there is reallythere. They are beyond our immediate experience. This was the"all being" or "at one with God" experience described by theGreeks. By always keeping track of this experience—i.e., remem-bering oneself each instant—this "one being" experience, the "I,"was God, and all else was illusion.

Some early Greeks held a conflicting view. For them, all waschange and there was no God, no omnipotent, unchanging Being.The moment or instance of "I" awareness was the illusion. Theonly reality was continuous change or movement. This was allthere was. There were no things at rest. To hold on to the illusionof "I" was incorrect and impossible. You change. Moment followsmoment. Time marches on whether or not we wish it to do so.Returning to the original example of you holding this book inyour hands, notice that even to grasp the idea that you are nowreading requires change. You cannot hold the moment still. Evenyour awareness that you "know" this has, just this instant as youread on, passed into the past. There is no "I." There is no you.There is only change and movement.

Thus arose the conflict between change and Being. And it ledto many lively discussions on the shores of ancient Greece. Thebeginnings of the scholastic tradition of thinking and writingabout such matters was the next step after the dawn of con-sciousness. The mystery of God, spirit, matter, and motion werebeing pursued with vigor. Out of this debate arose the very spiritof science. The roots of quantum mechanics were strengthened. Ifthings change, then how do they do so?

The Idea of Discontinuity

I have always found Charlie Chaplin movies amusing. The littleguy is always getting in trouble by sticking his nose where itdoesn't belong. But, miraculously, he escapes from every predica-ment. Usually he manages this by moving in a very disjointed ordiscontinuous manner. I am amused, of course, because I knowthat motion doesn't really take place the way it appears in aChaplin movie. In read life, motion appeeirs smooth and con-tinuous—not at all Chaplinesque. The **jumps" that we see in thefilm are artificial. They occur because the real life motion hasbeen replaced by a moving series of still pictures.

The notion of the continuity of motion being composed of aseries of stationary instants has been with us for a long time.Since we are also able to experience being at rest or sitting stillwhile posing for a photograph, it is natural to try to imagine howwe can move from one place to another.

The first scientific thoughts about the discontinuity of move-ment undoubtedly occurred to the early Greeks. The Greekthinkers Zeno and Aristotle^ pointed out the difficulty withattempting to analyze the motion of an object as a series of "stillframes."

Zeno presented his idea of the discontinuity of motion asthree paradoxes. He pointed out that there is a differencebetween what we mean by motion as we imagine it occurring andwhat we actually see occurring in real life. He showed this differ-ence by analyzing the motion of an object as if it consisted ofconsecutive still frames in a motion picture film.

Later, Aristotle attempted to salvage the idea that motioncould not occur this way, that in real life an object moved as acontinuous "whole." He felt that Zeno's "motion picture" concept ofmovement had to be wrong. And he demonstrated his perspectiveby pointing to two different ways of interpreting Zeno's idea ofmotion. Aristotle's attempt to show Zeno's error turned out to bequite successful. It paralyzed further thinking about motion asoccurring discontinuously and it led to the faith that, "in princi-ple," motion could be understood as a continuous stream ofinseparable still instants.

This idea of continuity of movement has proven extremelydifficult to shake. It is at the heart of modem mathematics,particularly evident in the concept of continuous functions andmodern calculus. The entrenchment of Aristotle's concept ofmotion, together with the Greeks' reluctance to analyze nature,

Welcome to the Machine

kept these early thinkers from discovering the discontinuousmotion of atomic-sized objects. Despite Zeno's theory, this dis-covery would not take place for another two thousand years.

Zeno and Moving Things

Zeno lived in Elea, which had already been established as a homefor scholastic thinking. And think he did. Although often over-looked in a typical course in science, Zeno was the forerunner ofthe modern theoretical physicist. The job of theoretical physicistsis to explain observations. If we are unsuccessful in doing so, weare to point out that something is askew in our understanding ofthose very same observations. In short, we earn our money eitherway. Either we show how to understand an observation that waspreviously not understood or we tactfully point out that we havebeen mistaken in thinking we understand what we have seen.

Zeno fulfilled the second role of the theoretical physicist verywell. He pointed out to his fellow scholastics that "their headswere filled with beans." He used logical argument (a newfoundtool of thinking after the bicameral breakdown) to prove thatmotion is impossible.

Now of course Zeno knew that motion was not impossible.These Greeks were not stupid. But Zeno was concerned withthe understanding of motion, and he was offering, through aseries of arguments, an analysis of motion. This was not an easything for his fellow thinkers to accept, since Zeno was attemptingto prove that the way motion took place was not the way theythought it did.

Zeno provided three paradoxes concerning motion. Eachdealt with the way an object moves through space and time. The

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question Zeno brought out was, "How can we understand move-ment if an object is to occupy a given place at a given time?"

Indeed, an object must occupy a given place at a given time,for it cannot occupy more than its given place at any one time orit would have to be in two or more places at the same time. "Thuswe must assume," as I imagine Zeno presenting himself, "a givenobject must occupy a given place at a given time and certainly nomore."

Now we come to Zeno's second point. He continues: "If it istrue that the object behaves as I have stated, then it must leaveits given place at the given time in order to reach the next placeat a later time. And therein lies the rub." Let us look at this"rub" in its three paradoxical parts presented by Zeno.

Zeno^s First Paradox

"Motion cannot exist," says Zeno, "because in order for a runnerto reach the endpoint of his race, he must first reach the pointhalfway between the endpoint and the starting point." We wouldcertainly concur. The runner must go at least halfway to the goalline before he can cross it. "But," Zeno continues, "don't you seethe paradox in this? Before he can reach the halfway point, hemust reach the point midway between the halfway point and thestarting line." Again we see no problem here. "Well, there is aproblem," Zeno retorts, "because the statement I just made canbe applied to any distance in this race. Before the runner canreach the quarterway point, he must reach the one-eighthwaypoint, and before that, the one-sixteenthway point, and beforethat..."

Zends race- The runner neve^ can get Startecl-

Welcome to the Machine

Okay, so we see that for the runner to go any distance in therace, he must go halfway first, and there appears to be no end tothe number of halfway points along the route to the finish line."That's it," cries Zeno. "There are an infinite number of thesehalfway points, and each of them marks off a finite distance therunner must reach before he can go on to the next point. There-fore there is no first distance he can run to, because. ..." Becausehe must go halfway first and so on—we finally see the point. Therunner is stuck at the starting gate with no way to go. But ofcourse runners do run, and Zeno knew this. Therefore, thequestion still remained, "How do we explain this?" Before we do,let us allow Zeno to present his second paradox.

Zeno's Second Paradox

"Achilles can never overtake the tortoise in a race," Zenodeclares. "Even though the slower tortoise is ahead of Achilles bya modest distance, the faster Achilles cannot reach him. Becauseto do so, Achilles must first reach the point just departed by theturtle before he can catch up to the turtle. And as my firstparadox demonstrated, there would be an infinite number of suchpoints for Achilles to face. Certainly as long as there is anydistance between them, the turtle will have left any point beforeAchilles arrives there."

Do you see that Zeno's second paradox is very much like hisfirst? Instead of a runner racing along a fixed course, we haveAchilles racing to catch up with the tortoise, which is always a littledistance, and therefore a variable distance, in front of him.Hence, Achilles has his work cut out, for no matter how smallthat distance may be, it too contains an infinite number ofmidway points along the way.

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The Passive Observer

Zeno's third paradox will be different. It will directlyconfront our conception of motion as a series of still instances.As Zeno presents this paradox, imagine you are looking at a stripof home-movie footage containing several frames of an arrow inflight.

Zeno's Third Paradox

'The arrow cannot fly. It cannot fly because an object that isbehaving itself in a uniform manner is either continually movingor continually at rest. The arrow is certainly behaving itself insuch a uniform manner. Now watch the arrow as it travels alongits flight path. Clearly, at any instant, the arrow is occupying agiven place. Therefore, if it is occupying a place, it must be atrest there. The arrow must be at rest at the instant we picture,and since the instant we have chosen is any instant, the arrowcannot be moving at any instant. Thus the arrow is always atrest and cannot fly."

You may be tempted to point out to Zeno that an objectoccupying a given position could be moving and not necessarilybe at rest. However, you must remember that Zeno insists thatthe object behave itself in a uniform manner and that means itmust behave consistently. If on object occupies space, it stays inthat space. Filmmakers use Zeno's consideration of consistencyto create animated movies. They shoot each frame as a stillphotograph, minimizing jiggles and nonuniformities in their care-fully laid-out mattes. They would agree that an object in a filmscene must be at rest in each frame it occupies.

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Thus Zeno was asking us to think about how we move fromone still frame to another. How can an arrow appear in differentpositions in each frame? We know the answer with the animatorswho shoot films. They alter the setup when no one is looking andso create a magic illusion of motion. Zeno wondered how natureor God performed her or his magic show.

Aristotle felt that Zeno's ideas were very important. He alsofelt that he had an answer to Zeno's paradoxes of motion. Theanswer was continuity or, better, the wholeness of continuity andthe mistrust of analysis.

Aristotle's Attempt to Resolve Zeno's Paradoxes

Although Aristotle attempted to dispose of Zeno's arguments, hestill considered them important. He presented Zeno's paradoxesand his own resolutions in Physica. Aristotle wrote Physicanearly one hundred years sifter Zeno lived. I'm sure that if Zenohad been around at that time, their debate would have been quitelively. In fact, the conflict between these two thinkers remindsme of a later debate between Bohr and Einstein. We will get achance to "overhear" their discussion in a later chapter. Itconcerns a very similar issue: is nature continuous?

Aristotle showed that Zeno's paradoxes of motion could beresolved if we understood that there were two very different waysto interpret Zeno. The key was the idea of the infinity of spaceand time, the space and time occupied by an object as it movesfrom one place to another.

"For there are two distinct meanings to an infinite number,"Aristotle explained, "depending on whether we are dividing up oradding together. When we are adding up small pieces of space ortime, we soon run out of either if we go on to infinity. But if wehave a finite region of space or interval of time, then we can go ondividing it up forever by making each piece as small as we wish.

"Thus," he continued, "a runner reaches the endpoint of hisrun without difficulty. The distance covered is finite and can bedivided into as many small pieces as we wish on to infinity. Thesame is true for the time of the runner's race. Time, too, is finiteand can be divided up to infinity. So motion exists because itdoes not take an infinite amount of time for the runner to coverthe distance. Both the time taken and the distance covered arefinite, even though they can be infinitely subdivided.

**When we apply the same argument to Achilles and thetortoise, we can see that the faster-moving Achilles will overtakethe tortoise in the race. The distance between them is finite andtherefore it will take Achilles a finite time to overtake the turtle.That ends the first and second paradoxes.

"As far as Zeno's third paradox is concerned, the arrow willassuredly fly. It is quite simple to see how—just add more framesto its motion picture as is done in high-speed motion photog-raphy. The time interval between any two frames can be sub-divided again into an infinite number of subintervals so tiny thateach represents a 'point of time' perfectly frozen. If a singlesnapshot is taken for each of these frozen instants, we will have acontinuous dissolve of one frame to the next showing that thearrow moves continuously."

Although I've updated Aristotle's language a little, I'm surethat if he were around today, he wouldn't mind. His argumentsare quite convincing. Yet they are based upon the subtle assump-tion that it is possible to subdivide to infinity. We certainlywould agree with him that we cannot add up to infinity.

But hold on. To see the arrow move as a series of continuousdissolving movie frames, we must view many more than themodern filmmaker's usual twenty-four frames per second. Weneed an infinite number of frames passing before our eyes eachsecond. So dividing up motion to infinity is really no differentthan adding up to infinity.

This subtlety eluded Aristotle and everyone who came afterhim for the next two thousand years and more. By assuming thatthe arrow's motion was continuous, it was natural to imaginecontinuity as "made up" of an infinite number of still frames,even though we would never attempt to make such a motionpicture. We just believed that "in principle" it was possible.

By 1926 that hope was demolished. Werner Heisenberg, theyoung physicist who demolished it, was later to be awarded theNobel prize in physics for his realization that Zeno was correctafter all. Heisenberg's Principle of Indeterminism (or Principle ofUncertainty, as it is often called) reaffirmed Zeno's objection that"an object cannot occupy a given place and be moving at thesame time." Heisenberg recognized that observation, as weactually experience it, does not allow us to analyze motion on toinfinity. Sooner or later we see that our activity introduces dis-continuities in whatever we are observing. These discontinuitiesare fundamental to the new physics of the twentieth century.

In dismissing Zeno's arguments, Aristotle was reaffirmingthe already firmly fixed idea that, "in principle," passive observa-

22 Welcome to the Machine

tion could be continued no matter how we subdivided time andspace. Thus the continuity concept and passive observation wenthand in hand. There was no point in seeking still movie frames ofdiscontinuous motion—they were not to be found. Motion was awhole. It was a continuous dissolve. It was its own thingundivided.

Retrospect: The End of Passiiity

Aristotle's thoughts would continue to play a role in Westernthinking for nearly two thousand years. Although it was not"good physics" to analyze motion by actually stopping an objectin flight and then assume that motion was a series of connected"stops," it was certainly all right to do so as a mental exercise.Anytime humans intervened, they interfered with naturalmotion. But there was no harm in thinking about motion as con-nected stops.

Aristotle believed in natural motion. Humans' interferenceproduced discontinuous or unnatural movements. And, toAristotle, such movements were not God's way. For example,Aristotle envisioned the idea of "force." The heavy cart beingdrawn along the road by the horse is an unnatural movement.That is why the horse is struggling so. That is why the motion isso jerky and uneven. The horse must exert a "force" to get thecart moving. The horse must continue to exert a "force" to keepthe cart moving. As soon as the horse stops pulling, it stopsexerting a "force" on the cart. Consequently, the cart comes to itsnatural place, which is at rest on the road.

Aristotle did not seem to enter into the debate between thosewho believed in an "all is one" divine Being and those who sup-ported the "all is change" philosophy. However, he did feel thatthe mind, spirit, and soul were more important than the physicalworld. It is possible that the fifth element in Aristotle's physics,the ether, was the same "physis" mentioned by his forefathers inElea. This "physis" was the essential essence of all matter. Per-haps Aristotle saw the origin of movement in the vibrations ofthis essence. He certainly wondered about it. "How come thearrow flies continuously," he asked, "now that the bow thatcaused its flight is no longer in contact with it?" Somehow theperfection of natural movement was being imitated by humaninterference.

The Passive Observer 23

Within the world of the mind, these thoughts occurredthousands of years ago. Scientists were passive then. It wouldtake a while before they would attempt to reach out and touch, totry ideas and see if they worked. Then scientists would no longersimply accept the naturalness of motion. They would have to seefor themselves by setting up experiments that would isolate andseparate motion into parts. They would learn something fromthis. What they would learn eventually would not resolve any ofthe paradoxes of motion however. It would turn out that both"truths" of Zeno and Aristotle were correct. Motion was con-tinuous and smooth, provided it was unseen. Motion was discon-tinuous, whenever it was observed, provided we looked hard enoughto see it.

These discoveries would not occur until the twentiethcentury. Before then, we would attempt to analyze motion assum-ing that, "in principle," our manipulations were nondisruptive.This period of scientific history may be regarded as the age of theactive observer. It would produce some remarkable successes. Itwould also produce some still-to-be-resolved mysteries concerningmotion.

Chapter 2

The Active Observer

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With the coming of active observation, the invisible wind becamevisible. It was seen as a hailstorm of molecules, tiny littleparticles only billionths of an inch in diameter. All motion wasanalyzed or, in principle, could be analyzed or envisioned as con-sisting of these tiny "hailstones." A new spirit of inquiry hadappeared. It foretold the coming of the Mechanical Age or Age ofReason. It would lead to mechanics or the science of motion.Quantum mechanics would emerge from the human desire toreach out and touch things.

In the latter part of the sixteenth century, edmost twothousand years after Aristotle lived, the fear of active analysiswould at last be overcome. Passive observation had ended. Theactive observer was eager to explore and take things apart.

This period of unrestricted inquiry would take precedence forthe next four hundred years. It would begin with a small numberof dedicated scientist-analysts working as individuals throughoutwestern Europe. These would include Copernicus, Kepler, Bruno,Galileo and Descartes. Later Isaac Newton would refer to thesemen as having provided the firm foundation for his thinking. Ashe would state, *'If I have seen farther than others, it is because Ihave stood on the shoulders of giants."^ Newton would see far.And after Newton would come a "Golden Age of Certainty."

A new faith in the "mechanical universe" would be bom.Michael Faraday would discover how to turn electricity into mag-netism. James Clerk Maxwell would invent a mechanical model oflight and show that light was a form of electricity andmagnetism.

These were a new breed, these scientist-analysts. Their aimwas to take things apart, analyze everything, be critical, and uselogic ruthlessly. The image of the cold, withdrawn scientist startshere. Unfortunately, the image of this kind of scientist is stillwith us today.

In the typical, corny movie, the wild-eyed, splatter-haired,and white-coated scientist is seen experimenting on his newestmonster. He is a fictional relic from the Age of Reason. Scientistswere building machines to take machines apart. The human-made machines were designed to peer into the nature-mademachines. Nature was no longer something to just sit back fromand ponder over. Science was an activity requiring careful experi-

Welcome to tne Machine

mental or "hands-on" abilities. There was no limit to what onecould see by searching into the smallest of things. The newscientist-analysts had faith that mathematical analysis wouldcorrectly describe the behavior of even the tiniest things theydiscovered.

Welcome to the machine

This approach would have been near heresy to the earlyGreeks. Mathematical analysis, like actual "hands-on" analysis,would not have been trusted. The idea that motion was a con-tinuous dissolve from one stationary point to another wasaccepted by these later analysts. Newton and Leibnitz wouldeven develop a mathematics of continuity, which we today call"the calculus." This mathematics of continuity would describemotion as observed in Newton's laws of motion. The never-endingnumbers of explorers into the Lilliputian land of physics wouldalways be able to dissect every line into an infinite array ofpoints, each point joined to the next.

The "whole" observed by the Greeks was always more thanthe sum of its parts. No longer. The "whole" envisioned duringthe Mechanical Age exactly equaled its sum of parts. No moreand no less. This was essential to the mechanical picture. Therewere no missing pieces. Everything measurable was accountable.Laws of conservation arose. Mass or matter was conserved.Momentum, the product of mass and velocity, was also con-served, providing you measured not only the speeds of theobjects involved, but also the directions in which they weregoing. Energy was conserved. Things were what they were—nomore and no less.

As scientists carefully studied its parts, the world of physicsbecame simpler, more understandable. By piecing together theseparts, they found they could understand any complex motion.Only by a careful study of the tree could the forest be seen. Theacorn was, after all, just an acorn. The emerging oak tree grewaccording to laws of motion, even if we didn't happen to knowjust how to apply those laws to it.

Newton's laws of motion were the supreme laws of the uni-verse. But within their formulation was a carefully hiddenassumption: The observer does not disturb; the observerobserves what is there. The physical world was a gigantic clock-work. It could be taken apart and put back together. It wouldwork the same. And Newton's laws predicted a strange kind ofsymmetry. The clock would work just as well running backwardas running forward. From any given moment in time, the futurewas completely determined and could be predicted by followingthe continuous mathematical description offered by Newton'slaws.

Furthermore, by knowing the "now," the past could be recon-structed. But the reconstruction would not be based on hindsightand fallible human memory. Rather, it would follow the "timesymmetry" in Newton's equations. The past was continuously

28 Welcome to the Machine

connected to the present. The future was continuously connectedto the present. Thus all was determined. By the nineteenthcentury, the mechanical Age of Reason had become the Age ofCertainty.

And with the end of the nineteenth century, a new and yetancient view would begin to emerge. It would start with twomysteries. The first would be the discovery that something wasmissing in the mechanical picture of light, that light wavestraveled without any substance to wave in. The second would bethe realization that the colors of light from any hot glowingmaterial, such as the filament of a light bulb, could not beexplained by the mechanical movement or vibrations of thatmaterial.

With the new spirit of analysis and the discovery that lightand heat behaved in mysterious ways, quantum mechanics wouldbegin to break the soil of the grounded Age of Certainty. Withoutthe efforts of all of the scientists during this pre-twentieth-centuryperiod, quantum mechanics would not have occurred.

All of this began with that small group Newton called"giants."

IVeivton's Giants: The Age of Reason

The first of the Age of Reason new breed Newton called "giants"was Nicolaus Copernicus. In the sixteenth century, when hewrote that the earth could not sit at the universe's center, it washeresy even to say such a thing. Saint Thomas Aquinas in thethirteenth century had brought his Christian theology togetherwith the Aristotelian view that the earth was positioned in thecenter of the universe and the stars moved in perfect continuouscircles around the earth. Therefore, to suggest that the earth wasnot at the center was to risk death at the hands of the church'sinquisitors.

In 1514, Copernicus published his first work, a monographsuggesting that the earth was not at rest. Possibly fearing to betoo explicit, Copernicus wrote his work in an overly philosophicalstyle. The work went virtually unnoticed.

Undaunted, he continued for the next twenty years gather-ing what scant data existed to support his theory. In 1543, just afew hours before he died, Copernicus saw for the first time theresults of his two decades of labor in a published form. His

The Active Observer 29

second book, De Revolutionihus Orbium Caelestium {The Revo-lutions of the Heavenly Spheres ),^ was shown to him by a youngLutheran professor who, we can assume, must have had his ownreasons to be disenchanted with Christian theology. Copernicus'book had been published in Nuremberg and was soon banned bythe Catholic church. It was not to be seen again for the next threehundred years.

Giordano Bruno was Newton's second giant.^ Bom in 1548,the Italian Bruno had somehow heard of Copernicus' theory. Thevery idea that the sun was the center of the universe and theearth moved around it must have seemed like magic to theyoung Bruno. "How can it be so?" I can imagine Bruno asking."When I look to the sky, I see the sun rise and circle the earthupon which I stand. Now to think that it is the earth, and I withit, that moves overthrows all that I have believed was true."

Bruno's imagination soared. He saw multitudes of solarsystems, sun-centered universes, scattered among the stars. Ineach solar system, he saw parallel earths just like ours. Heenvisioned life on other planets. And he told of what he had seen.In 1600 he was burned at the stake as a heretic.

Johannes Kepler, Newton's third giant, was born in Germanyin 1571. Having a fondness for astrology and astronomy, heworked with astronomer Tycho Brahe as his assistant.'* Whileattempting to confirm Copernicus' view that the earth revolvedaround the sun, he devised three laws of celestial motion. Thesethree laws would later serve as the basis of Newton's laws ofmotion and lead to his discovery of the law of universal gravita-tion. Moreover, they would provide a new vision of the universe:as a gigantic clockwork of orderly moving things.

Kepler would be the first of many to use mathematics toformulate his observations. This approach to observation hadbeen left unturned by the Greeks. The assumption was thatmathematics could provide a basis for understanding observa-tion. Of course, Aristotle would never have been satisfied withjust a mathematical explanation. Music, for example, was morethan mathematical vibrations. And even Kepler felt thatsomething else was needed to back up his mathematics.

The fourth giant was Rene Descartes. In 1619 during a snow-storm in Bavaria, he had shut himself up in a heated room fortwo weeks. During this time he said he had three visions. Thesevisions left him in total doubt concerning anything he hadthought he knew or understood. He rejected all religious dogma.He put aside all authority figures. There was only one thing heknew for sure, and that was: "I think, therefore I am.''^ He had

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returned to the ancient position of the Greeks. It was the oldbeing versus change argument. But Descartes had taken thatargument a step further.

Recognizing that he thought, he concluded logically that heexisted. In other words, his awareness that he existed was hisonly proof of his own existence. We might point out that thisevidence is conclusive. It is an overwhelmingly powerful andsimple argument. Of course, I can imagine existence after I amdead or before I was born, but I cannot prove it. Thus Descartesrecognized that being and change were complementary. All wasneither total being nor total change.

"I am" meant being. "I think" meant change. Therefore,being was the background for change. And change was necessaryfor awareness of one's existence. Descartes offered a firmshoulder for Newton. That shoulder was the foundation of logicalthought. Even today, French schools follow the Cartesianmethods of analysis and thought. There must be reasons forthings. If the planets revolve about the sun, there is a reason.

Descartes made a bold attempt to construct a completetheory of the universe using nothing but the elements of beingand change.^ These were called matter and motion. He evenattempted to resolve the Copernican view of the universe withthe Aristotelian view. He saw motion as relative, not absolute.For example, when two ships at sea are left unanchored and onecollides with the other, which is at fault? Which ship moved intothe other? Though each might claim that the other had been atfault, Descartes would demonstrate that the problem was one ofperspective and the relative motion of each ship to the other. Thecrew of either ship would see the other ship moving toward them,while their own ship would seem to be at rest. Similarly, the suncould appear to move around the earth, or the earth could appearto move around the sun.

Because of these four scientist-analysts—Copernicus, Bruno,Kepler, and Descartes—a new reason for motion would bedevised. The absolute movement of all things to their naturalplaces was no longer accepted as a sufficient answer to thequestion of why things moved. Mathematical description was notto be avoided. Analysis would become a trusted tool of science.But the efforts of a fifth giant would be required to provideNewton with all that he would need to explain being and motion.He would be the first experimental physicist, the first to actuallyreach out and touch the universe. His name was Galileo Galilei.

The Active Observer 33

Galileo: The First Active Observer

Galileo is the prime example of the modern physicist.*^ He devisedmethods of observation, description, and analysis that today wetake as the basis for all physics. His essential contribution to theeventual discovery of quantum mechanics was the replacementof the passive observer with the active observer.

Passive observation was any observation that the observerwished to perform that left the observed undisturbed by theobserver. In other words, passive observation required that thepresence of the observer have no effect on the outcome of what-ever was observed. For example, the sun rises whether or not welook at it. Our observations have no effect upon the movementresponsible for that observation, which we now recognize is therotation of the earth about its axis. There is little if anything wecan do to stop the earth from spinning. We take this for granted.

Until Galileo's time, little had been done to attempt todiscover reasons for motion other than those offered by Aristotle.Experimentation or actual analysis of motion was difficult andwas not even attempted. But Galileo was part of the new breed.When he was barely seventeen years old, he made a passiveobservation of a chandelier swinging like a pendulum in thechurch at Pisa where he grew up. He noticed that it swung in thegentle breeze coming through the half-opened church door.Bored with the sermon, he watched the chandelier carefully, thenplaced his fingertips on his wrist, and felt his pulse. He noticedan amazing thing: the pendulum-chandelier made the samenumber of swings every sixty pulse beats.

"How could this be so?" he asked himself. "The wind comingthrough the door changes the swing at random. Sometimes thechandelier swings widely and sometimes it hardly swings at all.Yet it always swings at the same rate." Persisting in his passiveobservation of the chandelier, he had discovered the principle ofthe first mechanical clock. The movement of a pendulum could berelied on to measure time.

Later he would remember this experiment. Time wouldprovide the necessary background for the measurement of allmotion, not just the years it takes to observe the movements ofplanets, but also the seconds it takes to observe motions nearerto the earth. Unlike Newton's other giants, Galileo was bringingobservation down to earth. Not satisfied with just looking, hehad to bring instruments into the play of science.

In a popular story, Galileo stands before his inquisitors,

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begging them to peek through his telescope and observemountains and craters on the moon. No, they say. The instru-ment cannot be trusted to give a true view. It is not worth theirwhile to look into it. "What we would see is produced by thetelescope and does not exist objectively and independent fromit," they claim. Galileo points out the features of the lunarsurface. But even when one of the inquisitors finally peers intothe instrument, he does not see anything that resembles whatGalileo had described. "The craters are in your mind," theantagonist cries. "No," Galileo insists, "they are really there.Why can't you see them?"

In another story, Galileo appears before the Medici,a wealthy ruling family in medieval Italy. He has set up aninclined plane, a plank with one end elevated above the other,and proceeds to roll various objects down the plank. He hasdevised this experiment to demonstrate that objects accelerateas they roll down the incline, that they do not move withconstant speed as Aristotle predicted. Even more surprising, allthe rolling objects, whether light or heavy, accelerate at the samerate and all reach the bottom at the same time. This is definitelynot according to Aristotle, who said that the heavier objectswould roll faster and reach the bottom of the inclined plane aheadof the lighter objects.

The Medici are unimpressed. Indeed, they suspect thatGalileo has provided nothing more than a good magic show."How can we trust your prestidigitations, Galileo? Clearly, youmust be pulling a fast one. For nothing you have shown us makesany sense according to Aquinas and Aristotle. Do not mistake usfor fools. We, too, are distinguished philosophers and observers.But we wouldn't presume to equate the tricks of such primitiveplaythings with God's true motions. Such activities on the partof any observer must be discouraged. You, Galileo, are respon-sible for these observations, not natural law." Their words echo inGalileo's ears.

In both of these stories, Galileo brought before his skepticsa new way of science. It was the doing of science, the activeparticipation of the observer with the observed. Yet, in the firststory involving Galileo's telescope, the skeptical inquisitorscannot see the moon's craters. They do not trust the instrument,and their minds cannot accept that Galileo's creation can makevisible what their eyes alone cannot see. It is beyond "reason"that such should be true. In the second story, Galileo's attemptsto demonstrate natural law are ridiculed because his methods aretoo gross. His detractors are offended that nature's continuous

movements should be disrupted by Galileo's rude interventions.

But Galileo understood that such experiments were onlyapproximate indications of the true nature of motion. He agreedthat his methods were crude. He didn't agree, however, that hewas disrupting nature. Instead, he was attempting to reveal thenatural laws of motion by removing those disruptions that keepus from seeing the truth. Through careful analysis, he was ableto pierce all the extraneous influences that otherwise cloud ourobservations. In Galileo's mind, analysis meant simplificationand discovery of God's laws. By reaching out and touching theuniverse, Galileo had set the precedent of modern experimentalphysics.

Now all it would take to fulfill modern physics was aprecedent for modern theoretical physics. And that would comefrom Isaac Newton.

The Contmuity of Mechanics

Isaac Newton was able to bring together the concepts of passiveobservation and active observation. In fact, with his point ofview any distinction between the two approaches vanished.Active observation was, for Newton, nothing more than anextension of passive observation. Instruments simply detected;they did not alter the existing world they explored. Active obser-vation and such thoughts as these allowed this scientist of thelate seventeenth and early eighteenth centuries to see the greatcontinuous ocean of truth. As he said,

I do not know what I may appear to the world; but to myself Iseem to have been only a boy, playing on the seashore, anddirecting myself in now and then, finding a smoother pebble or aprettier shell than ordinary, whilst the great ocean of truth lay allundiscovered before me.^

Whether Newton peered through a telescope or contemplatedGalileo's many experiments made little difference. The importantfact was that good mathematical and experimental tools werehelping scientists to see more clearly and grasp more firmly theuniverse about them.^ The telescope, the microscope, and vacuumpump were opening up new worlds. Analytic geometry and thecalculus were new mathematical forms to play with. The cross-fertilization of mathematics with experimental methods was

38 Welcome to the Machine

resulting in major insights. Scientists were looking up into theuniverse and peering down into the tiniest objects observable. Allinstruments of science were simply extensions of the humansenses. Following on Descartes' philosophical discourse, mindwas distinct from matter. The observer, therefore, was distinctfrom the observed. Everything that was not ethereal was fairgame to Newton's analytical mind.

Basing his work upon that of those who preceded him,Newton wrote his now famous Principia (Philosophiae NaturalisPrincipia Mathematica, London, 1687). In it, he broughttogether, with meticulous logic, centuries of thought aboutmotion and the universe. The idea of continuity was extremelyimportant for Newton. From this single concept, he was able torealize his three laws of motion. In fact, without continuity noneof these laws would make sense. Even the infinity concept, whichZeno and Aristotle brought forward to explain time and spacecontinuity, would present no stumbling block to Newton. Tograsp his ideas, we might imagine him in conversation with someof his students. The question is raised, ''What is time. Sir Isaac?"

A Conversation nidi Isaac IVeivton

I can imagine Newton responding, "What is time? Nothing to it.It is absolute, true, and mathematical. It flows continuouslywithout any relation to anything else. Pieces of time, which wecall durations, are relative, apparent, sensible, and measurable.We measure these pieces by their motion. We assign differentnames to these pieces according to the amount of their motion.A year is the motion of the earth around the sun, a month is themotion of the moon around the earth, and so forth."

"What about space. Sir Isaac?" another young student asks.And Newton answers, "Space is immovable and infinite. Italways remains just as it is. But length is a different matter. It issensible and it is relative. We measure length by comparison. Aman is as high as an elephant's eye, etc."

"But then how do things move?" yet another student asks.Newton answers, "Things move because that's all they can do.Motion is natural. It's only when motion is disrupted that weshould wonder what's going on. All things in the universe move,taking part in the great flow of time. If everything in theuniverse was left unattended and alone, all things would move

The Active Observer 39

just as they had eons ago. Whatever motion they had then, theywould have now. Everything would flow in a continuous way.But things do interact with each other. And each interactioncauses their motion to "bend" or accelerate. The planet's pathbends into a circle around the sun because the sun pulls on theplanet with a force. I call that force gravity. The ball falls fromthe high building to the earth for the same reason. The ball'smotion is changed by gravity. The ball accelerates, gathersmomentum as it falls. All of this is explained by my laws ofmotion and theory of gravity."

"But, Sir Isaac," our young student asks, "do you mean thatforces make motion discontinuous?" Newton replies, "No, not atall. The motion is still continuous. Though the force causes themotion to change, the change takes place continuously. Eachinstant, the accelerating ball falls a tiny bit faster. Each instant,the planet's path bends just a little from a straight line. Aftermany instants, the planet finds itself following a circle instead ofa straight line. That's how we know that a force has actedupon it."

"Can all motion be explained this way?" queries the student."Yes, indeed," Newton answers. "The laws of mathematics I havewritten show that. And they show even more. My third law statesthat action equals reaction. This means that if a body bends yourpath or causes you to accelerate, then you are doing the samething to it."

"Hold on," says the student. "Certainly the earth is bendingthe moon's path. But is the moon also bending the earth's path?"Newton replies, "Indeed, it is so. But the moon, having lessmatter, suffers the greater bend. The earth, having more than sixtimes the moon's mass, suffers a smaller deviation."

We can imagine Newton's students asking questions andNewton answering their questions on and on into the night.Newton had answers, all of them supported by mathematicalanalysis. His laws and insights made the world seem bothsimpler and more complex.

On one hand, the world seemed simpler because Newtonprovided the basis for analyzing any motion. If a motion wasbent, the cause could be found, and one could predict with totalcertainty what would happen to the object that was moving.Newton's mathematical tools were based upon the firm assump-tion that all motion was continuous and could be separated intoparts. These parts could be examined, one piece at a time. Andeach piece would follow a firm law.

On the other hand, the world seemed more complex because

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it had so many parts. These parts made up the whole of theuniverse. Nothing need ever be left out. Any observance thatmotion deviated from Newton's laws meant that there wasanother body around influencing things. The whole was—had tobe—the sum of its parts. The universe was a machine.

Everything that influenced anything was part of this greatmachine. And all of the machines built during this time workedin accordance with the new understanding provided by Newton'sanalysis. A mechanical philosophy was appearing. It becamepopular to regard both the physical world and the nonphysicalworld as mechanical. For every effect, there had to be a knowncause. For every cause, there had to be accountable effects. Thefuture, therefore, became a consequence of the past. It seemed therewas little anyone could do to alter the world. Even our thoughts wereto be explained somehow by Newton's machine. The "hand ofGod" had set the machine in motion eons ago, and no one couldstop it. All consequences, all ideas, all human thoughts occurredbecause of this initial cause a long time ago. In other words,nothing was left to chance. Everything had already been deter-mined by God. This view was known as determinism.

The IVightmare of Determiiiisni

Picture a quaint French drawing room, circa 1800. White wigged,white stockinged, drawing room society is enjoying an eveningof folderol. The butler, or whatever he is called in such circles,announces the arrival of a famous philosopher and scientist,the Marquis de Laplace. Conversations hush and becomemurmurs. The Marquis enters. People move aside quietly as if towelcome a king into their ranks. Perhaps more to the occasion,we should view the Marquis as a famous actor-artist. Chairs aredrawn into semi-circular rows. The presentation was about tobegin.

Pierre Simon Laplace, known as the Marquis, became thedarling of Paris' early nineteenth-century drawing room crowd.He was known for his dramatic and eloquent presentations ofthat mysterious and quite abstract science known as celestialmechanics. He held his audiences completely suspended as hetold of the worlds beyond, all of them caught in that action-at-a-distance force, which Newton called gravity. No cosmic strings,yet powerful was the influence of this never-observed, yet totallypresent, cause of acceleration.

The universe and all its worlds followed well-defined lawsaccording to the same guiding principles. Everything was,and is, predictable. Only find the force, know the masses,positions, and velocities of the objects under study at one singletime, and all is predictable. It matters not what the objects are.Planets, stars, and rolling cobblestones—all fall victim to theforce.

The universe is a gigantic Newtonian clockwork. Cause andeffect rule. Nothing is by chance; everything is ultimatelyaccountable. Read Laplace's words (translated, of course):

We ought then to regard the present state of the universe as theeffect of its previous state and as the cause of the one which is tofollow. Given for one instant a mind which could comprehendall the forces by which nature is animated and the respectivesituation of the beings who compose it—a mind sufficiently vastto submit these data to analysis—it would embrace in the sameformula the movements of the greatest bodies of the universe andthose of the lightest atom; for it, nothing would be uncertain andthe future, as the past, would be present to its eyes.^o

Perfect determinism, from a heartbreak to an empire's riseand fall, was no more than the inevitable workings of the GreatMachine. The laws of physics are to be obeyed, because it is

impossible to disobey them. The dream of an ultimate under-standing of nature was the discovery of the hidden force that wasthe cause of the yet-to-be. Once this force was found, therewould be no room for free will, salvation, and damnation, orfor love and hate. Even the most trifling thought had beendetermined in a far-gone age.

Ethics, morality, pride, and prejudice were jokes. You mayimagine that you are a free-thinking person, but even thatimagination is nothing but the universal clockwork turning insome yet-to-be-discovered way. Discovery of how the wholeuniverse works was still to be achieved, but nevertheless, inprinciple, this materialist philosophy was the basis for theuniverse.

The idea that free will had vanished was called the "night-mare of determinism." Even thinkers and philosophers of thisperiod who were not disturbed by the "nightmare" felt the impactof Newtonian thinking. Because physics was able to explain aremarkably large number of physical phenomena, from themovements of planets to the kinetic motions of the tiny particleswithin an enclosed volume of gas, with only a few principles, itbecame the model of human knowledge.^^

Nineteenth-century thinkers sought to emulate the precision,universality, and orderly procedure of physics. They soughtgeneral laws to explain history and human behavior. Karl Marx,for example, suggested that matter is the only subject of changeand that all change is the product of constant conflict betweenthe opposing forces inherent in all things. When one force over-comes the other, change is produced. Thus, for Marx, a revolu-tionary movement can never be a cooperative venture betweenthe ruling and working classes, for the force of one class musteventually overcome the opposing force of the other class. Thistheory, known as dialectical materialism, sounds very much likeNewton's second law, which states that force is the cause ofchange in motion and matter is what force acts upon.

Even Clarence Darrow, the famous lawyer who defended thetheory of evolution in the Scopes "monkey trial" of 1925, wasinfluenced by Newton. In another of his well-known cases, thenotorious Leopold and Loeb murder trial, Darrow defended hisclients by pointing out that they were victims of heredity andenvironmental forces. Although Leopold and Loeb were clearlyguilty, Darrow defended the two murderers on the grounds thatthey had no choice in their actions, that there was a lengthyseries of causes leading inevitably to the eventual death of theirvictim. Even the environment in which the two murderers grew

up was presented as a product of that long chain. Therefore,how could society presume to punish these two for a situationover which they had no control? They were as much victims oftheir crime as the individual they killed. All were powerless tostop the Newtonian clockwork.

It is understandable that Laplace, Marx, and Darrow shouldbe so influenced by Newtonian machinery. ^^ Certainly it is easierto imagine that the whole is simply a sum of its parts and thatunderstanding the part will inevitably lead to understanding thewhole than to consider a world in any other way. What other waycould there be? Why, even mind itself must ultimately prove tobe nothing more than an extremely complex mechanical device.Since mind must come from matter, what else could it be? Indeed,mind must show itself as a direct outcome of its material base.So thought Sigmund Freud.

Freud associated certain dream images with primitive ideas,myths, and rites.^^ He claimed that these dream images are"archaic remnants" —psychic elements that have survived in thebrain from ages long ago. The subconscious mind is a trash heap.No wonder we suffer guilt, for we suffer not only for ourselves,but also for our ancestors who may have raped, murdered, andpillaged thousands of years ago.

Hugh Elliot (1881-1930), editor of England's Annual Registerduring the time of transition from classical physics to quantumphysics, was a champion of mechanistic science andmaterialism.^'* He posited three principles: (1) the laws of theuniverse are uniform, and while the universe may appeardisorderly, careful scrutiny by science reveals that theseuniversal laws are to be obeyed; (2) teleology is a myth, for thereis no such thing as a purpose to the universe and all events aredue to the interaction of matter in motion; and (3) all forms ofexistence must have some kind of palpable material charac-teristics and qualities. Elliot wrote:

It seems to the ordinary observer that nothing can be moreremotely and widely separated than some so-called "act of con-sciousness" and a material object. An act of consciousness ormental process is a thing of which we are immediately andindubitably aware: so much I admit. But that it differs in any sortof way from a material process, that is to say, from the ordinarytransformations of matter and energy, is a belief which I verystrenuously deny.^^

I enjoy quoting Elliot, because few individuals haveexpressed such confidence in the totality of a materifd universe as

46 Welcome to the Machine

well as he did. He went on to say that **there exists no kind ofspiritual substance or entity of a different nature from that ofwhich matter is composed. . . . there are not two kinds of funda-mental existences, material and spiritual, but one kindonly "16

And thus is the stage set. We are, all of us, machines.

By the end of the nineteenth century, classical physics hadbecome not only the model for the physical universe, but themodel for human behavior as well. The wave of mechanicalmaterialism, which began as a small ripple in the stream ofseventeenth-century thought, had grown to tidal wave propor-tions, sweeping all Greek thinking aside. Physicists investigateddead things and physicians sought clockworks in living people.

Somewhere along the way, Descartes' "I think, thereforeI am" was lost. Or, rather, it was turned around and became"I am, therefore I think." The search for objective reality, causeand effect, the hidden mechanical order was on. The horizon ofscience was clear.

Speaking about the future of science, one celebrated theoristsaid that it would only consist of "adding a few decimal placesto results already obtained."* However, there were others who didnot express such confidence in the mechanical universe. One ofthese individuals, a man known as Lord Kelvin, became anauthority in European circles during the mid-nineteenth century.Toward the end of that century, he said that he saw only twodark clouds obscuring the horizon of the Newtonian ''landscape."These two clouds were two mysteries in the otherwise perfectmechanical explanation of light and heat.

An Explanation of Light and Heat • • •with Something Missing

By the end of the nineteenth century, a world picture had beencompleted. Scientists felt they understood the physical universe,and the Newtonian mechanical model was being used to explaineverything else as well, including those qualities that Aristotlefelt were beyond mere explanation as parts of a whole or the

* This famous remark was made by A. A. Michelson in 1894. Michelsonbelieved he was quoting Lord Kelvin and later confessed that he regrettedever having said such a thing. [L. Cooper, An Introduction to the Meaningand Structure of Physics (New York: Harper & Row, 1968), p. 431.)

machine. Scientists were eager, therefore, to find a mechanicalexplanation for the invisible parts that made up the materialuniverse. Two specific areas of physics needed explanation. Theywere heat and light.

A century earlier, the Italian physicist Amadeo Avogadrohad modeled a gas as consisting of many tiny particles. And inthe seventeenth century, Robert Boyle had discovered the generalgas law that related the pressure in a gas to its volume. JosephLouis Gay-Lussac in 1800 discovered the effect of temperatureon a confined gas and found that when a gas was heated, thevolume it occupied increased if the pressure in the gas remainedconstant. The realization soon followed that heat was simply therapid movement of the tiny particles of the gas. That is, heat waskinetic energy of matter and nothing more.^^

But something was missing. How did the sun's heat reachthe earth? Were there particles along the way between the sunand the earth? Did the movement of these particles conductthe sun's heat from one place to another? The space betweenthe sun and earth was thought to be empty so heat could not bejust the motion of matter. Somehow heat could travel withoutthe medium of matter. In this respect, it resembled another formof energy known as light.

Through the first half of the nineteenth century, manyscientists began to accept the idea that heat and light were atleast qualitatively identical. According to Newton, lightconsisted of tiny particles, or corpuscles, that were able to movethrough the vacuum of space. Thus it was that light traveledfrom the sun to the earth. Light, therefore, was defined assubstance. Heat, too, was considered a substance. This was thepicture up to around 1820.

But Thomas Young discovered a property of light thatupset the Newtonian particle picture.^®* He found that lightparticles can somehow interfere with each other. The patterns

• Young's announcement that his result supported the wave theory of lightwas not well received by the scientific establishment. Indeed, it was metwith ridicule and hostility, because it dared to conflict with the sacrosanctNewtonian particle light theory. Henry Brougham, a British politician andamateur scientist, wrote in the Edinburgh Review in 1803: "[Young's] papercontains nothing which deserves the name, either of experiment ordiscovery, and ... is destitute of merit. . . . We wish to raise our feeble voiceagainst innovations, that can have no other effect than to check theprogress of science, and renew all those wild phantoms of the imaginationwhich . . . Newton put to flight from her temple." F. Rutherford, G. Holton,and F. G. Watson, Project Physics Course [Authorized Interim Version,1968-69] (New York: Holt, Reinhart, & Winston, 1968), text 4, chapt. 13, p. 14.

Welcome to the Machine

produced by light when it traveled from its source to a screencould not be explained by light particles. What Young discoveredcan be seen by anyone who holds two fingers to his eye and looksat a light source (not the sun, however—it's much too bright).The retina of the eye takes the place of the screen used by Young.

Simply look through your fingers as you carefully squeezethem together. Just before you extinguish the light comingthrough, you will see a series of alternating light and darkbands. These bands are called an interference pattern. Theycan only be produced by light waves, not particles. The alter-nation of light and dark is due to waves of light interfering witheach other.

This interference is caused by the oscillatory movement ofwaves. All waves are produced by vibrations within the mediumholding the wave. The familiar sweet sound of a lyrical voice isnothing more than a continual repetition of air moleculesvibrating against your eardrums. The familiar harmony of abarbershop quartet is the wave interference of four differentvibrational frequencies, each coming from a different singer.Similarly, light waves can interfere with each other and producea ''light harmony"—the interference pattern of light anddark bands.

A dark band results when the high crests of one wave aremet by the low troughs of another wave. Under normal circum-stances, we do not see these interference patterns. The crests and

Thomas Young's original drawing, showing interferencee-f-fects expected when waves from slits A and B overlap.(Place "the eye near the left edge and sight at a grazingar^gle along the diagram) At the screen or\ the right,nolight is received where the waves from A constantlyinterfere destructively with the waves "from £>.

A light wave'interferencG pattern formed when lightis sen-t through cx.\/exy narrow Keyhole.

troughs of light waves are very tiny. But when they are forced totravel through a very narrow space, such as the space betweenyour two fingers, these waves bend into each other. The patternof light and dark is a result of this bending.

We are more fgimiliar with the bending of sound waves. Forexample, we know of the presence of a moving truck around ablind corner when the truck honks its horn. The sound wavesproduced by the horn bend around the corner and reach our ears.

Once Young had discovered that light was a wave, heat wasalso imagined to be a wave phenomenon. Together the twotraveled the vast distance that separated the sun and earth,moving as waves move. But there was one problem with thispicture. Waves must move through something. They don't travelin a vacuum. This was obvious to the scientists of the nineteenthcentury. They had found that when they placed a ticking clockinside of a glass enclosure from which the air is slowly evacuated,the sound waves vanished as soon as the air in the enclosure wasexhausted. Sound waves wave in air. Thus, light waves and heatwaves must wave in some invisible substance that filled all ofspace.

Scientists called this substance "ether," drawing from theworld picture the early Greeks had painted. The ether was

invisible and yet had to be a form of matter so fine that no onehad yet discovered its existence. There were other indications ofits existence, and these appeared as a result of two seeminglyunrelated discoveries. The first discovery was that electricitycould be turned into magnetism and turned back again intoelectricity.

Michael Faraday in England had discovered that an elec-trical current could produce a magnetic field. In fact, he inventedthe term magnetic field. He also constructed a device that wasthe forerunner of the modern electromagnetic generator. Byrotating a bar magnet in the vicinity of a current-carrying wire,he showed that the magnetic field could "induce" the current. Inother words, he found that the moving magnet was capable ofgenerating the electrical current. This discovery, which made itpossible to turn magnetism into electricity as well as electricityinto magnetism, does not support the ether idea by itself. But itdoes suggest that electricity and magnetism can be interchanged,and this interchange, called electromagnetism, led to thetheoretical discovery of electromagnetic waves.

By 1860, the idea of electromagnetism was accepted. JamesClerk Maxwell, also in England, had discovered, through hisattempts to make a mathematical model of Faraday's discovery,that in theory the process of turning electricity into magnetismand magnetism back into electricity could be repeated. In fact, itwas theoretically possible to repeat the process very, veryquickly. This led Maxwell to the idea of electromagnetic oscilla-tions. These oscillations or vibrations were, however, only amathematical theory. They were predicted to occur only on paper.The question was: could they be observed? What would theylook like?

While pondering this mystery, it occurred to Maxwell thatthe light waves experimentally discovered by Young may beproduced by the electromagnetic oscillations he had discoveredtheoretically. By playing with his equations, he found anastonishing fact: the equations describing the electromagneticvibrations had solutions that described electromagnetic wavesmoving at the speed of light! Could light waves be electro-magnetic vibrations? If so, what was vibrating?^^

Maxwell's successful attempt to show that electromagneticwaves were theoretically able to travel at the speed of light andYoung's experimental discovery that light could interfere withitself was convincing evidence that light was an electromagneticwave. And since heat was also able to travel across vast spaces,it too had to be an electromagnetic wave.

In 1887, Maxwell's theory finally received support from theexperiments of Heinrich Hertz. Hertz had successfully shownthat an electromagnetic wave of invisible radiation was emittedby an oscillating electric current. Hertz had invented radiowaves. He was also able to show that these invisible radiationswere, indeed, waves exhibiting all of the characteristics of inter-ference, wave bending, and so forth exhibited by visiblelight waves. Hertz's experimental detection and production ofelectromagnetic waves convinced everyone; light and heat mustalso be electromagnetic waves.

Yet the problem still remained: how did these waves travelfrom their sources to their places of detection? In other words,what did these waves wave in? The substance, scientistsassumed, was the ether. However, no one had ever directlydetected the ether. It had never been seen.

The Ether Is Missing

The first dark cloud originally mentioned by Lord Kelvin wasabout to make its appearance on the clear Newtonian horizon.In 1887, A. A. Michelson and E. W. Morley, two collegeprofessors from Cleveland, Ohio, attempted to measure thepresence of the ether existing between the sun and the earth.20They were quite convinced of its presence. Young's observationsand Maxwell's theoretical discovery "proved" that light was awave. Therefore, light had to travel through a material substancethat filled the space between the earth and the sun.

To perform their experiment, Michelson and Morley neededto measure the speed of the earth relative to this fixed immovableether. If they succeeded in obtaining this measurement, theresult would be convincing evidence of the existence of the ether.Unfortunately, this was not an easy experiment to carry out.The situation might be compared to a school of fish attemptingto discover the water in which they live. To find the water, thefish would have to discover ripples in it. These ripples, or waves,would travel from one fish to another, but the speed at whichthe ripples traveled would be fixed.

Today we can observe the fixed or constant speed of waterwaves by observing the waves extending from the bow of amoving motor boat. These bow waves travel at a constant speedaway from the boat. The boat, however, can increase its speed.

Thus, the boat can catch up with its own waves. In anotherexample, the supersonic jets of today's high-speed society oftensurpass the speed of sound. That is, they travel through the airfaster than their own sound waves. The well-known sound barrierconcept arises because of the sound wave buildup that occurs justahead of the jet as it approaches the speed of sound. When the jetpasses through the barrier, a sonic boom is heard.

In this way, the fish underwater could measure the speedof their movements through the water, and thereby its existence,by noticing how fast they were traveling in comparison to thespeed of water waves. Thus, the fish could claim that the waterhad to exist because they were able to observe changes in theirspeed through the waves that they were emitting in that water.All a fish had to do was move away from a wave and then moveback toward the wave as the wave approached it. From thefish's point of view, the water wave would appear to move fasterwhen the fish swam toward it and slower when the fish swamaway from it.

Michelson and Morley were prepared to be fish in the ether.The waves they would attempt to measure were, of course, lightwaves. The difference they expected in the speeds of the lightwaves would be due to the earth's velocity through the ether.This difference in speed would at last prove the existence of theether—that tenuous but continuous material that provided themedium for light waves.

The sad result of their experiment was failure. Even thoughthe experiment was perfectly capable of measuring the smallspeed difference due to the earth's movement, no difference wasdetected. The two experimenters were dejected. Later on, theywould be heralded as the early discoverers of the constancy ofthe speed of light, a cornerstone of Einstein's theory of specialrelativity. But at the end of the nineteenth century, there wasno way to reconcile the missing ether and the wave picture oflight. How light got from there to here was still a mystery.

The Ultraviolet Catastrophe

Meanwhile, a second dark cloud was appearing on the clearNewtonian horizon: hot things glow. They glow different colorsas they are heated. Before light bulbs were frosted they were

clear enough to reveal their insides. The filament in a bulb wasvisible and it carried an electric current. As the current wasincreased, the filament would begin to glow and produce light.The color of that light would also change. The higher the currentin the bulb, the hotter the filament got. And the hotter it got, themore the color changed. The question was why?

What was responsible for the changing color of the light?All hot bodies, such as electrified light bulb filaments and heatedbranding irons, emit light. Furthermore, if the light they emit isallowed to pass through a glass prism, the light will spread outinto a palette of colors that blend together like a rainbow. In fact,a rainbow is nature's own palette, produced when sunlight passesthrough very tiny prisms made of water droplets. The spread ofcolors is called a light spectrum.

Sunlight produces a balanced spectrum of colors. There areequal amounts of all colors present. That is why sunlightappears "white" or colorless. All objects, no matter what theirchemical nature or composition, send out light with the samecolor balance, if these objects are heated to the sametemperature. It was a change in the balance of colors in thespectrum that was producing the different colors observed in thelight bulb filament and elsewhere. That balance depended on howhot the glowing body became.

Thus the characteristic color of any object changes in a verypredictable manner as it is slowly heated to higher temperatures.Cool objects give off no apparent light. A hot poker glows red.At a higher temperature, it starts to glow orange-yellow. At stillhigher temperatures, it glows blue. Look at a burning match andyou will see that the flame has different colors running throughit. The temperature of the flame is not the same throughout,but the bluer colors of the flame are the hottest parts, so becareful.

When the spectra from various objects are examined atdifferent temperatures, we find that various colors are emittedin differing amounts. The shifting of these amounts of colorschange the characteristic color of a glowing object. However,the hotter an object becomes, the whiter its color becomes andthe more balanced its spectrum is.

The connection between the temperature of a material andthe color of the light it emitted had to be a mechanical one. SinceGay-Lussac's work in 1800, it had been known that highertemperatures produce greater kinetic energy or more rapidmotions of a heated material. Since the heated material was made

of atoms, the atoms had to be moving or oscillating to and fromore rapidly. Thus, it was natural to suspect that the colors ofthe light were somehow determined by the movements of the tinyatoms or oscillators composing the heated material. Thefrequency of the observed light was, or had to be, the same asthe frequency of the vibrations of oscillators within the materialsubstance.

After Maxwell's success in expledning that a light wave isan electromagnetic oscillation, scientists began to suspect thatthe different colors of light emitted by a heated object were causedby the different vibrational frequencies. Thus, red light wasthought of as having a lower vibrational rate or frequency thanblue light. Although the search for the ether had led up a blindalley, scientists still felt that color and vibrational frequencywere related.

All of the above facts concerning hot glowing objects and thecolors they emitted were known by the end of the nineteenthcentury. At that time Lord Rayleigh, a well-known expert onsound waves, attempted to explain the colors of heated objects.21His arguments were based upon the wave picture of light.According to this picture, the light energy emitted by a glowingbody should tend to be given off at a higher frequency ratherthan a lower one. The reason for this is light wave economics.There is a direct relationship between the frequency of a waveand its length. The higher the frequency of the wave, the shorterits length. Light waves with very short wave lengths (in otherwords, very high frequencies) are able to take advantage of thespace they find themselves bouncing around in. There are moreways for short waves to fit within any volume of space than forlong waves. This geometric factor influences any glowing objectand tends to produce short waves rather than long waves, or highfrequencies rather than low ones. That meant that a red-hot pokershould not be red at all, but blue. And that wasn't the end of it.A poker glowing blue shouldn't be blue —it should glowultraviolet (a color that vibrates at a higher frequency than violetand is invisible), while an ultraviolet poker should glow at aneven higher frequency, and so on. In other words, any hot pokershould give off its electromagnetic energy at beyond ultravioletfrequencies.

This argument was known as *'the ultraviolet catastrophe."But it was catastrophic only in theory because Rayleigh hadpredicted that any heated object would soon emit all of itsenergy at frequencies beyond visibility. However, as any person

The Active Observer

who strikes a match can see, the colors in its flame are quitevisible. Scientists' inability to explain the light from heatedbodies using the mechanical and continuous theory of lightemission was the second dark cloud on the Newtonian horizon.

Question • Why is there an ultraviolet catastrophe usingclassical mechanics'"

Answer- All the energy goes into shorter and shorterwaves.

56 Welcome to the Machine

The End of the Mechanical Age

Even with two clouds partly obscuring the Newtonian mechanicallandscape, the painting was not abandoned. Far too much hadbeen invested in this picture of reality, including the followingassumptions concerning the physical and therefore mechanicalworld:

(1) Things moved in a continuous manner. All motion, both inthe large and in the small, exhibits continuity.

(2) Things moved for reasons. These reasons were based uponearlier causes for motion. Therefore, all motion was deter-mined and everything was predictable.

(3) All motion could be analyzed or broken down into itscomponent parts. Each part played a role in the greatmachine called the universe, and the complexity of thismachine could be understood as the simple movement of itsvarious parts, even those parts beyond our perception.

(4) The observer observed, never disturbed. Even the errors of aclumsy observer could be accounted for by simply analyzingthe observed movements of whatever he touched.

These four assumptions would eventually be proved false.But it would take nearly fifty years for the true story to be told.The mystery of the movement of light and its unexplainedbehavior in relation to heated and glowing objects would start arevolution in the scientific world. The active observer would bereplaced by the disturbing observer.

Part Two

When

the Universe

Jumped

The DisturbingObserver^

An act of desperation...a theoretical explanation

had to be supplied

at all cost, whatever

MAX PLANCK

(on the di»rovery of the quantum)

The Movement of Reluctant Minds

Who could have foreseen it? Who could have known that byreaching out and touching the universe we would be disturbingit? Perhaps if Zeno and Aristotle had been alive at the turn ofthe twentieth century, they would have forewarned us. Themechanical age had scarcely begun and already it was coming toa halt. Although machines of all types would come into existenceduring the twentieth century, we would lose faith in ourmechanical philosophy. The world was not a machine, after all,and could not be constructed by putting together tiny parts.

By exploring the depths of matter and energy, by analyzingthings both mathematically and experimentally, physicists wouldfind that they had to abandon the Newtonian continuousmechanical picture of the physical world. The two dark cloudsthat had spoiled their view had forced these physicists to give upcontinuity. Light waves traveled without anything to wave in.Hot glowing materials emitted a continuous rainbow of lightcolors, and these colors were not to be explained by thereasonable assumption that the light energy was continuouslyemitted by the hot substance that glowed these colors.

This was only the start. By 1935, all of physical reality, thewhole material universe, would once again be looked at with greatwonder. Two distinct schools of thinking would appear: thosewho believed in the mechanical picture, in spite of the evidence,and those who welcomed the new nonmechanical picture with its"Zeno-like" discontinuous jumps. Debates are nothing new inscience. This debate continues today.

Yet these discoveries would not have occurred when they didif the "new physicists" had more quickly abandoned theNewtonian and Galilean precedents for analysis. Two thousandyears earlier, the Greeks had done so and failed to discover thequantum, the discontinuity of motion that is vital to all atomicand subatomic processes. It would be this discontinuity thatwould lead two new physicists, Werner Heisenberg and NielsBohr, back to that earlier Greek picture of wholeness.

Heisenberg and Bohr, perhaps more than any other scientistsduring this period of discovery, would welcome the discontinuousquantum of energy. Because this quantum was involved in every

60 When the Universe Jumped

observation, even observation would lose its objectivity. Theobserver must give or take a whole quantum of energy if he is tosee anything at all. This whole quantum was totally ignorable,on the large scale of everyday observances. But it could not beignored when the observer was looking for an atom. Observationwould disturb the atom, disrupting violently its desire for stasis.The act of reaching out and touching atoms led to uncontrollabledisruptions. Yet these disruptions were what was experienced ofthis tiny atomic world.

If every time you touched a kitten, no matter how gently,you were bitten on the hand, would you continue to imagine thatthis soft little cat is tame? Kittens are cute, but this one bites.Consequently, you change your model of kittens. Could themechanical model of atoms be wrong? Reaching out and touchingatoms led to an unclear picture of what was being reached for.

The story of this period of the discovery of the quantum ispresented in the next five chapters. In chapter three, we will seehow the quantum nature of light was discovered and how a newmathematical law of physics appeared. Light was seen both as awave in a nonexistent substance and as a stream of particles ofsubstance. The new law expressed the relationship between thewave and the particle. Light would act in a disruptive mannerwhenever it interacted with matter. This discovery began thedeath toll for the mechanical continuous universe.

Chapter four describes the new model of matter that wasproposed. Niels Bohr applied the new wave-particle relationshipto the inside of an atom and a new explanation for atomic lightpresented itself. This time it wasn't light coming from a solidor liquid substance; it was light coming from a gas. And thatlight was not continuously emitted—it was emitted from atomsthemselves. The discontinuous emission spectra of light meantthe atom was undergoing a discontinuous jumping motion.Chapter five reviews physicists' attempts to picture thatdiscontinuous jumping motion in terms of waves. Physicists hadhoped to salvage mechanics by making matter a continuousspread. That is, they imagined matter to be waves. Later, inAmerica, these waves were observed directly, much to thesurprise of many.

But the wave picture was not the final word. It too had adiscontinuity. And like its precedents, it led to a paradox. A newunderstanding was sought. In chapter six we will explorescientists' attempts to come to grips logically with these newparadoxes of matter and light. The matter-wave idea wasdropped. In its place came the idea that the wave was not a real

wave at all, but just a concept. This was called the probabilityinterpretation. But, as you may guess, it too led to anotherparadox. The first third of the twentieth century had turned intoa real Pandora's box and the ancient Greek idea of unbrokenwholeness reappeared. To observe is to disturb, for observationbreaks the wholeness of nature. This led to the philosophy ofindeterminism.

But even this was not the end. New ideas in any field alwaysmeet with resistance. And the quantum was a whole too big toswallow for a large group of reactionary physicists led by one ofthe quantum's creators, Albert Einstein.

In chapter seven, we will look at what attempts were madeto reconcile the new quantum with the old Newtonian pictureof continuity. The early leaders of the action and reaction groupswere Bohr and Einstein. Both groups agreed that the old ideaswould no longer work. Their debates and continuing efforts toreconcile our image of the physical world with our experience ofit would produce a fruitful bounty of insights.

This part of our story starts with Max Planck. Like manywho would follow him, Planck would make his discovery theoreti-cally. And like his distant predecessor Zeno, Planck would pointout to us that something was wrong with our thinking.

Averting a Catastrophe nith Lumps of Energy

Lord Kelvin had called the phenomenon a dark cloud obscuring theNewtonian mechanical picture of light energy. Lord Rayleigh,a long-time expert on the movements of waves, had failed to solveit. Even James Clerk Maxwell's mathematical relations, whichshowed that light was produced by electrical fields snaking anddancing in space with magnetic fields, had not been able toexplain it. No one knew how hot things glowed.

How did heat energy become light energy? Why did hot thingsgive off the colors they did? Everyone knew that the differentcolors of light indicated the presence of different wavelengths oflight. Red light had longer separations between the successivecrests of its waves than blue light. The shorter the wavelength,the higher or more rapid the frequency of the oscillator that producedthat light wave. This much was certain.

Light was made of waves, though Michelson and Morley hadfailed to detect just what those waves were waving in. But no

When the Universe Jumped

matter. The colors of light and Young's early experiments by 1820had convinced everyone. Light had to be a wave phenomenon. Theproblem was to explain how the heat added to the oscillators in theglowing solid or liquid substance was being changed into light.

On December 14, 1900, an apologetic, soft-spoken, articulate,forty-two-year-old professor presented a strange concept to theaugust body of the German Physical Society.^ This date would laterbe regarded as the birthdate of the quantum. On that day. ProfessorMax Planck offered a mathematical exercise that averted the nowwell-known ultraviolet catastrophe. Planck explained why heatenergy does not always get converted to invisible ultraviolet lightwaves. This explanation was, to Planck, merely a refinement,a sanding down of a rough theoretical edge. But it was this edgethat brought Herr Professor Max Karl Ernst Ludwig Planck^ beforethe Physical Society on that bleak winter day.

Six weeks earlier, he had called what he had done a "luckyguess."^ His discovery did not take place in any laboratory; it tookplace in his mind. And he didn't believe it, even after Einstein usedthe idea to explain away another "rough edge" five years later. He

PlcxncK dreamingci lucky guess.

felt somehow a mechanical justification for his "guess" would beforthcoming. He was, remember, past the age of brilliance—a careful, middle-aged academic. He fervently wished to change hisguess to a "statement of real physical significance.'"* He recountedthe event twenty years later during his Nobel Prize address:"After a few weeks of the most strenuous work of my life, thedarkness lifted and an unexpected vista began to appear."^

What was his discovery? Planck was astonished to find thatmatter absorbed heat energy and emitted light energy discon-tinuously. "Discontinuously" meant in lumps, and these lumpswere totally unexpected. To better grasp Planck's astonishmentand the significance of his discovery, I ask you to consider ananalogy. The analogy deals with the familiar experience of droppingstones into a pond. Remember that Planck's discovery was in thenature of an explanation. Planck was, like Zeno, a theoreticalscientist. His job was to explain what we saw or, if our conceptionof what we saw was incorrect, to correct our thinking. Ideally, thenew insight would lead to a better understanding and a newprediction based upon that understanding.

Throning Stones in a Quantum Pond

In this analogy, imagine you are standing before a calm pond on ahot summer day and dropping pebbles into the water. You wouldcertainly expect to see ripples of surface wave energy generatedcontinuously by the falling pebbles. The more pebbles dropped persecond, the more ripples produced per second. Or so you wouldexpect.

But now imagine that some of your pebbles have just droppedthrough to the pond's bottom and produced no ripples at all. Youare surprised when the whole pond suddenly becomes a torrent ofsloshing waves and then just as quickly calms down to become aglassy mirror once again. There doesn't seem to be any directconnection between the appearance of ripples and the dropping ofstones. So you stop dropping stones and wait. Sure enough, aftera few more storms on the pond, it all becomes glassy again. What'sgoing on?

Timidly, you start dropping pebbles again. You throw themout into the pond in small handfuls, but nothing disturbs thewater's glassy calm. Then, quite unexpectedly, the pond boils intoturbulence. You watch carefully and note that the waves being

produced undulate slowly with long separations between crests.You throw more pebbles in. As long as you throw pebbles in steadyamounts, the pond continues to show its "jumpy" movement,sporadically boiling up into waves and just as quickly calmingdown again.

Now you increase the tempo. You throw your pebbles in fasterthan before. As you have come to expect, nothing happensinstantly. But when the pond boils into activity again, you noticethat the waves have changed. You see higher frequencies andshorter wavelengths than you saw earlier. The ripples are moreclosely spaced to each other.

The pond is an analogy for hot matter. The pebbles representheat supplied to the material and the ripples are the light wavesgenerated by the heated material. However, two surprising featuresmake the ''quantum pond" different from a real pond. The first isthat the quantum pond responds sporadically to our efforts to heatit up. The waves appear to be produced in spurts of wave energyand not in any continuous way. These gaps and discontinuities inthe behavior of the pond are more pronounced when we throw ourpebbles languidly. Later, when we increase our tempo, the gapsbetween our efforts and the pond's responses decrease. Ourquantum pond begins to look more like a real pond, with all kindsof waves being generated by the pebbles in a seemingly regularmanner.

The second unusual feature of our quantum pond has to do withhow it responds when it responds at all. It seems our pond canproduce longer waves with greater aplomb than shorter ones.A real pond would not behave this way. The length of the wavesand the frequencies of the waves should always depend upon theshape of the pond's boundaries as well as the energy used to excitethose waves. In the quantum pond, the greater preponderance ofof lower frequency, longer length waves over their shorter, higherpitch counterparts is more pronounced when we are languidlytossing pebbles. But, again, as we increse our tempo, thedistribution of waves appears more like a real pond. Shorterwaves appear and soon dominate the pond.

Planck explained these surprising, nonmechanical,discontinuous features in a surprising manner: he invented asimple mathematical formula. Now, most nonscientists may beunable to appreciate that inventing formulae is not the usualwork of scientists. Each mathematical relation must be backedup by painstaking experimental effort. Each time a discrepancyoccurs in our understanding of anything physical, physicistsdon't simply trot out their writing pads and invent a

mathematical relation to explain their observations.

Rather, it is usually a more conservative approach that istaken. What Planck was about to propose was not a conservativeidea. It was, so to speak, a crackpot idea, one that had no basisin the mechanical universe. Planck's idea related the energygiven to the wave by the oscillating material to the frequencyof that wave. And that was something new under the sun.

The Energy; the Whole Energy; or IVothing at All

Light waves did not behave like mechanical waves. Planckpostulated that the reason for this discrepancy lay in a newunderstanding of the relationship between energy and wavefrequency. The energy either absorbed by the material or emittedas light depended in some fashion on the frequency of the lightemitted. Somehow the heat energy supplied to the glowingmaterial failed to excite higher frequency light waves unless thetemperature of that heat was very high. The high-frequencywaves simply cost too much energy. So Planck created a formulathat has since been named after him. That formula said simplythat energy (E) equals the frequency of the light emitted (f)times a constant (h). And with this single formula, E = hfjthe quantum age had begun.

Higher frequency meant higher energy. Consequently,unless the energy of the heat was high enough, the higherfrequency light was not seen. The constant of proportionality —the h in this equation—is called Planck's constant. It was anentirely new idea that such a constant should exist. Nomechanical model had ever predicted such a relation between thefrequency of light and the energy needed to produce that light.

Planck's constant turned out to be an extremely tinynumber—approximately 6.6 divided by one billion and thenagain divided by one billion and then once again divided byone billion. This number is so tiny that one would expect it tohave unobservable consequences. No wonder the quantumnature of light remained hidden until the twentieth century.

The Planck equation of E = hf explained why the high-frequency light waves were being discriminated against. Andit also explained a brand-new idea. Since the quantity, hf, ofenergy was a certain whole amount of energy —not y2hf nory^hf nor any other fraction—the energy in any given light wave

could only be a whole multiple of the basic "chunk" of energy.

Somehow the material could only produce light waves withchunks of energy, whole amounts. The idea of the quantum wasfirst recognized by this chunk picture. Quantum means a wholeamount. Energy at any particularly frequency, f, was like acandy bar. It had to be cut up into whole, equal-sized chunkswith no half or quarter chunks left over. This picture alsoexplained and supported the discrimination taking place againstthe high-frequency light waves. If the frequency were madehigher, the energy candy bar would have to be cut up into largerchunks. And that meant fewer chunks available. Thus higherfrequency waves were discriminated against appearing becausethere would be fewer of them emitted. The lower frequencychunks were smaller and thus more of them were produced for agiven amount of energy.

Energy "candy bars"

A wave could have whole pieces of energy; but not anypart of a piece The top bar has greater but fewer energypieces The bottonn bar has smaller bat more energy pieces.

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The formula E = hf forced Planck to explain why lightwaves could not be produced in a continuous manner. AgainPlanck offered a theoretical picture, since he could not actuallywatch what occurred whenever a piece of material generated awave of light. Indeed, the light that Planck was talking aboutseemed perfectly continuous in its spread of colors; each colorblended into the next as in a rainbow. Planck was forced to acceptthe discontinuous emission of light in order to explain thecontinuous color band of light.

But, of course, this was not the first time that a newmathematical idea had "forced" the appearance of a new andsomewhat paradoxical physical picture.

Thus Planck's magic formula, though totally unexpectedand not justified by any logical mechanical explanation,succeeded in explaining the heretofore unexplained behavior oflight. And it did more. For the first time in the history of science,no one was able to really picture what was going on. Themathematical formula had replaced any visual experience. Itworked, but it hardly made any sense.

The Reluctant Planck

With his simple formula, Max Planck started a furor. A newprecedent in science, particularly in physics, had been set. Therewas no independent evidence for Planck's E = hf formula. Itwas simply a mathematical construct. And the embarrassingthing was there simply was no way to explain it. There was noway to see it, visualize it, or even connect it with any otherformula like it. My attempts with the quantum pond andquantum candy bar are analogies, not descriptions of what wasactually happening inside a heated substance.

Thus Planck was quite reluctant to fully accept thediscontinuous behavior of matter when it was involved with theemission of light or the absorption of heat energy. Despite hisdisavowal of his own discovery, it was too late. Anotherphysicist, a little younger and perhaps a little braver thanPlanck, would take the idea seriously. His name was AlbertEinstein, and he was destined to give a new insight into theenergy E in Planck's formula. The E stood for the energy of anundiscovered particle, a particle of light.

68 When the Universe Jumped

Einstein Draivs a Picture: The Photon Is Bom

Einstein upset the applecarts of the Newtonian mechanicallandscape and replaced them by the Einsteinian mechanicalpicture.^ A new mechanical picture, one that provided an evenfirmer grip on the movements of matter and light, was offered byEinstein. But as new and outrageous as these ideas of relativitywere, they were still mechanical. Cause produced effect, even ifclocks and yardsticks were no longer as fixed as we hadpreviously thought them.

Yet Einstein also sowed, during this same year, the seedsof a new nonmechanical apple tree.^ He took Planck's theoreticaldiscontinuities to heart. He reasoned that the cause of thediscontinuities in the emission and absorption of light and heatwere not to be found in the oscillating bits of matter producingthat heat and light. They were instead in the heat and lightenergy. He felt that somehow, even though the wave theory oflight was successful, light was not fundamentally made of waves.The light only appeared as waves if one observed it over fairlylong time intervals. If one could just freeze the moment, stopthe picture of the steady progression of these light waves longenough, one would see that the waves were made up of tinygranules of light.®

These granules are what actually interact with the oscillatingbits of matter in the glowing heated material. That is why theprocess is so disruptive and discontinuous. The oscillators aren'tactually making waves, they are emitting light granules. Byanalogy, if we imagine each oscillating bit of matter to be aperson singing a song, the melodies are coming from the singers'mouths in the form of blown-out watermelon seeds rather thansmooth, continuous sound waves.

Einstein had not fully realized that he was sowing the seedsof the destruction of the mechanical universe with this picture. Itstill seemed mechanical to him. Light waves were made of stuff.Each bit of that stuff had an energy E. These bits, just likeany old bits of matter, did what all pieces of matter do. Theymove, they have momentum and they have energy. The light bitsdid just the same thing. Einstein even called these bits by thename quanta^ to indicate their countability, their appearances asseparate things, as quantities of stuff.

But, according to E = hf, the energy of each bit somehowstill had to depend on the frequency of the light wave. Andthat was not explainable by any mechanical picture so far. I'm

sure that even Einstein's picture would have been dropped if ithadn't been able to account for another mystery.

That mystery was the sudden appearance of electrons ofmatter outside of the boundary surfaces of cold metals wheneverlight was shined on those surfaces. Not only could hot metalsglow and emit light, but they also were able to "boil out" chunksof tiny matter. These chunks were discovered to be electrons, tinybits of solid matter, each of which possessed a minusculeelectrical charge of negative electricity.

That was no surprise. Heating up the bacon was alwaysa spattering affair. What surprised everyone was that heatenergy was not involved. The electrons were boiling out withoutany heat energy being added. Einstein's quanta ideaexplained why.

Each grain of light either smacked into an electron in themetal or passed through without incident. If a collision occurred,it was catastrophic for the electron. The tiny electron was thenhurtled out of the metal as if it had been shot from a cannon.All of the light quantum's energy went into the effort. It gave upall of its energy to the electron in one instantaneous moment.

Einste-in saw Qrains oflight, later cxil led photons,Ihe first quant urns.

When the Universe Jumped

By refining the experiment, physicists saw that Einstein's use ofE = hf was correct. When they changed the frequency of thelight shined on the metal surface, they observed that theelectron's energy also changed. By using high-frequency bluelight, the electron's energy was observed to be greater than whenthey used red light, which had a lower frequency.

Later Einstein's quanta would be called photons. The coldemission of electrons would be called the photoelectric effect. For

A series ofphotographsshowing thepicture qualityobtainable trornvarious numbersot photons.

The Disturbing Observer

providing the correct theoretical explanation for the photoelectriceffect, Einstein won the Nobel Prize in 1921.

Like Planck before him, Einstein's contribution wastheoretical. Both of these men explained what had been unex-plainable, and both were lauded for their mathematicaldiscoveries. This in itself was a new trend in physics. New ideaswere being entertained in many phases of society. Could the newPlanck-Einstein idea be put to use anywhere else?

KJunnber of photons,

a 3,000

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f 28,000,000

Quantum Jumps

''The time has corae^^

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and sealing wax

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boiling hot

And whether pigs

have wings.^^

LEWIS CARROLL

A Liord Eats a Raisin Pudding Atom

Planck and Einstein had set the stage. By 1911, the quantumnature of light was already making its way into respectability.Light was a wave that somehow had a particulate graininessassociated with it. Using highly developed vacuum techniquesand the newest electrical equipment, scientists played withelectrical discharges in gases that were sufficiently rarefied to bestudied. They were also looking at the light that these electricaldischarges produced. Today we call such phenomena"neon signs."

In 1896, J. J. Thomson had discovered the electron by usingthe vacuum and electrical discharge technique. This discoverywas hailed as monumental. The secret of electricity was containedin this tiny bit of matter. By using electric and magnetic fields,Thomson was able to focus and steer a beam of electrons, thusdetermining the electrical charge and, later, the mass of eachelectron. These tiny bits were found to be extremely light inweight when compared to atoms of a gas. One atom of hydrogen,the lightest atom known, weighed nearly two thousand times asmuch as an electron. Thus it seemed natural to suppose thatelectrons were parts of atoms. Indeed, it was taken for grantedthat the electrical power used in the electrical discharge in thegases ripped the atomic gases apart and thus produced electrons.

Since matter was assumed to be made of atoms, it was alsonatural to imagine that heated solid or liquid matter glowedbecause of the movements of the lighter electrons. Theseelectrons were thought to oscillate back and forth inside of theirrespective atoms. And these oscillations, it was supposed, broad-cast light waves just as Hertz had demonstrated in 1887 that hiselectrical oscillations broadcast radio waves. The only questionwas how to picture this. Remember, the Newtonian classicalworld view of physical processes still persisted in spite of thePlanck-Einstein E = hf formula.

The size of the atom was known. It was less than twobillionths of an inch in diameter. This diameter is so tiny that itis nearly inconceivable. To grasp how tiny an atom actually is,consider the following imaginative exercise. Suppose you had agolf ball in your hand. And suppose that you could inflate this

74 When the Universe Jumped

golf ball—that is, blow it up like a balloon until it was largeenough to enable you to see an atom within the golf ball. To bespecific, supposed that you wished to blow the golf ball up untilone of its atoms was as big as a normal sized golf ball. For thatatom to become big enough to hold in your hand, the originalgolf ball would have to be inflated to the size of our earth! Nowonder no one knew what an atom looked like or, in particular,how electrons fit inside of it.

By 1911, J. J. Thomson had become Lord Thomson. He hadhis own laboratory in England. He was the director of theworld-famous Cavendish Laboratory. He also was the leaderof a certain school of thought regarding the structure of atomsand the whereabouts of electrons within.

Thomson's atom was pictured as a tiny raisin pudding.Embedded within this ''pudding" were even tinier electron"raisins." The number of electrons depended on the particularvariety of atom. Hydrogen had just one electron raisin, one bitof negative electrical charge to balance out the observed positivecharge and make the atom electrically neutral. By putting theatom into an electrical discharge, that single, negativelycharged electron could be pulled out of the pudding and leavebehind a positively charged atom "pudding." The result was ahydrogen ion. Helium ions were observed to be doubly charged;thus, it was clear that a helium atom had to have two electronswithin it to balance out its charge. And so on.

Another school of thought held that the atom looked morelike a miniature solar system than a raisin pudding. Eachelectron in any given atom was pictured as a planet that movedin a closed orbit about a tiny nucleus at the atom's center.Instead of a more or less random distribution of electron raisinsembedded in the large and somewhat soft, tenuous background ofa positively charged pudding, there was instead a well-organizedseries of electron planets, each in its own orbit, following a well-defined mechanical and repeatable movement. These electronplanets moved like real planets. Each had its own respective"years." In other words, there was a periodicity or frequency totheir motions. The deciding feature between these two modelshad to do with the rest of the atom, the positive matter thatheld the electrons within.

The correctness of the pudding or planetary model of theatom could not be determined from the light emitted by atoms.Nor could anyone shine light on an atom and take a look. Atomswere much too small. The wave lengths of light were thousandsof times longer than the diameters of atoms. Such details as the

Quantum Jumps 75

location of electrons or the distribution of the heavier, positivelycharged atomic matter would never be seen by using light waves.But there were other ways to explore an atom. You could throwother atomic particles at it and observe the scattering and atomicdebris that would result from a collision. Just as the debris froma midair collision between airplanes can reveal the cause ofthe accident, atomic debris can reveal what the insides of theatom look like.

The question of whether matter in an atom was spread outlike a pudding or gathered together in a tiny sunlike nucleus atthe atom's center was finally given an experimental test in 1911.Within a vacuum enclosure, a beam of helium ions was fired ata very thin foil of gold, and the truth was discovered. The heliumions scattered from the atoms within the gold foil with a patternthat suggested that the atoms of gold had nuclei. The puddingmodel was dropped.

The new atomic model was definitely planetary. Thesurprising thing of the planetary model was how small thenucleus appeared. If the golf ball-sized atom was once againinflated, this time to the size of a modern sports arena or footballstadium, the nucleus of that atom would be the size of a grain ofrice. Somehow the electrons whirled about, filling in the vastspace within the tiny atomic world.

These experiments were carried out by Lord ErnestRutherford and his assistant Ernest Marsden.^ Rutherford wasalso given his own laboratory in the industrial Midlands ofManchester, England. With the success of what is now called theRutherford nuclear atom, Lord Rutherford led his group ofscientists in an attempt to picture how the electron "planets"were able to maintain themselves in orbit and yet radiate energyin the form of light waves. Rutherford's success was, I'm sure,not too palatable for his counterpart, Lord Thomson,down south.

Into this slight animosity a young innocent was about tostep. His name was Niels Bohr.

Bohr's Quantum Atom

Dr. Bohr had just completed his doctoral thesis in Copenhagen,Denmark, when he reported to work for J. J. Thomson at the"Cavendish." Lord Thomson, Bohr's first employer, probably

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felt less than enthusiastic over meeting the twenty-six-year-oldBohr. Besides possessing an incredible mind, Bohr was quiteforthright and outspoken. Thomson's model for an electron hadbeen the subject of Bohr's thesis, and Bohr immediately pointedout some mathematical errors in Thomson's earlier work.

By the autumn of 1911, Bohr found himself, much toThomson's urging, on his way to Manchester to join Rutherford'sgroup. He quickly joined in with this newly excited group ofphysicists and began his own search for the electrons withinatoms.

The simplest and lightest-known atom in the universe washydrogen. It contained, according to Rutherford, a tiny nucleusand a single electron orbiting that nucleus. It was hoped that, if asuccessful model of this atom could be made, all other atomswould fall into line and be explained. So Bohr attempted tomake a model of the hydrogen atom.

There was, however, a severe stumbling block in the way ofthe planetary picture of an atom. The problem was how could theelectron keep a stable orbit? If the atom was as big as it appearedto be, its electron would necessarily be whirling around inside itwith greatly accelerated changes in speed and direction, fillingout the space like the tip of a whirling propeller blade fills out acircle. The electron would have to do this and not emit anyenergy. Certainly, it could not emit its energy continuously. Todo so would be a disaster for the model. The reason for this isthat the planetary model predicts a spiraling motion of the planetinto the sun for any planet that gives up energy continuously.That would mean the electron would crash into its nucleus everytime it emitted its light energy. The whole atom would besuddenly deflated and all matter would undergo a rapid collapse.It is amazing to consider how tiny atoms would be if the atomicelectrons were gobbled up by their nuclei. A football stadiumwould be shrunk to a grain of rice. The earth would be shrunkto the size of a football stadium! All matter would thus appearwith enormous density. (Neutron stars do appear in our universewith these densities. The force of gravity crushes the atomstogether.) And all matter would be dead and lifeless. The lightwould be gone.

But if the electron could not emit energy continuously, howwas it to radiate any light? Light emission took energy. Theelectron would have to radiate energy sometime or no light wouldever be seen. The question was how to make up a planetarymodel in which the electron would only radiate energysporadically or in a discontinuous manner. Thus Bohr attempted

to visualize under what circumstances the electron would be"allowed" to radiate energy and under what circumstances itwould be "forbidden" to do so. This was not an easy decisionto make. Bohr's model would have to show a reason for thediscontinuity. How could Bohr explain it?

He explained it very simply. He postulated that an atomwould only be allowed the privilege of emitting light when anelectron jumped discontinuously from one orbit to another. Itwould be forbidden from doing so otherwise. Like Planck andEinstein before him, Bohr was setting out on a bold path. In fact,he was encouraged by their example. He felt that somehowPlanck's h factor had to be invblved in the process. He knewthat h had been used by both Flanck and Einstein to point tothe discontinuous movement of light energy in solid matter.Perhaps it could also be used inside of an atom. But how? Bohrfound out.

This new secret was actually no mystery to anyone familiarwith physics. It had to do with something that physicists callunits. A unit is a measure of a physical quantity. Any unit canalso be composd of other units. Take the common example of amonetary unit. An American dollar is a unit of money, and it iscomposed of other units as well. For example, a dollar is tenunits called dimes, or one hundred units called pennies. Similarly,it is also one-tenth of a unit called a ten dollar bill.

Planck's constant h also was a unit. And it too could bemade up of other units. It was a unit of energy-time, somethingthat physicists call action, and it was a unit of momentum-distance, just as a dollar is also ten dime units. But Bohr hadnoticed that h could be viewed as a unit of angular momentumand that observation had a direct bearing on his atomic model.

Angular momentum is a familiar experience for children.It results whenever a moving object passes a fixed point inspace. If the moving object joins or connects with the pointit is moving past, the object begins to whirl in a circle. Angularmomentum can be thought of as momentum moving in a circle.When children run towards a tether ball hanging from a pole,they often leap and swing in a circle about the pole. By hangingon to the tether the children exhibit their angular momentum"about" the pole. Angular momentum is the product of ordinaryor linear momentum and the radius or distance from the objectto the reference point. Since Bohr's electron was traveling in anorbit about the nucleus, it too was tethered, held to that nucleusby an invisible tether of electrical attraction between the electronand the atomic nucleus. Thus the electron had angular

momentum. Could Planck's constant h be used as a unit of theelectron's angular momentum?

To grasp the significance of this question, imagine that youhave a ball attached to a string. Holding the loose end of thestring in your hand, whirl the ball around over your head,cowboy style, as if you were about to rope a calf. The faster youwhirl the ball, the greater the force you feel, holding on to therope. When you whirl the ball faster, you increase its angularmomentum.

Now picture an ice skater whirling in a spin. Notice that asthe skater brings her arms toward her body, she whirls faster.Her arms are acting like balls attached to ropes. But, unlike thewhirling balls, although she is spinning faster, her angularmomentum remains the same. This is because the distance fromher spin axis to her arms has decreased to compensate for herincreased speed of rotation.

If you now picture the tiny electron whirling around in itsorbit, you will realize that for a given force holding it to itscircular path and for a given fixed amount of angular momentum,the speed of the electron is determined. The radius of the orbitis also determined. Everything depends on the delicate balanceprovided by the amount of angular momentum the electron isallowed to possess.

Bohr tried out a calculation imagining a circular orbit forthe electron with one unit of angular momentum. He calculatedthe size of the orbit requiring that the electron have one unitof h. The orbit was the correct size; it filled out the atom. Hethen tried a new orbit with two units of h. It proved to be anew orbit with a larger diameter, four times the original orbit.When Bohr calculated an orbit for the electron with three unitsof hy the orbit grew in size to nine times the original orbit.Bohr had discovered a new model for the atom.

In this model there were only certain allowed orbits. Byrestricting the electron to these special or "quantized" orbits, asthey were later called, Bohr successfully predicted the correctsize for the atom. Each orbit grew in size as the electronincreased its angular momentum. But the scale was correct.

This wasn't the only discovery. Bohr also discovered whythe electron wasn't radiating as it whirled in its orbit. In otherwords he found a reason for the atom's stability. By allowing theelectron to have only whole units of h and not any other amountsof angular momentum, Bohr discovered the rule that kept theelectron in a stable orbit. Only electrons with whole amountsof angular momentum (i.e., integer multiples of Planck's

6>ohr and his atom

Each circle represents anorbit for a planetaryelectron.The orbital diajneter6are in the ratio 1-4:9. In orbitone, the electron has oneunit of hjn orbit two (dia-meter 4) it has t^^ units ofh, and in orbit three (dia-meter ?) (t has threeunits of h

82 When the Universe Jumped

constant: l/i, 2/i, 3/i, etc.) would be allowed the privilege oforbiting peacefully inside of the atom. These quantized orbitswere known as Bohr orbits. The integers of 1, 2, 3, and so forthwere called the quantum numbers of the orbits. A quantummodel of the atom had appeared.

The only thing still needed was the "rule" that allowed theelectron to radiate light energy. Again, there was no physicalreason for the quantization rule that held the electron in a stableorbit. Bohr had made it up. So Bohr again postulated that theelectron would radiate light whenever it changed from one orbitto another. He calculated the energy of the electron in each of itspossible orbits. By comparing the difference in energies betweenthe orbits and using Planck's E = /i/formula, Bohr successfullypredicted the frequencies of the light observed whenever anelectron made an orbital "jump."

In January of 1913, a former classmate of Bohr's showedhim a paper written by a Swiss schoolteacher named JohannBalmer. Balmer had observed light coming from hydrogen gas in1880. Instead of a continuous spread of colors, the light fromhydrogen showed missing colors when it was passed through aprism and analyzed. The spectrum it produced appeared as ahorizontal strip containing several vertical lines, like teeth in acomb. Only some teeth were missing. Ordinarily, the lightwe see—for example, sunlight or light from an incandescentbulb—does not break down into such a spectrum. Instead,sunlight or light from any hot solid or liquid shows a continuousspread of colors like a rainbow. But Balmer's incompletespectrum had been produced by hydrogen atoms in a gas. Bohrread Balmer's paper on atomic light and became very excited.Not only could he calculate the energy of the electron in eachatomic orbit, but he could also calculate the energy that theelectron radiated away when it changed orbits.

Balmer's hydrogen spectrum had missing "teeth" becausethe energy given out by the jumping electron was so wellprescribed. Since there were only certain orbits for the electron,there had to be only certain frequencies for the light. Thefrequency of the light depended on the difference in energies ofthe electron involved in the quantum jump from one orbitto another. Balmer's atomic light was explained.

All well and good. However, Bohr's successful predictionwas based on a very disturbing picture. The electron makingthe light was not oscillating or orbiting the nucleus to make theKght. In fact, it wasn't doing anything that anyone could reallyimagine. To make the light it had to jump. It leaped like a

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desperate superman from one orbit to another inside the atom.It was not allowed to move in between orbits. Bohr tried tocalculate that and failed. The best picture he could come up withwas that of a quantum jump, a leap from one place to anotherwithout passing in between. As unreasonable as this picture was,it replaced any completely classical mechanical picture of thatprocess.

Yet Newton's mechanics were not to be completely aban-doned. Some features of the classical picture were not abandonedat all. First of all, the idea of an orbit and a planetary atom werestill classical pictures based upon a continuous movement of theelectron. What was not classical was the refusal of the electron toradiate when it was in a Bohr orbit. This was entirely unreason-able for a very important reason: all accelerating electrons havebeen observed to radiate energy. Either the Bohr-orbitingelectrons were accelerating or Newton's second law was beingrepealed.

When the Universe Jumped

According to Newton, there was a force acting on theelectron. That force pulled the electron into a circular orbit,changing the momentum of the electron. Therefore, there had tobe an acceleration of the electron. And it also followed that,because the electron was a particle of electricity, the electron hadto give out energy whenever it accelerated. Bohr's picture did notseem to correspond with this observed fact.

But Bohr was not to be dissuaded. He noticed that his ruleof allowed and forbidden radiation was dependent on the sizeof the electron's quantum jump. A jump from the second orbit

What looks continuous is i^ally discontinuous.

The classioal electron radiates light wavescontinuously

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The Bohr electron follows a discontinuouspath ol" quantum jampc».

Quantum Jumps 85

to the first was extremely tiny, but a sizable change on the scaleof the first orbital diameter. It was, therefore, a relativelyenormous jump. On the other hand, a jump from orbit 10,000 toorbit 9,999 was very large when compared to the first orbitaldiameter, but an extremely small change in orbit on the scale ofthe 10,000th orbital diameter. Thus, it was a relatively tiny jump.When Bohr calculated the radiation from a change in orbitsbetween large atomic diameter orbits, the result he found was inagreement with classically predicted results. In other words, thesmaller the relative change, the more classical and continuousthe result seemed to be.

Bohr had determined another exciting feature of quantummechanics. It applied just where it was necessary. Wherever theworld appeared to be continuous, the quantum "rules" corre-sponded with classical rules. This was called the Principle ofCorrespondence. Bohr felt very encouraged. He believed that hewas on to one of God's secrets. He knew why the world appearedcontinuous even though it was fundamentally a discontinuousand quantum jumping world. It was all a question of relativescale. To Bohr, discontinuity was a fundamental truth.

But neither were the continuists to be dissuaded. Theyweren't ready to throw the whole classical towel into the ring.Although Bohr, in his excitement over the correspondence rule,was ready to drop all classical pictures, the continuists feltequally encouraged to find a classical reason for the jumps. Littledid they know then that they would have to give up the particleworld of matter in their attempts to rid themselves of quantumjumps.

/ never saw a moorI never saw the sea;'Yet I know how theheather looks^And what a wave must be

EMILY DICKINSON

■ '■'r'. y'.\|^^\y:^:J.'■■^^■Ur

A Prince Imagmes a Wave

The flame of desire for a mechanical model of the atom was aboutto be refueled. Bohr's orbits were too disturbing. Electronsshould have some physical reason for not radiating wheneverthey are confined to such periodic movements. Furthermore,there must be a natural and physical reason for Planck'smysterious E = hf formula that would relate the energy ofEinstein's photon of light with the frequency of that light's wavemotion. But what explanation could there be? While classicalNewtonian mechanics did not provide any insights, perhaps the"new" mechanics of Einstein's special theory of relativity wouldshed some light on light. And perhaps this was the desire of onewell-to-do prince of the French aristocracy, Louis Victorde Broglie.

De Broglie came from a long line of French royalty.^His notable family dated back to the American Revolutionarywar, where his ancestors fought for the revolutionaries. Althoughhe completed his education in history by 1910, his brother,a well-known physicist, persuaded him to return to school andstudy physics. De Broglie soon became fascinated with thequantum controversy and the ideas of Albert Einstein. By 1922,after interrupting his studies to fight in World War I, hepublished two papers on Einstein's wave-particle concept oflight.2 He called attention to the dual behavior of light. Onetype of observation, in which the time for observing is spreadover many millions of cycles of wave oscillation, shows that lightis a wave. Another type of observation, in which there is aninstantaneous transfer of energy from light to matter or viceversa, showed that light consisted of particles called photons.

De Broglie wished to provide a mechanical explanation forthe wave-particle duality of light. Thus, he needed to find amechanical reason for the photons in the wave to have an energythat was determined by the frequency of that wave. It was whilethinking about light that the idea occurred to de Broglie thatmatter, too, might have a wave nature.

He knew of Bohr's strange result. The electron in a hydrogenatom would orbit its nucleus only in special orbits. In each orbit,the electron had to have a whole number of angular momentum

88 \Mien the Universe Jumped

units, multiples of Planck's constant h. De Broglie was struckwith another wave analogy. He remembered standing waves.

If we consider a violin string for a moment, we will seede Broglie's analogy. When the string is plucked or bowed, itvibrates. The string moves up and do\\Ti in a characteristicmanner. The ends of the string, of course, are held do\\Ti tightlywith pegs. If we watch carefully, we ^411 see that the stringresembles a wave. The middle of the string vibrates up and down.This kind of wave is called a standing wave. It oscillates up anddo\^Ti, but does not move along the string. The sound of theviolin string is produced by this standing wave pattern.

It is also possible to see and hear another vibration on thissame string. In this second example, the middle of the stringremains at rest while the rest of the string, not including thefixed ends, vibrates. The sound we hear is an octave higher. Thisstanding wave pattern, called the second harmonic, has a higherfrequency than the first one. Again, by watching closely we seethat there are two up-and-down movements, one on each side ofthe fixed middle point.

A third harmonic occurs when there are two points alongthe string, in addition to the endpoints, that remain at rest whenthe string \ibrates. Each resting point on the string is called anode. As the number of nodes on the string increases, thefrequency of the standing wave increases and the pitch of thesound wave it produces increases.

De Broglie noticed a connection between the angularmomentum of the electron in a Bohr orbit and the numberof nodes in a standing wave pattern. The orbiting electron couldonly have one unit of h, two units of h, etc. Could these discon-tinuous changes in the electron's angular momentum, thesechanges in the amount of h allowed, be due somehow to a similarchange in standing wave patterns?

What de Broglie had noticed in analogy was that the numberof nodes was a whole number for any standing wave pattern. Thelowest frequency standing wave had two nodes, the end pointsof the string. The next higher frequency had three nodes. Thenext wave had to have four nodes, and so on. Since, accordingto Planck's E = hf formula, energy was frequency, could thehigher energy orbits in the hydrogen atom correspond to higherharmonic matter-wave frequencies?

De Broglie realized that the Bohr orbit could be seen as acircular violin string, a snake swallowing its own tail. Would theorbit size predicted by his standing "matter waves" correspondwith Bohr's calculated circles? In other words, what would hiswaves do if they were confined in a circle?

Fundamental

rir<5tharmonic

Secondharmonic

Thirdhannonic

liW

That's aholt wove.

That's awhole wave-

That's a1'/^ wave.

Thats atwo wave

Standing wave patterns for a jump rope.

De Broglie discovered that his matter waves fit Bohr'sorbits exactly. When he calculated the wavelength of the lowestorbit, he discovered another astonishing mathematical connectionbetween the wave and the particle. The momentum of theorbiting electron equaled Planck's constant divided by thewavelength. He quickly reviewed his calculation and looked atthe next orbit. It had a higher energy. It also checked out the

When the Universe Jumped

The deBroghe'brbit^a wave in a circle.

DeBroglie andhi5 atom.

Bohr^ orbits are replaced by standingwave patterns. The first orbit has onewhole wave, the second has twowhole waves, and the third hos three.

same. For each Bohr orbit, the electron's momentum equaled hdivided by the standing wave's wavelength.

De Broglie had discovered a new formula, one as startlingand revolutionary as Planck's formula. It stated that themomentum of a particle p was equal to Planck's constant /i,divided by the wavelength L. That is, p = h/L.

With this new mathematical discovery, Bohr's orbits couldbe explained. Each orbit was a standing wave pattern. The lowestorbit had two nodes. The next one had to have four nodes, sincean orbit with three nodes would cancel itself out. The third orbithad to have six nodes, and so on. The energy of the electron ineach orbit was given by h times the wave frequency. Themomentum of the electron in each orbit was given by h dividedby the wavelength. The mathematics worked out.

The atom was a tiny tuned instrument. These mathematicalrelations balanced the tiny electron into a tuned standing wavepattern. Orbits had determined and fixed sizes in order that thesedistinct, ''quantized" wave patterns could exist.

Louis de Broglie published his results as a thesis dissertationfor his doctorate in physics. He presented it, somewhatreluctantly before the Faculty of Sciences at the University ofParis in 1923.^ His thesis was certainly original, perhaps a littletoo original. The study of atoms was a branch of physics, notmusical composition. There was no experimental justification forthis ''crazy" idea. In fact, using such em absurd idea to explainBohr's absurdity was a little too much for the reserved faculty.

Albert Einstein was called in. Einstein replied, "It may lookcrazy, but it is really sound!" The thesis was accepted, and a whilelater, the prince was awarded a Nobel Prize for his dissertation.Someone in America had actually discovered a de Broglie wave.

American Grains of Waves

Einstein welcomed de Broglie's picture. It was a return tocontinuous mechanism. The wave that guided the electron in theatom had been undetected so f£U*. De Broglie's calculation of themomentum indicated that, for the light-weight, high-speedelectron, the wavelength L would be extremely short. In fact,these tiny waves confined to the minuscule orbits within atomswere less than two billionths of an inch long. Even light waveswere about five thousand times longer.

92 When the Universe Jumped

De Broglie's wave was envisioned as accompanying anyparticle wherever the particle went. Like a shadow, the matterwave traveled alongside its particle. The two belonged together.The frequency of the wave could always be determined by theparticle energy; the wavelength could be determined from themomentum of the particle. Matter, like light, had a dual nature.This was the wave-particle duality.

Although these new discoveries were sweeping Europeanscience back and forth, little of the furor crossed the Atlanticto the United States. Americans were more concerned withpractical discoveries. The Bell telephone laboratories exemplifiedthe practical side of American research. But Clinton Davisson,who worked for Bell,"* had noticed a peculiarity in his research.He had found that the electrons he was using in his experimentswere reflecting from the clean surfaces of nickel crystals in anunexpected pattern. Trusting his results, he published themwithout offering any explanation.

Davisson's results made their way across the Atlantic.Two German physicists, James Franck and Walter Elsasser,grew excited when they saw these electron reflection patterns.^The patterns did not appear to make any sense unless they werewave interference patterns produced by the electron matterwaves reflecting from the nickel atoms. By checking the momentaof the electrons that Davisson had used, Franck and Elsasserwere able to determine a reflection pattern for the electrons. Thatpattern depended on the de Broglie calculation of the wavelengthin his p = h/L formula. The calculated pattern matchedDavisson's measured results. De Broglie's waves had beendetected.

Other experiments followed. With the discovery of theneutron, a new particle contained within the atomic nucleus,physicists made neutron diffraction patterns that appeared justlike the electron patterns observed by Davisson. Scientists soonrealized that any kind of particle would produce a wave patternif a beam of those particles were directed to an appropriatelysized crystal that would allow the waves to interfere with eachother.

Matter waves were now accepted. In fact, they were acceptedso completely that physicists began to doubt even the existenceof particles. Perhaps the waves could be made to interfere witheach other and, in so doing, produce a particle. Could this idea bebacked up by a careful mathematical analysis?

Such an analysis was needed for another reason as well. DeBroglie's waves only held for particle beams and closed Bohr

Matter vyove interference patterns. By changing thefnomentum of each electron.i:1ie wavelength changes.The separation between the "teeth" increases asthe wovelepigth gets longer.

orbits. But how does an electron change from one orbit to thenext? What is mechanically and continuously going on inside theatom? Newtonian mechanics was not dead; it had only beenmodified to accommodate a new form of matter—the matterwave. Somehow there had to be a way to describe the movementinside of an atom that would allow the electron to change orbitsand radiate away its excess energy as light. To find such ananswer, an expert on waves was needed.

Schroedinger's Unimagiiiable Waves:The End of Pictures

There was certainly something to be said for de Broglie's waves:at least they offered a picture of what was going on inside of anatom. However, more was needed. A way to visualize the shifting

When the Universe Jumped

patterns of the wave when it changed its energy and producedlight was needed. Neither Bohr's jumping electron particles norde Broglie's wave patterns were enough to explain the lightcoming from different atoms. But Erwin Schroedinger, anAustrian physicist, found a mathematical equation thatexplained the changing wave patterns inside an atom.^

Schroedinger's equation provided a continuous mathematicaldescription. He viewed the atom as analogous to the vibratingviolin string. The movement of the electron from one orbit toanother lower energy orbit was a simple change of notes. As aviolin string undergoes such a change, there is a moment whenboth harmonics can be heard. This results in the well-knownexperience of harmony or, as wave scientists call it, thephenomenon of beats. The beats between two notes are what wehear as the harmony. These beats are perceived as a third sound.The vibrational pattern of the beats is determined by the differ-ence in the frequencies of the two harmonics.

This was just what was needed to explain the observedfrequency of the light waves or photons emitted when the electronin the atom undergoes a change from one orbit to the other. Thelight was a beat, a harmony, between the lower and upperharmonics of the Schroedinger-de Broglie waves. When we seeatomic light, we are observing an atom singing harmony. Withthis explanation, Schroedinger hoped to save the continuityof physical processes.

Schroedinger'sdancing maihematicQlw/Qvea were inhis mind.

However, physicists were not altogether comfortable withhis wave equation. No one could imagine what the waves lookedlike. They had no medium to wave in, and they had norecognizable form in physical space. They didn't look like waterwaves or sound waves. Instead, they were abstract, mathematicalwaves described by mathematical functions.

Although a physical picture of a mathematical function isdifficult to imagine, it is not impossible. If you have ever steppedinto a shallow wading pool—one that has been recently visitedby young children—you may have experienced a disconcertingphysical manifestation of a mathematical function due to thechildren's unfortunate lack of bladder control. As you movedfrom one place to another in the pool, you undoubtedly noticedthat there were warm spots and cold spots. The temperature ofthe water was not the same everywhere. Temperature was amathematical function of location in the water. In time, thetemperature could even change at a given point in the water.Temperature was also a function of the time of observation. Inother words, the temperature was a mathematical function ofspace and time.

Similarly, Schroedinger's wave was a mathematical functionof space and time. The only problem was that no one knew howto look for its "warm and cold spots"—in other words, its troughsand crests. Furthermore, as the atom became more complicated,the wave also became more complicated. For example, the wave

Schroedingers hydroqen atorn- A pattern of probability

0^^ <r/(rcMo^ /5 fiy^A/i^/it'/U" /^ -^^f^ AJ-or^

96 When the Universe Jumped

wi?»^-

i..'3^ •

■^V^^00i':\ •

Schroedinger:5 hydrogen atom^ Just before it ludiotes.

describing one electron is a function of that electron's locationin space and time. That's not too difficult. But if we are lookingat a helium atom, there are two electrons present, but only onewave. The wave behavior, then, depends on the location of bothelectrons at the same time. And as the atomic number of an atomincreases, the number of electrons contained within that atomincreases. Uranium, which has an atomic number of 92, has 92electrons and only one wave function describing it all. There wassimply no convenient way to picture this wave.

But despite its unimaginability, Schroedinger's wave provedindispensable. For it explained a great many physical phenomenato which the classical model could no longer be applied. It was asuccessful mathematical way to explain light from any atom,molecular vibrations, and the ability of gases to absorb heat atextremely low temperatures. Physicists were excited and eager toapply Schroedinger's mathematics to anything they could gettheir hands on. They were like a gang of kids who had invadedthe kitchen and, after many disappointing attempts to bake acake, had suddenly discovered mother's cookbook. Schroedinger'sformula gave the correct recipe in every physical applicationimaginable.

Everyone believed in Schroedinger's wave, even if no oneknew how it waved in space and time. Somehow the wave had toexist. But even without a picture, the mathematics was enough—provided you knew how to read the mathematics cookbook. Could

the wave make a particle? Was there a way to use theSchroedinger cookbook to bake a particle? Even that was notimpossible for the master chef. But how could one use waves tomake a particle? The answer lies in our concept of a particle.It is a tiny object distinguished from a wave by one outstandingcharacteristic: it is localized. It occupies a well-defined region ofspace. It moves from one region of space to another. You alwaysknow where it is. It exists at one place only at any given time.

Waves are different; they are not localized. They are spreadover wide regions of space and can, in fact, occupy any region ofspace containing many locations at the same instant of time.

But waves can be added together. And when many waves areadded, surprising results can be achieved. Schroedinger waveswere no exception to the rule. Schroedinger waves could beadded like ingredients to a recipe and produce a Schroedingerpulse.

A pulse is a special kind of wave. If you attach one end of ajump rope to a wall and take the other end in your hand, you canmake a pulse by stretching the rope taut and giving it a suddenup-and-down movement. The pulse travels from your handtoward the wall and then reflects from the wall. This actionresembles that of a ball thrown against the wall and bouncingfrom it. Perhaps that's all there was to an electron. It was a pulseon an invisible rope.

A |?AKfi<./£'

A jump rope vdu can shake a pulse oniook6 liKe a particle moving along.

When the Universe Jumped

But there was something awfully embarrassing about theidea of a Schroedinger pulse: it got fatter as it got older. Thatis, it spread out and became wider each second it existed. Theproblem was it had nothing to hold it together. It was made up ofother waves, and each of these waves had its own speed.Withtime, each wave would move apart from the others. The pulsewould stay together only so long as the waves remained inharmony with each other.

] \t/hAhi^

_^-v

Schroeclingera free particle: The instant afteryou find \t/it spreads.

Imagine, if you will, the pulse as a closely bunched herd ofhorses galloping around a racetrack bend. The horses can staytogether for only a short time. Eventually, the group spreads out

When a Particle Is a Wave

as each horse assumes its own pace. The slowest horses fall to therear of the group, while the fastest ones move to the front. As timegoes on, the distance between the slowest and fastest horseslengthens. In a similar manner, the pulse grows fatter as itsslower waves fall out of synchronization with its faster waves.

Though big objects, like baseballs, also were made of waves,the larger the object was initially, the slower its waves spread.Thus a baseball maintained its shape because it was so big tobegin with. The Schroedinger pulse describing the baseball wasno embarrassment.

But an electron was a horse of a different color. While it wasconfined within an atom, the electrical forces of the atomicnucleus held its waves in rein. Its waves were only allowed tospread over a region the size of the atom, no further. But when anelectron was no longer in such confinement, when it was set free,the waves making up its tiny pulse-particle size would begin tospread at an extremely rapid rate. In less than a millionth of asecond, the electron pulse-particle would become as big as thenearest footbedl stadium! But, of course, no one has ever seen anelectron that big. All electrons appear, whenever they appear, astiny spots.

This contradiction between our observations of electrons andSchroedinger's mathematical description of them uncovered anew problem: what prevented Schroedinger's pulses fromgrowing so large? Little did anyone realize that question was toopen the doors of paradox and mystery and lead us to a quitedifferent picture of the universe. The answer to the question was:human observation kept them from growing so large. We were onthe verge of the discovery of a new discontinuity.

A'sKinny'^ SchitDedinger pube gets widei- astime marches on.

^aW ^hSKt /5 //.^

Chapter 6

]\ro One Has Seenthe Wind

The universe is not onlyQueerer than we imagine^but it is queererthan we can imagine.

X B. S. HALDANE

God Shoots Dice: The Probability Interpretation

It may be difficult for the nonscientist to imagine how repugnantthe idea of a discontinuous movement of matter is to physicistswho desire continuity. Starting with Einstein, the discontinuityin the movement of light was connected with a mechanicalpicture. Light consisted of granules. But then came Bohr and hisquantum jumping electron inside of the tiny atom. This conceptupset continuists because they could not understand how aparticle could behave in this fashion. When de Broglie andSchroedinger appeared with their wave interpretation, thecontinuists breathed a sigh of relief.

Schroedinger's picture of the atom, although complicatedand dependent upon a nearly unimaginable wave function, wasnevertheless quite reasonable. The atom's electron was a wave.The atom radiated, not because its electrons jumped from orbit toorbit, but because of a continuous process of harmonic beats. Thelight was given out when the atom "music box" played both theupper energy and lower energy frequencies at the same time. Thedifference between the two electron matter-wave frequencies,which corresponded in Bohr's conception of the atom to thedifference in the electron's orbital energies, was exactly thefrequency of the light waves observed.

Gradually the upper frequency matter-wave tone quieteddown, leaving only the lower harmonic. Thus the atom stoppedradiating light. There was no longer a higher harmonic to beatagainst. The atom simply continued vibrating its electron waveat the lower frequency, which (according to the Planck E = hfformula and the de Brogliep = h/L formula) had to beunobservable and tucked safely away inside of the atom.

Later, Schroedinger's picture would be destroyed, but hisequation, his mathematical law, would remain. And he wouldexpress to Bohr, after days of long and arduous discussion, hisdisgust with ever having been involved in this quantum jumpingthing. The problem was that, no matter how the wave shook anddanced, there still had to be a particle somewhere. Max Bornwould be the first to provide an interpretation of this "particle"discontinuity. The wave was not the electron. It was a wave ofprobability.

101

In 1954, Professor Max Born was awarded the Nobel Prizefor his interpretation of the wave function. The award camenearly thirty years after he first offered the interpretation.^ Butthen, Nobel Prizes come more slowly for ideas in physics than forexperimental discoveries. Born explained his motives foropposing Schroedinger's picture of the atom.^ He simply had toomuch connection with experimental work. He knew of thecollision experiments being carried out in his own institute atGottingen, Germany. Sophisticated refinements with vacuumtechniques and electrical focusing of beams of electron particleshad led to detailed studies of collisions between atoms andelectrons. Despite the discovery of electron waves, these collisionexperiments were convincing evidence that the electron was stillvery much a tiny particle—literally, a hard nut to crack.

There was no doubt that Schroedinger's mathematicsworked. His equation described correctly all observable atomicphenomena. But how could the Schroedinger equation be used inthose very same experimental collision studies at Bom*sinstitute? In other words, what kind of wave function describesan electron beam colliding with a rarefied gas of atoms? Since theelectrons in the beam were not confined within any atoms, theymoved freely through space toward their eventual target, atoms.

Schroedinger's pulse describing a single electron wasinadequate. It just got too big too quickly. It couldn't be a realtiny electron, the kind seen every day in Born's laboratory. ButBom knew his mathematics. Wide electron pulses spread slowly.So if a pulse was wide to begin with, it would hardly spread at allas it moved from one end of the apparatus to the other end.However, since the pulses had to be many times wider than anatom, how could the electron fit inside of an atom?

Bom realized that, in the experiments at Gottingen, no onewas really able to locate a single electron in a beam of electrons.Could it be that the width of the wave pulse was connectedsomehow with our knowledge of the location of each electron?When Bom allowed the pulses in his mathematical equations tobe as wide as the dimensions of the beam, he found that thespreads of the pulses virtually vanished.

Born's efforts suggested that the time had come for a newinterpretation of the meaning of the wave. The wave was not thereal particle. Somehow the wave was connected with ourknowledge of electron locations. It was, in fact, a probabilityfunction.

Probability functions are familiar today. They are used todescribe the distribution of likely occurrences. A typical example

103

Max Born viewedSchroedingerswave as probabilityin space toi- findingthe electron.

104 When the Universe Jumped

is the probability function for a coin that is spinning in the air.As it falls, the probability function for it to land heads up is .50.Once the coin has landed, the probability function changes. Ifit has landed heads up, the probability function becomes 1. If ithas landed tails up, the probability function becomes 0.

Insurance companies use probability functions to describethe distribution of automobile accidents. The stream of motoristsdriving into San Francisco each day is intense. That means theprobability for any one car to collide with another is large. Andthe greater the intensity of the stream of motorists, the higherthe probability of a collision. The situation is less intense,automotively speaking, in San Diego. Therefore, the probabilitydensity or distribution is lower for a collision to occur in thatarea. If we were to view the entire state of California from asatellite and watch all of the cars driving about, it would be quiteeasy for us to predict where collisions would be most likely tooccur. We would simply note those areas where the flow of trafficwas greatest —that is, most intense.

Born pictured the flow of electrons in much the same manner.Wherever there was a greater concentration of electrons in thebeam, the Schroedinger wave had a greater intensity. Bycalculating that intensity. Born found he could predict theprobability of a collision between an electron and an atom.

Born's picture made a tremendous impression on his fellowphysicists. Again, sighs of relief were heard coming from physicslabs all across Europe. But the picture still had a hole in it.Born's system made sense so long as it was applied to a beam ora concentration of actual numbers of particles. Physicists, likeinsurance actuaries, were quite used to probability ideas whenthey were dealing with a large number of practically uncountableevents. In the experiments at Gottingen, the events wereuncountable. But what about just one electron? One atom? Howshould the Schroedinger wave be interpreted in that case? Didthe wave describe a single electron?

Was there a wave in these isolated cases? Was it, in otherwords, a real wave? And if the wave was a fundamental part ofnature that belonged to each individual particle of nature, thenwho determined where the electron was to be found? Was natureessentially a probability game? Did God play dice with theuniverse?

A new interpretation was sought. Something was wrong withthe probability picture. But what could replace it? The answer tothis question had been brewing in Germany since the end ofWorld War I. A new and revolutionary principle of reality was

occurring to one man, a principle that was to completely changeour thinking about the physical world.

Heisenberg^s Uncertainty Principle:The End of Mechanical Models

If I had a time machine and could return to any period of time, whichperiod would I choose? I would pick the Roaring Twenties;however, it would not be the United States that I would return to.No, indeed. Instead, I would go to post-World War I Germany.And because I am fascinated by pseudodecadence and cafesociety, you would find me among such contemporaries asBertold Brecht and Thomas Mann. Bauhaus art and designwould be flourishing and outrageous Dada art would be creating"authentic reality" through the abolition of traditional culturaland aesthetic forms by the technique of comic derision. For,during that period, irrationality, chance, and intuition wereguiding principles. Freud was out. Jung and Adler were in. Lifehad a certain cabaret feeling.

Now add the physicists. Though they numbered perhapsless than a hundred, a new breed of young, enthusiastic fellowswas making its way into the new physics. Planck was past sixty.Einstein had seen his fortieth birthday. Bohr was a middle-agedthirty-five. These older and wiser moderates were to be theguiding lights for the new breed. It was time for Dada physics,and it was happening in Gottingen, Germany. In early summer,1922, Professor Niels Bohr, who then headed a brand-newinstitute of physics in Denmark called the Copenhagen School,had come to give a lecture.

Among the students who had gathered to hear Bohr wastwenty-year-old Werner Heisenberg. This occasion would be thefirst of many meetings between Heisenberg and Bohr. Togetherthese two would change the meaning of physics. Eager to rid physicsof mechanical models, they would herald a new school, a school ofdiscontinuists. Their interpretations would lead to a revolutionof thought.

Heisenberg wrote of this first meeting with Bohr in his book.Physics and Beyond. After some remarks concerning Bohr's atomictheory, he wrote:

Bohr must have gathered that my remarks sprang from profoundinterst in his atomic theory. ... He replied hesitantly . . . and asked

When the Universe Jumped

me to join him that afternoon on a walk over the Hain Mountain. . . .This walk was to have profound repercussions on my scientific career,or perhaps it is more correct to say that my real scientific career onlybegan that afternoon. . . . Bohr's remark [that afternoon] remindedme that atoms were not things. . . .^

But if atoms were not "things," then what were they?Heisenberg's answer was that all classical ideas about the worldhad to be abandoned. Motion could no longer be described in termsof the classical concept of a thing moving continuously from oneplace to another. This idea only made sense for large objects; it didnot make sense if the "thing" was atom-sized. In other words,concepts are reasonable only when they describe our actualobservations rather than our ideas about what we think ishappening. Since an atom was not seen, it was not a meaningfulconcept.

Heisenberg's thoughts had been influenced by Einstein. In1905, Einstein had carefully laid out the steps to relativity. He

had recognized that, in order to speak about such notions asspace and time, one must provide operational definitions —definitions that detailed how these things were measured. Forexample, space is what a ruler measures and time is what a clockmeasures. For anyone armed with these empirical and objectiveforms, space and time lose their mystery. Everyone holding rulersand clocks can agree on the definitions, because they can agreeon which operations to do with these instruments.

A concept is useful when we all know how its measurementis to be accomplished. This viewpoint led Heisenberg to questionany concept that had no operational definition. Atoms were notobservable, but the light coming from them was observable.Thus, Heisenberg developed a new form of mathematical toolsbased upon the frequencies of the light that was seen, rather thanthe position and momentum of an unobservable electron withinan unseen atom. These new mathematical tools were developedfrom the mathematics of operators and not the mathematics ofnumbers.

An operator in mathematics performs a duty. It changes ormodifies a mathematical function in a defined way. For example,the operator called "square" will multiply any mathematicalfunction by itself. (Thus when "square" operates on "x," it makes"x2." When it operates on 5, it makes 25, etc. Operators are alsocapable of being operated upon. Thus "square" can be multipliedby the number 3, which can be an operator as well as a simplenumber. This makes "3«square," a new operator. When"three»square" operates upon 5 it makes 75 instead of 25. Two ormore operators can also be multiplied together.) Heisenbergdiscovered, with the help of Max Born, that his mathematicaloperators, which corresponded to the observed frequencies andintensities of the light from atoms, obeyed a strange law of multi-plication. The order in which you multiplied the operators wasimportant. If the operators were, for example, A and B, then ABdid not equal BA. (If we use the previous example of "three«square,"we see that "three•square" is not the same as "square*three."For when "three•square" operates on 5 it gives 75, but"square•three" operating on 5 gives the result of multiplying3 times 5 and then squaring. This gives 225, instead. Thus"three^square does not equal "square»three.") Did that meanthat the physical world depending as well upon the order inwhich you observed things?

Later, Born and Pascual Jordan carried Heisenberg'smathematics a step further. They were guided by Bohr's Principleof Correspondence that showed that the classical mechanical

108 When the Universe Jumped

viewpoint would correspond with the quantum mechanical view-point whenever the quantum numbers describing the old Bohrorbits were quite large compared with 1. By following this princi-ple, they were able to find mathematical operators for theposition and the momentum of the electron instead of thefrequencies and intensities used by Heisenberg. The surprisingfact was that these operators, too, depended on the order inwhich they were carried out. A new and previously unsuspectedpicture of the universe was emerging.

The new tools of operator algebra were later found to berelated to the mathematics of matrices. A matrix, an array ofnumbers, must be handled in a careful, well-defined way. Therules governing the use of matrices were found to be identical tothe mathematical rules used to handle operators. Consequently,Heisenberg's development of quantum mechanics came to becalled matrix mechanics. The wave mechanics of de Broglie andSchroedinger was still being investigated, however, andeventually it became apparent that the two forms of mathe-matical expression were simply disguised versions of the samething. Schroedinger discovered this and offered formalmathematical proof of their equivalence. For a while, interest inthe purely operational matrix mechanics dropped.

Yet Heisenberg wasn't ready to dismiss the insights he hadgarnered from his matrix mechanics. He began to explore hisobservational basis for reality using the Schroedinger wave.Bom's probability interpretation suggested how he shouldproceed, and, following the tradition of Einstein, Heisenbergattempted to describe the method by which the position andmomentum of an atom-sized object could be measured.

To see something, we must shine light on it. Determining thelocation of an electron would require our sense of sight. But for sotiny an object as an electron, Heisenberg knew a special kind ofmicroscope would be needed. A microscope magnifies images bycatching light rays, which were originally moving in differentdirections, and forcing them all to move in much the samedirection toward the awaiting open eye. The larger the apertureor lens opening, the more rays of light there are to catch. In thisway, a better image is obtained, but the viewer pays a price forthat better image.

The price is that we don't know the precise path taken by thelight ray after it leaves the object we were trying to view in thefirst place. Oh, we will see it all right—a fraction after itscollision with the little light photon that was gathered up by the

(

microscope. But was that photon heading north before it wascorralled by the lens, was it heading south, or southwest? Oncethe photon is gathered in, that information gets lost.

But so what? We do get an exact measurement of theposition of the electron. We can point out just where it was. Well,not exactly. We still must worry about the kind of light weuse.Try to imagine painting a fine portrait the size of a Lincolnpenny. What kind of brush would you use? The finer the hairs ofyour brush, the better your ability to create the miniature. If youwere to reduce the size of the portrait even further, you wouldneed an even finer brush.

Different kinds of light vary in their wavelengths in muchthe same way that brushes vary in the fineness of their hairs. Tosee something very tiny, you need to use light with a small wave-length. The smaller the object you are looking for, the tinier thewavelength you will need. Since an electron is very tiny,Heisenberg needed to use a kind of light that has a very smallwavelength. This light is beyond our normal range of vision,though still detectable in a way similar to ordinary light. Butaccording to de Broglie's formula, the smaller the wavelength ofthe light, the greater the momentum of the photon. Therefore, forHeisenberg to see the electron, the photon would have to hit itwith a tremendous amount of momentum.

In Zen Buddhism, one speaks of using a thorn to remove athorn as the process of finding out what is real. In Heisenberg'smicroscope, the tiny wavelengthed photon is as big a thorn as theelectron it is inspecting. Thus, if we are able to catch the photonray in the wide open lens of the microscope and if we areconsequently able to **see" the position of the electron, we willhave absolutely no idea of where the electron will be next. Ouract of viewing the electron disrupts its motion. Though we learnthe electron's position, we are left uncertain of its momentum; wesimply do not know how fast or in what direction the electron wasmoving at the instant of impact.

We may attempt to remedy the situation by doing one of twothings. First, we can use photons that do not give the electron sobig a "kick." That is, we can use light that has a longer wave-length. But this remedy has a disadvantage: we lose informationabout the precise location of the electron. Like the painter with abrush of coarse hairs, we cannot manage the details of ourelectron portrait. Our second option is to make the lens opening,the aperture, smaller. For by taking in less light, we are able todetermine more accurately the direction the photon takes after its

When the Universe Jumped

how diffraction biur6 the image of the electrons.

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collision with the electron. Unfortunately, this remedy alsohas a disadvantage. Light behaves very much like a wave withrespect to the aperture. That means it bends or diffracts as itpasses through the hole. The narrower the space offered to thelight, the worse the bending. Consequently, narrowing theaperture brings us less information about the location of theelectron, because the image we receive is distorted by the bentlight rays.

If you have ever tried to convince someone to change hisway of life, you may have noticed how he had some good reasonwhy the change you suggested could never work. Even thoughthe person sought your advice, he had a ready answer defeatingyour marvelous idea as soon as you offered it. Your stubbornfriend, you probably realized, had simply made up his mind inadvance. Similarly, Heisenberg had discovered nature's stubbornstreak. Yet there seemed no way to catch her in her act. The moreone knew of the position of the electron, the less one knew of itspath to the future, its momentum. And the inverse was also true.But was nature just hiding from us? Heisenberg didn't think so.

Remember that we began this section with the premise thatwe can define only what we can measure. Since we cannotmeasure both the position and the momentum of any object inthis universe with exact precision, the very concepts of "position"and "momentum" are in doubt. So how can these concepts begiven any meaning? Heisenberg contended that although thenotion of "path" implies clear knowledge of both "position" and"momentum" simultaneously, it could be retained in quantumphysics. His rationale was extremely provocative. He said, "Thepath comes into existence only when we observe it."*

To grasp Heisenberg's statement, let us take another look atthe Bohr atomic model. Accordingly, if an electron is in an orbitwith a large quantum number—say, orbit 10,000—it will behavein a nearly classical manner. The size of this orbit is quite visiblewith ordinary light, for its diameter is about one-half inch inlength. However, the correspondence principle warns us that itwill be quite difficult to see any difference between orbit 10,050and orbit 10,000. These orbits are too close together for us toperceive the difference with ordinary light. Thus, if we shineordinary light on the atom when the electron has a large orbit,we cannot be certain which orbit we are witnessing.

Is the electron in a specific orbit? In other words, does theelectron occupy a given point in space at a given time, and does itfollow a smooth and continuous trajectory to the future pointalong that trajectory? According to our observation, we will not

be able to determine the actual orbit for the electron. But shall westill assume that it has such an orbit? Certainly we know moreabout the electron after we observe it than we did before weobserved it.

But how did we gain this knowledge? According to Bom'sinterpretation of the Schroedinger wave, the wave describing theelectron is a description of our knowledge. In other words, thewave shape and size tell us where the electron is likely to beobserved. But, if after we actually observe an electron we knowmore than we did before we observed it, the Schroedinger wavemust have changed its shape and size to correspond to ourchange of knowledge. But what caused the Schroedinger wave tochange, and how?

If we imagine that no attempt was made to observe theelectron, then the wave pulse composed of those Schroedingerwaves, which satisfy the Schroedinger equation, would continueto spread. In fact, they would continue to spread indefinitely.Meanwhile, we are losing information concerning the location ofthe electron. Even though the light we use is not a very preciseguide to determining the electron's location, it is better to lightone little match than curse the darkness.

Once we see the light reflecting from the electron, we havea much better idea of its actual location. With our location of theelectron, there is a corresponding change in size of theSchroedinger pulse describing the electron. Following Bom'sinterpretation, the size of the pulse is a measure of our knowledgeof the electron's location. Since we now have a better knowledgeof the electron's location, we must have a correspondingly morenarrow Schroedinger pulse describing that electron. But thatwould mean the Schroedinger pulse describing the electron musthave gotten thinner as a result of our observing the electron. Ithad to thin down because we have more information with thelight on than we did without observing the electron. We can see,for example, that the electron is on the right side rather than theleft side of an observing screen. Our observation process hassomehow reduced the pulse to a smaller size.

This reduction in pulse size is not part of the mathematicaldescription of the electron. We cannot use the Schroedinger waveequation to tell us just where we will find the electron when weobserve it. The Schroedinger equation can only tell us about thepulse that is unobserved. It tells us where we are likely toobserve the electron. After our observation of the electron, thepulse undergoes a discontinuous change brought on by ourobservation.

113

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If our observation used long wavelength light, the pulsewould not have been too thin to start with. Since unobserved,wide pulses do not grow much wider very quickly, our loss ofinformation concerning the location of the electron is nottoo severe.

In today's electronics industry, electrons are used in avariety of tasks. Engineers have good control of electronsbecause they work with extremely wide electron wave pulses. Ofcourse, we mean "wide" on an atomic scale. These atomicallywide pulses are nevertheless quite definable on a large industrialscale. For example, electrons are used inside of the big cathode

114 When the Universe Jumped

ray tube in a typical television set. The Schroedinger pulsedescribing the electron must travel the length of the tube inabout ten billionths of a second. This time is short enough toprevent the electron pulse from spreading too much; particularlysince the initial pulse need only be several thousandths of an inchin width. This tiny macroscopic, or large-scale size, is more than amillion times larger than an atom. Our modern use of electronmicroscopes is based not upon the wave nature of the electron,but upon its ability to be a particle for very short time periodsand our noninsistence that the electron's wave pulse be too smallto begin with.

These practical considerations make the electron appear tobe a solid particle. Practical considerations also make nearlyevery other object that exists on a human-size scale appear''normal." The spreading time (that is, the time it takes for apulse to double its size) depends as well on the mass of the objectobserved. Large-mass objects on the scale of grams, even if theirinitial pulses were defined within a millionth of an inch, wouldneed the age of eternity, billions of years, to spread any amountat all. However, such big and heavy pulses are not needed. Whatabout thin and light-weight pulses? Here quantum physics takesits toll. They spread quickly.

When we are dealing with electrons and atoms, we need toconsider such things as spreading time. It is just when this timeconcerns us that we begin to lose our picture of what is going on.The reduction of a fat pulse to a thin pulse is necessary for anyobservation to take place. It is a vital and mysterious process thatis ignorable for fat and heavy pulses, but not for initially thinand light-weight pulses. Of course, I am referring to pulses thatdescribe a light-mass particle with only a limited range ofpossible locations. With such objects, information is lost veryquickly. The Schroedinger equation is the only mathematical toolwe have to keep track of such objects. But it doesn't do a goodjob; it simply tells us how we lose information. Once we actuallyperform an observation, we gain back some of what we lost. Thisprocess of gaining back is a discontinuous process.

If we insist that the universe is composed of such tinyobjects, then the whole universe comes into existence wheneverwe observe it. Furthermore, we pay a price for our acts ofobservation. Each act is a compromise. The more we attempt tomeasure the position of an electron, the less we can determine itsmomentum, and vice versa. The Bom interpretation was ameasure of our uncertainty in this regard.

No One Has Seen the Wind 115

This uncertainty meant that no matter how accurately onetried to measure the classical quantities of position andmomentum, there would always be an uncertainty in the measure-ment. Predicting or determining the future of atomic objectswould be impossible under these circumstances. This was calledthe Heisenberg Principle of Uncertainty or the Principle ofIndeterminism. It had little relevance in the worid of ordinary-sized objects. They were hardly bothered by disturbancesproduced through observation. But the uncertainty principle wasserious business when it came to electrons. Indeed, it was soserious that it brought the very existence of electrons intoquestion.

Later the principle was found to apply to any pair ofobservations, provided that pair of observations never producedthe same result when carried out in a reverse order. This includedthe energy of a particle and the time span over which thatenergy was to be measured.

As you can expect, the uncertainty principle was quite anupset to the continuists. It signaled the end of mechanicalmodels. How could there be a mechanical universe out there, ifthe universe changed every time we altered how we observed it?First locating an electron and then finding out how fast it ismoving gave an entirely different result than determining theelectron's speed and then locating its position. How could amechanical universe be fundamentally indeterminate?

To answer these questions would require as clear a statementof the issues as possible. That meant a debate. The outcome wasdestined to affect the entire history of physics.

Chapter 7

.V'

Resistance toUncertainty

There is no law

except the law that there

is no law.

JOHN A. WHEELER

Heisenberg's Principle of Uncertainty could be interpretedanother way: to observe is to disturb. Up to the time ofHeisenberg's principle, it was assumed that the "out there"universe existed quite independently of the observer whomeasures it. To have a universe that depends upon the observerwho measures it is disturbing on both physical and mentalaccounts. After two thousand years, modern physics was facedwith the same dilemma as the early Greeks. It was the old storyof Zeno and the arrow. How did the arrow move? Continually,said the continuists, with no help from the observer. In jumps,said the discontinuists, with a little and unavoidable help fromthe observer.

By October, 1927, the issue of the role of the observer hadbrought together thirty or more well-known physicists. Theywere gathered for the fifth Solvay conference (named afterBelgian industrialist Ernest Solvay, who had sponsored it andoffered considerable financial support). The first four conferenceshad also dealt with the new quantum mechanics, but thisconference promised to be a real showdown. It was the start ofthe strangest debate in the history of the understanding of theworld. Its protagonists were Niels Bohr for the discontinuists andAlbert Einstein for the continuists. Also included were Born, deBroglie, Heisenberg, Planck, and Schroedinger. For this was tobe a top-level discussion on one of the most important problemsof the time: the meaning of the new quantum theory.

The members of the fifth Solvay Congress, l?27.

117

The first to enter the arena was de Broglie. He argued for thereality of the matter wave. Certainly it was a wave of probability,but it also was a guiding wave determining the real trajectory ofthe particle in its journey through space and time. The vote wasthumbs down. To vote against an idea in such circles is easyenough; all one had to do was not discuss the idea. A year later,de Broglie abandoned his "pilot wave" theory. In fact, in the fallof 1928, when he assumed his post at the Paris Faculty ofSciences, he thought it unjustified to teach in his own course.

After de Broglie, Bom and Heisenberg presented their paperon the probability interpretation of the Schroedinger wave. Thevote was thumbs up. Next, Schroedinger presented his wavemechanics for a system composed of many bodies in interaction.The climax of the meeting was a general debate. The preliminarybouts were over. The ringmaster Hendrik A. Lorentz opened withhis dissatisfaction over the rejection of determinism proposed bythe majority of speakers. But it was time for the main bout.Lorentz called on Bohr to address the assembled. Bohr presentedhis latest ideas on the wave-particle duality for his openinggambit. His words were clearly intended for the ears of one man.Albert Einstein had never before heard Bohr's new ideas onwave-particle duality, a concept that Bohr calledcomplementarity.^ Einstein had not even taken part in any of thepreliminary bouts. Even now, at the end of Bohr's presentation,he remained silent.

Several others piped up. Bom asked the group to considerthe question of reconciling the particle character of matter withthe wave character. He referred to the Heisenberg example ofobserving an electron in an atom. Each time the electron was"seen" the pulse instantly thinned down, redefined within thelimits set by the wavelengths of the light. The longer the wave-lengths of the light used, the softer the light's impact upon theorbiting electron. The position of the electron was not welldefined. Its Schroedinger pulse was large enough to encompassseveral possible orbits for the electron particle. Somehow thepicture was consistent. The particle was defined in its location bythe act of observing it.

But how did this take place? The pulse would, according tothe Schroedinger equation, continue to spread, even after thelight interacted with it. The Schroedinger equation did notdescribe what we would see by shining light on the orbitingelectron. It only told of the probability of observing the electron.The actual experience determined the location of the electroninsofar as the light's wavelengths could paint the picture. In

other words, Schroedinger's equation did not describe actuality,only potentiality.

The question was how did the spreading waves regroup whenan observation took place? This phenomenon was known as thecollapse of the wave function. The collapse was not containedwithin the mathematical formulation of quantum mechanics. Yetif the wave description was a reality, the collapse had to occur.Several physicists in attendance attempted to explain thecollapse, and someone offered an explanation of an alternativemultidimensional space in which no collapse of the wave occurs.But as Born admitted, "This does not lead us very far concerningthe basic problem. "^

It was then that Einstein entered the ring. Rising from hisseat, he told the assembly, ''I have to apologize for not havinggone deeply into quantum mechanics. Nevertheless, I would liketo make some general remarks."^ The seeds of what was todevelop had been planted seven years earlier, in the spring of1920. Now the debate had officially begun. Einstein was clearwhere Bohr was obscure. Einstein asked the members to consideran experiment, the first of a series of "gedanken (thought)experiments." It was a simple thought experiment in which thegroup was asked to imagine a particle passing through a verynarrow slit. Accordingly, the wave associated with the particlemust be diffracted, and like ripples from a dropped pebble in apond, the wave will spread. Behind the slit is a sensitized screenshaped in the form of a hemisphere. This hemisphere will act as adetector of the particle, for after passing through the slit, theparticle must arrive somewhere on the screen. The arrival of theparticle is an event whose probability of occurrence at anyparticular point on the screen depends on the intensity ofthe wave.

Everyone agreed with these statements, even Bohr. But,Einstein continued, there are two different viewpoints as to whatis actually happening. According to the first viewpoint, the wavedoes not represent a single isolated particle, but rather anensemble of particles, all of which are distributed through space.The wave intensity corresponds to our usual interpretation ofmultitudes of similar events: it is a probability distribution nomore mysterious than an actuarial table or a census giving thedistribution of age and sex among the states and cities. If thisfirst is correct, then the wave describes our real ignorance ofthings, nothing more, and matter is really material behavingcausally and moving so within space and time. But a second viewis also possible.

120 When the Universe Jumped

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According to this second viewpoint, we are not ignorant ofanything, and quantum mechanics is complete in its descriptionof individual events. The particle is a wave moving towards thescreen. Thus, Einstein objected, the particle is potentially

present at every point on the screen, with nearly equalprobability of appearing anywhere thereon. However, at somepoint, it becomes localized and appears suddenly to pop up at asingle isolated point. "It seems to me," Einstein continued,

that this difficulty cannot be overcome unless the description ofthe process in terms of Schroedinger's wave is supplemented bysome detailed specification of the localization of the particle. . . .[The second viewpoint] contradicts the postulate of relativity.*

It was the collapse of the wave that most disturbedEinstein. He imagined the wave impinging on the screen like surfon a beach. According to the second viewpoint, a peculiar action-at-a-distance takes place, which prevents the wave from hittingthe beach at two or more points at the same time. As a result, thewhole wave collapses like a genie into a bottle and beaches itselfat one point on the shoreline. Consequently, Einstein favored thefirst viewpoint.

The difference between the two viewpoints was the keyfulcrum upon which hung the delicate balance of reality. Thoughit might not have experimental consequences, still it would havefar-reaching effects. The first view suggests unidentified,mechanical, controlling factors called hidden variables. Thesecond view denies that anything further can be said. It deniesthe very need for such factors.

These two views, although couched in the modernterminology of quantum mechanics, were nothing more than theancient Greek views of continuity and wholeness versus discon-tinuity and wholeness. The continuists state that the whole is itssum of parts and that any apparent discontinuities can beexplained by a continual movement, a smooth mathematicaltransition from one point to the next. On this, Einstein andAristotle agreed. Their point of view reaffirms causality,continuity, and a deterministic universe.

The second viewpoint, which Bohr presented and Zeno wouldhave accepted, denies these things. There is no need to explainthe collapse of the wave. The wave is not the ultimate reality. Theparticle is not the ultimate reality. Reality is not the ultimatereality. There is, instead, one unbroken wholeness that appearsparadoxical as soon as we observers attempt to analyze it. Wecan't help but disrupt the universe in our efforts to take thingsapart. To Bohr, there was no wave to collapse unless the wavewas observed, and then no collapse would be seen. He viewedanedysis as observation, and observation was fundamentally adiscontinuous event. It could not be connected to any past

When the Universe Jumped

The BohK- Einsteindebate- It was as ifthe left half andright half of thecosmic brain werein dialogue-

Einstein

occurrence. The connection with the past was not a reality.

Although Bohr's position was obscure and difficult to pindown, it provided the groundwork for what is today called theCopenhagen interpretation of quantum mechanics. Thisinterpretation is the officially accepted understanding, and itpresents a reality that is stranger than we can imagine it to be.Our brains are filled with memories, with a desire for security.Therefore, we have a natural, built-in desire for continuity in allthings. But all of this is denied to us by the Principle ofUncertainty. All physical processes are impossible to envision.All physical processes are incompatible with the properties ofmechanical models.

This does not mean that we should throw away all of ourmachines. Just the opposite is true. Our mechanical models workbeautifully for large objects because of the smallness of Planck'sconstant. God's gift is a tiny h. But we must remember that weare the artists in the game of the universe. If h were any larger,the ultimate chaos would overwhelm us. With such a small unitof action, we have just the right amount of freedom to create

Resistance to Uncertainty

123

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nearly whatever we want. Just exactly what our limits are is asubject that is still being explored.

Things are only an approximate description of reality. Thelimits of our description are discovered in the Heisenberguncertainty principle. Bohr called his philosophy the Principle ofComplementarity. The wave-particle duality and the picturesassociated with this duality, such as the collapse of the wave andthe jumping of the particle, were a result of the fundamentalclash between two contrasting mental constructs of theappearance of reality.

Bohr's complementarity views need much room for airing.They are presented in chapter eight. Einstein did not give in tothese views. Instead, he adhered to the idea of an orderlyuniverse. God did not play dice, he asserted, and in his lateryears, Einstein provided the devil's advocacy against Bohr'sfundamentally discontinuist view.

Bohr's views offered a new vision of the world. And hecarried his ideas of complementarity over into the life sciences.He felt that there was no real contradiction between the

124 When the Universe Jumped

humanistic sciences and the natural sciences. The apparentconflict was nothing more than a complex form of the wave-particle duality. In anthropology, for example, there are twomodes of behavior: that based upon instinct and that based uponreason. Instinct could be viewed as a sudden discontinuityhaving no history. Reason, on the other hand, was a processfounded upon logic and continuity. In the study of primitivecultures, the observer must be aware of the disturbances hebrings into those cultures if he is to extract the "reasons" forthose cultures.

In the remaining chapters, we shall further contrast the Bohrand Einstein views. The resistance that each view offered theother resulted in a great deal of new thinking. Scientists wouldconstruct exciting parallels between many avenues of life thatwere previously thought of as very different. However, the debatebetween Bohr and Einstein has still not ended, though both arenow dead. Indeed, the battle of continuity versus discontinuitymay never end.

Pan Three

Is There

an ''Out There''

Out There?

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WALT WHITMAN

The Act of Creation: Observation

What do we mean when we speak of "reality"? We usually meanthe world that we sense. That world out there is made up ofthings that we can see, hear, taste, smell, and touch —real, solid,substantial objects of our everyday existence. We take it forgranted that these things would exist in their same sensible formeven if we were not there to observe them. Our observationssimply verify an already existing reality.

Yet, that isn't what quantum mechanics seems to be tellingus. It appears to indicate a drastic departure from what we couldcall our classical mechanical heritage. Certainly this is theposition of what later came to be known as the CopenhagenSchool or the Bohr Principle of Complementarity. According tothe tenets of the complementarity principle, there is no realityuntil that reality is perceived. Our perceptions of reality will,consequently, appear somewhat contradictory, dualistic, andparadoxical. The instantaneous experience of the reality of Nowwill not appear paradoxical at all. It is only when we observersattempt to construct a history of our perceptions that realityseems paradoxical.

The first new physicists gather aftei^ Bohr announces thePrinciple of Complementarity (como, (?27].

Enricofermi

WernerHeisenberg

WolfganqPauli

127

The reason for this paradoxical appearance of reality—atleast, atomic reality as observed by physicists—is that no cleardividing line exists between ourselves and the reality we observeto exist outside of ourselves. Instead, reality depends upon ourchoices of what and how we choose to observe. These choices, inturn, depend upon our minds or, more specifically, the content ofour thoughts. And our thoughts, in turn, depend upon ourexpectations, our desire for continuity.

Both the wave and particle descriptions of nature areremnants of our desire for continuity. They represent our bestattempts to understand physical reality in terms of pictures,mechanical constructs of thought based upon continuity. Whenwe observe anything on an atomic scale, we disrupt thatcontinuity. This disruption has two consequences: (1) it createsa picture of atomic matter in our minds, and (2) it indicates, atthe same time, the incompleteness of that picture. The incom-pleteness of that picture is the result of our thoughts, our failurein our attempts to maintain that picture throughout time.

These concerns regarding observation I call the constructionof reality by mental acts. These are the acts of creation. Now,much of what we observe is not at all disturbed or affected byobservation. The effects of observation upon elephants andbaseballs appear quite negligible when these massive objects areseen with ordinary light. Here the uncertainty principle plays avery small role. Both position and momentum are simultaneouslyobservable to all practical considerations. But we should notautomatically assume that our observations have no role in theuniverse when we are examining electrons. Furthermore, sinceelectrons are within us as well as outside of us, it is at leastconceivable that our observations of ourselves play a significantrole in our own human behavior.

All of the following examples and analogies concern a worldof observation that is unfamiliar to most of us. Thus I havechosen to use ordinary, familiar objects in these examples. Butthe reader must remember that the thoughts and conclusionsregarding the behavior of these objects are presented with thequantum mechanical perspective well in view. Ordinary objectsfall within the safe boundaries of Bohr's correspondenceprinciple; classical mechanical thinking is perfectly adequate indescribing the motion of such objects.

Yet if we choose to regard everything we see and do withinthe framework of the new physics, then we can say that, to someextent, reality construction is what we do every instant of ourconscious lives. We accomplish this construction by choosing

129

among the many alternatives incessantly offered to our minds.Thus, at the quantum level of reality, when we choose to "see"what we see, reality becomes both paradoxical and sensible at thesame time. Our acts of observation are what we experience as theeveryday world.

This way of thinking about the world is new to the Westernmind. It arose when physicists discovered that their acts ofobserving the atomic world introduced a duality, a double orparadoxical way of seeing. We shall examine just how it is thatthe act of observing the world can, at the same time, introduceand resolve this paradox. And we will begin our examination bylooking at an analogy that I call "The Paradoxical Cube." Thiswell-known analogy was already familiar to the artists VictorVaserely and Maurits Escher.

Next we will examine physicists' minds as I perform a"thought experiment" that sheds light on the duality of reality.The experiment, entitled "Complements of the Cosmic House,"shows us that all matter behaves in two complementary,contradictory ways: it appears to be particulate and well localizedin space, and it appears to be undulatory or wavelike and not welllocalized in space. How matter appears depends on our minds'choices; reality is a "matter" of choice.

Three acts of- obsen/ation: A particle is born, reborn, and reborn again

ObS^RVA^io^

-^pAce

130 Is There an "Out There" Out There?

Having come to realize that the reality we experience is onethat we choose from dualistic or complementary "sets," we shallnext look at the way we are victimized by our choices. We willexamine our victimization in the analogy of "The Magician'sChoice." This analogy will show us another side of the paradox:that no matter what we choose, the choice will appear to havebeen already made. In other words, it will seem to us that wenever really had a choice.

Then we will reexamine our physicists' minds as we takeanother look at a "thought experiment." We will see how it isthat the atomic world appears to have been chosen ahead of us,even as we come to realize that we are its choosers. I call this"The Case of the Vanishing Observer."

We shall take another look at the seemingly magical processof reality construction by choice as we examine the analogy of"Newcomb's Paradox." We will offer, perhaps for the first time, aquantum resolution to this amusing paradox of an omnipotent"being" versus objective reality. That resolution, according toBohr's complementarity principle, is that reality does not existuntil it is chosen.

All of the above examples should help us to understand howthe universe can appear to be both fundamentally paradoxical,chaotic, and indeterminate and, at the same time, logical, orderly,and quite determinate.

The Paradoxical Cube

Physicists have discovered that our universe follows the laws ofquantum physics. According to these laws, the physical universeis fundamentally paradoxical. Our universe seems to be composedof facts and their opposites at the same time.

Yet we don't seem to observe these paradoxes. Why not?Because when we observe something, we see either the fact or itsopposite, but not both at once. Without our acts of observation,the universe proceeds on its merry, magical, paradoxical waywith facts and counterfacts intermingling. This intermingling isnecessary; without it, no "real" world would ever be possible. Theobserver in his role behaves as Alexander did when confrontedwith the Gordian knot: he simply chooses to cut it, rather thanremain stymied by its ever-present, challenging convolutions.

How does an "act of observation" take place? Examine theillustration of the paradoxical cube. Which side is facing you?

The Paradoxical Cube.

At first, you may see the upper-most square in front, as if youwere looking up at the cube. But if you take a second glance, youmay find that you are suddenly looking down at the cube, andthe bottom-most square appears to pop out closest to you. Asthe observer, you have the choice of how you will view the cube.It is your act of observation that resolves the paradox. Accordingto quantum physics, all paradoxes dealing with the physicaluniverse are resolved in a similar manner by observation.

But there is yet another way to view reality. Look at theillustration again. That the illustration appears to be a cube is anillusion. In fact, it is eight points and twelve connecting linesforming sm abstract pattern. When you see this abstraction as acube, you are forced to make a choice: which face is in the frontand which face is in the rear? When you view the illustrationas an abstract form, however, no choice between these alter-natives is even possible.

In its abstract form, both the upper and lower squares of theillustration are, so to speak, in front at the same time or in therear at the same time. But in viewing the illustration as a cube,you the observer create the experience of this two-dimensionalform having front and rear faces. Your act of observation createsthe picture in your mind that "it" is a "cube." Seeing the "cube"as an abstract pattern of eight points connected by twelve linesis a complement to seeing "it" as a cube with a front face and arear face. It is only a paradoxical cube when we, observersconditioned to think that everything we see must be solid, insistthat "it" is a solid cube. Then the cube appears to "jump" fromone perspective view to another, seemingly playing tricks on us.

Is There an "Out There" Out There?

Two artists, Maurits Escher and Victor Vaserely, use ourpreconditioning to confront us with similarly paradoxical viewsof reality. In the detail of the Escher print that follows, we noticea man seated on a bench. Lying on the checkered patterned floorin front of him is a somewhat crumpled drawing of ourparadoxical cube. But look at the "cube" held by the man.Specifically, look at the struts the man holds in his hands. Theirparadoxical positions in space are as confounding to his mind asmaterial reality is to the mind of the quantum physicist.

Though the paradoxical cube is only an analogy of theabstract world of quantum physics, it demonstrates that there isa duplicity or duality to our acts of observation. Throughquantum physics, physicists have discovered that the world, likethe paradoxical cube, is also capable of being realized in comple-mentary ways. This realization is known to physicists as thePrinciple of Complementarity. Complementarity refers to aduality, like red versus green. The complementarity principlereminds us that while we are observing the redness of something,its greenness is invisible, and vice versa. Anything that is redand green at the same time would be gray, for example.

Similarly, the physical universe has a complementary nature.It is known as the wave-particle duality. In the next section,we will watch the mind of a physicist as he performs a "thoughtexperiment." Thought experiments are imagined experiences in

A detail from "Belvedere by Maunts Escher.

133

which the outcome is already known. They are usuadly performedahead of any real experiment. In the following "experiment,"the physicist will confront complementarity.

Wave-Pardcle Duality and thePrinciple of Complementarity

Physicists have discovered that our physical universe, or"cosmic house," appears like the paradoxical cube: there are twodifferent ways of observing it. We can view the universe in termsof particles, or we can view it as made up of waves. These twoways of seeing are complementary to each other; that is, we

"MEM" by Y. ybserely shows a blending of poradoxicQl andcomplementary visoal realities.

134 Is There an "Out There" Out There?

cannot see the universe both ways at the same time. I call theseways, "Complements of the Cosmic House."

Faced with this wave-particle duality, some physicists tendto disbelieve the particlelike behavior of the physical world andopt for its wavelike aspect as a better description. Not allphysicists think this way; the particlelike solidarity of ourexperiences paints a convincing picture. But adhering to this"solid" evidence that the world is composed of solid material"stuff" leads to a paradox much like that presented by ourexample of the "cube."

What do we mean when we speak of "the particle nature ofphysical reality"? Stop for a moment and pick up any nearbyobject. Hold it in your hand. For example, I have just reached fora pencil. My appreciation of its solidity comes when I hold itbetween my fingers. It gives me a secure feeling to know thepencil is there. This object is not elusive. It can be relied upon tobe what it is: a pencil. After a while, I become bored with itssolidity. So I play with it. Perhaps I break it into two pieces tosee what it is made of. My gut feeling is that it is composed ofmore "stuff." I want to see its inner stuff. My desire is to seekgreater security, greater solidarity, more reliability, and greatercertainty. I seek the ultimate "stuff" of the universal pencil. So Igo on destroying the pencil, but seeking greater security, lookingfor the fundamental building blocks that make up "pencilness."My fingers, however, are too clumsy to hold any of the smallstuff I may find. I must also refine my measuring instrument; Imust have pincers more delicate than my fingers. The problem isthat my new pincers, when I find them, are made of stuff that issimilar to the stuff I am examining.

Nevertheless, I continue my examination of the pencil. I putit into an oven, reducing it to atoms of pencil. By using heat, Ifree the pencil atoms from each other so I can get a better look atthem. Then I allow these pencil atoms to come out of the oven"on their own steam," through a very small aperture in the oven.Instead of pincers, I decide to use a black screen with a verysmall hole in it. Atoms come boiling out of the oven, and mostof them impinge on this screen. But every once in a while, oneatom goes through the hole. And I am waiting with anothercollecting screen to catch it. My catching screen is covered witha thin layer of atomically sensitive emulsion, like the inside ofa television picture screen. Whenever an atom strikes the screen,it leaves a small spot. The spot tells me that the atom is reallythere.

135

OVfc'NJ

An oven producing individual pencil atoms, which pos^through a black screen and torm a ring interferencepattern on the white screen.

But something odd is happening. Even though I havealigned the hole in the black screen with the aperture in theoven, I find that the atom doesn't continue to travel along thatline after it passes through the black screen's hole. Naturally,I think that the hole is probably much too large. The atom isso much smaller in diameter that it can pass anywhere throughthe hole and thus end up anywhere on my catching screen. So Imake the hole smaller. That way only those atoms that movealong the straight line between the oven aperture and the blackscreen hole will pass through the hole and continue along thatsame straight line until they hit the second screen.

But instead of correcting the problem, I have made it worse.The deviations increase as I decrease the diameter of the blackscreen's hole. The atoms that pass through the hole are makingmarks on the second screen that are further off the straight-linepath than before. The more I try to pinch the atom in the caliper-like hole of the black screen, the more slippery the atom becomes.

The universe is telling me something, I surmise. Absent-mindedly, I leave the oven on as I ponder the message of theuniverse. While I am pondering, atoms continue to boil out of theoven, passing through the oven's aperture, traveling on their wayto the first screen, where they pass through the hole and arecaught by the next screen. Millions of atoms are making the trip

Is There an "Out There" Out There?

from oven to the second screen after passing through the firstscreen's hole.

Suddenly I remember I left the oven on. I quickly returnto my experiment and shut the oven off. Almost as an after-thought, I look at the second screen, the one that collected allthose millions of atoms. I nearly fall off my chair when I see thepattern made by those atoms, all those independent particles ofpencil stuff, on the second screen. Instead of a small, blurredspot, an image of the hole in the first screen, I find a beautifulset of concentric, circular halos. Rings of ever-increasing size,each centered about the line that joins the oven's aperture withthe first screen's hole, greet my eye.

Two of the earliest electron wave interference patternphotographs CI^Zl).

There is no way that such a pattern could have beenproduced by independent particles acting individually, Iconclude. There must have been a conspiracy among the atoms.I test my hypothesis. I turn the oven back on and watch thepattern develop again. The individual atomic spots appear on thescreen, one after the other. Each spot occurs at random. Yetsomehow they seem to know just where to go to make the ringpattern. Why don't any of the atoms make spots in between therings, blurring the ring pattern into indistinction? Somehow theydon't do that.

My mind remembers that I have seen these patterns before,as a child. On hot summer days in Chicago, just after a suddenstorm, I would sit and lazily drop small pebbles in the puddlesleft by the rain in the deep pock marks made by bulldozersresting in the empty lot behind my home. Each pebble droppedinto the miniature pond would make ever-widening, circularpatterns of ripples. Sometimes I would drop two pebbles at onceand be surprised at the result. The two separate sets of ripplesdid not keep their separate identities. Instead, they interferedwith each other and produced a new pattern unlike either oneof them.

Somehow the pencil atoms must make waves, I decide. Eachatom must be magically transformed, like the toad changed intoa prince, from a solid little particle into a wave spread overspace. That would explain the ring pattern on the second screen.It was produced by the interfering wave fronts.

At this point it is worth mentioning that these wavepatterns are not observable unless one is looking for them. Thatis because each individual atom leaves just one small spot on thescreen. It is the overall pattern of all the atomic spots that tellsus something else is going on. These "wave" patterns are comple-mentary pictures to the individual "particle" spots.

Look at the illustration of the paradoxical "cube" again.Each individual "hit" you get when you see the cube as a solidis like the observation of an individual atomic spot. After several"hits" of the cube, you see it as a pattern. In its abstract patternform, what had appeared to be the sides of the cube are no longerdistinguishable as "sides." Only the overall "wave" pattern isseen. In the same way, the "wave" ring pattern of atomic "hits"is seen.

Of course, there are many other examples in common usagethat illustrate complementarity. Take the saying, "I can't see theforest for the trees." An individual's rights versus the rights ofthe state also illustrate complementarity. The important feature

i;J8 In riuMO an "Out riuMo" Out Thoio

Wav^ intwfcrvKe patterns.

for US is that the overall pattern is not random; it showsorganization —that is, an interference pattern impossible toproduce if the agent producing it is a random stream of separatedhot particles. Yet the particles are separate. Matter simply doesnot behave in accordance with our ordinary ideas about it.

This wave-particle duality appears in all matter, includinglight. There are no exceptions. Bohr, I am sure, would concurthat we, too, are part of the duality of nature. For nature isdualistic; she behaves according to the Principle of Comple-mentarity. Here's how a physicist might state it: The mostgeneral physical properties of any system must be expressed interms of the complementary sets of that system. These sets arejoined as complements of each other, and the more we determineor define a system in terms of the one of these complements,the less we know about the other. ^

The discovery of the Principle of Complementarity markeda change in our thinking. It taught us that our everyday senseswere not to be trusted to give a total view of reality. There wasalways a hidden, complementary side to everything weexperienced.

But this hidden side is not actually present. For example, inthe case of a coin that lands heads up, the hidden and comple-mentary side is not real until it is revealed. Our actions in theworld are always a compromise between two such opposites.The more we determine one side of reality, the less the otherside is shown to us. In everyday objects, this compromise is asmall price to pay. In atomic-sized objects, the compromiseexacts a dear toll. When we attempted to determine the exactlocation of a pencil atom by using the hole in the screen,we gave up all hope of determining the direction of that atom'smovement in the future. We could not determine its momentumat the same time that we determined its position.

By reducing the size of the hole in our first screen,we cause the interference pattern to spread out even moreacross our second, receiving screen. The smaller we make thehole, the more the pattern spreads. If we interpret this experiencein terms of atomic particles, we are faced with the indeterminatemeasure of the momentum of each particle. If we interpret thisexperience in terms of the wave, we are looking at "wavebending" or diffraction produced by the narrow aperture offeredto the atom waves as they passed through it. Eventually, thepattern becomes so spread out that we cannot be sure of what weare observing.

As we widen the hole again, the location of each atom

passing through it becomes more uncertain. But the compromisepays off. We observe the interference pattern "tightening up."The pattern squeezes down; the concentric rings move closer andtighter together. The wider we make the aperture, the tighter therings become. Now we are able to determine the wavelength ofthe atoms as they pass through. From de Broglie's formula, weknow the momentum p and the wavelength L are related:p = h/L. Thus, as we determine the wavelength of the atoms asthey pass through, we are also determining their momenta.

Further widening of the hole results in a complete loss ofall information regarding the location of the atom as it passesthrough the hole. We simply can no longer determine where theatom passed within the hole. But our compromise is balancedby our observation of the pattern on the screen. The wave inter-ference patterns have grown so tight that the separationsbetween concentric rings have vanished. Instead, we have a sharpshadow line image of the wide hole appearing on the screen.Each atom passes through in a straight line. The momentumof each atom is well determined. By changing the size of the holein the intermediate screen, we have altered the reality of theatom. The atom had no position going through until we measuredits position. The atom had no momentum going through untilwe measured the momentum. What we determine depends on thesize of the aperture.

Is the momentum hidden when we measure the atom'sposition? Is the atom's location hidden when we measure themomentum? Not in any ordinary sense of the meaning. Both ofthese attributes, momentum and position, are potentially presentin nature, but not actually present, until an attempt is made tomeasure these attributes. How we choose to compromise willdetermine whether the wavelength (momentum) side of realityor the particle (location) side of reality is manifested. And withan intermediate-sized hole, we have a little of both sides.

In a sense, we never actually lose information. Rather, weshape it. That is, we alter potential reality, making it actual.What is hidden in our acts of observation is still potentiallypresent. Thus, while the momentum seemed hidden, it had to bepotentially present in order to make the interference pattern. Forthe pattern could only be produced by wave interference, not byparticles colliding with each other. So even though waveknowledge was lost in the experiment, something of thatknowledge was retained. It was retained in an entirely comple-mentary picture, the picture of a wave through the de Broglierelation, p = h/L.

Heisenberg discussed this potential reality in connectionwith his Principle of Indeterminism. He called it a third orintermediate reality. He wrote:

The concept that events are not determined in a peremptorymanner, but that the possibility or "tendency" for an event to takeplace has a kind of reality —a certain intermediate layer of reality,halfway between the massive reality of matter and the intellectualreality of the idea or the image—this concept plays a decisiverole in Aristotle's philosophy. In modern quantum theory thisconcept takes on a new form; it is formulated ... as probabilityand subjected to . . . laws of nature.^

This potential reality is available for our choosing. Theexperiences we call "reality" depend upon how we go aboutmaking those choices. Every act we perform is a choice, even ifwe are unaware that we have made a choice. Our unawareness ofchoice at the level of electrons and atoms gives us the illusionof a mechanical reality. In this way, we appear to be mere victimssubject to the whims of a "higher being." We appear as victimsruled by a destiny we did not determine.

The Magician's Choice

In a world where destiny rules, no choice is possible. A humanbeing, like every other thing, living or dead, must follow alonga well-trodden, predetermined path. There is no room for willfulaction. You may feel your past actions were freely chosen, butwith a flash of hindsight, you probably see that you reallywouldn't have made any other choices. On the other hand,perhaps you look back at your past and wish you had madeother choices. Look again. You will undoubtedly find some littlereason, some plausibility, that convinced you, at the time, thatyou were making the correct choice. In other words, you behavedreasonably and logically.

Many people believe in predeterminism or destiny. When anunforeseen situation su-ises, these people are likely to say, "See,I told you so," or "It's karma," or, as I heard one afternoon in aParisian cafe, "Laugh too much at noon, cry too much atevening." On the other hand, there are probably just as manypeople who feel that they are in complete control of everything.To a child just beaten up by the neighborhood bully, they mightsay, "It was your own fault. What did you do to provoke it?"

Which view of the world is right? Fortunately, both viewsare wrong and right at the same time. We are, at once, thecreators of our reality and the victims of our creation—as weshall see in the next example.

During the mid-sixties, in addition to my regular work as atheoretical physicist, I performed professionally as a close-upmagician. And I was often struck by the fact that, like quantumphysics, all good magic is paradoxical. For example, a girl issawed in half and yet she is not. A man in the rear of the roominstantly appears in front of the room. A card that is shown tobe an ace is shown again to be a king.

One of the many secrets of magic I used regularly was called"The Magician's Choice."^ A spectator was asked to choosefrom among several objects—cards, coins, etc. The spectatorbelieved that he had a free choice, and so he was usually amazedwhen I was apparently able to see into the future, predicting hischoice even before he had made it. His degree of amazement,I suppose, depended upon his underlying belief structure—whether he believed he had free will or whether he believed hischoices in life were predestined. I'll tell you now, to break thesuspense, I never really knew what object the spectator wasgoing to choose. But I had prepared, in advance, a predictionfor each possible choice I offered to the spectator. In other words,I had all possibilities covered. In much the same way, ouruniverse is so prepared.

For a moment, think of God as a performing close-upmagicieui. Like spectators willing to be fooled and yet seekingsolutions to his or her prestidigitations, we are his ever-readyaudience, eagerly awaiting his next trick. Sometimes we thinkwe can catch the Great Magician at his act. But the magiciancalled God has all possibilities covered and has hidden a special"catch-22" that prevents us from seeing the revealed secret. Inthe following scenario, you will be able to choose reality; at thesame time, you will discover you really have no choice at all.

Imagine yourself sitting at a table in the living room of afamous close-up magician. The magician enters the room andadjusts his cape as he seats himself before you. He has a smallbag with him. He reaches into his bag and places a placemat ofgreen felt, stiffened by backing, on the table. He again reachesinto his bag and brings out a large manila envelope, which heplaces on top of the placemat. He opens the envelope and pullsout three large cards labeled A, B, and C, respectively. He laysthem in a horizontal row before you.

He says, "Here are three cards. You may choose one ofthem—card A, card B, or card C. Whatever choice you make hasalready been predicted by me and written down. I do not wish toinfluence you in any way—you are perfectly free to choosecard A, card B, or card C. I already know your choice and I willdemonstrate that fact by showing you written proof after youhave made your choice. Now choose."

Suspiciously you try to anticipate what he thinks you willthink. You might think that most people would choose card Bbecause it's in the middle. Your thoughts might run as follows:"I'll outguess him and choose card A, which is lying to the leftof card B. He could never know anyway—so really, whatdifference does it make? I'll choose A." You announce yourchoice: "I have chosen card A."

"Aha," the magician says, "I knew it! Open the envelope infront of you." He slides the envelope, the one from which heproduced the first three cards, toward you. You look in theenvelope and find a fourth card. One side of the card is blank.On the other side, written in the magician's big, bold hand-writing, are these words: "You have chosen card A." In disbelief,you examine the envelope again. It is empty.

Your mind races. "How did he do it?" you wonder. "Did heguess? Was it luck?" You look up at the magician's face. His cool,confident attitude tells you that it wasn't luck. He is verycertain, and furthermore, you have heard from others who havewitnessed the trick before that he never makes a mistake. Yet heseems human enough. It must be a trick.

At this point, a person's mind usually begins to sift throughthe memory of the past experience, attempting to eliminatesuperfluous thoughts from the essential ones in order to find acause-effect relationship that resolves the paradox. For example,you might think, "Somehow I was forced to choose Card A.It must have been a subtle force of choice. I did not have freewill, although it appeared that I did."

Not satisfied with this, you might seek further explanationfor the forced choice. "Maybe I was hypnotized. Of course, then Iwould not have had free will." Having resolved the paradox withthis solution, you might next seek an alternative cause-effectrelationship.

Your thoughts might be, "Maybe I don't have enough data.Let's see the trick again. Perhaps there are hidden variablesthat are beyond my control but are in the hands of this clevermagician. If I see it again, the whole trick will reveal itself to

me." Once again, your mind seeks to resolve the paradox byestablishing a cause-effect experience. The cause, in this case,would be hidden variables and the effect would be your choiceof card A.

You look up at the magician and say, "Let's see that again.Do it once more, will you?" *Tes," he replies, "but there is acatch." "What's the catch?" you ask. "The catch is that you mustforget that you ever saw this trick before!" "But that's no good,"you plead, "for if I can't remember what you just showed me,how will I leam how the trick is done?" And there is the rub.

If, for the moment, you could rewitness the trick withoutthe added catch, you would indeed see the answer, which is thatthe magician has hidden predictions for each choice. If you hadchosen card B instead of card A, he would have asked you tolook under the placemat on the table and there you would havefound another card attached to the underside of the placematupon which is written in the recognizable magician's hand-writing: "You have chosen card B." And a similar revelationwould have been produced had you chosen card C. He may havesimply asked you to read what he had written on the bottom ofyour chair or some other conspicuous place in the room: "Youhave chosen card C."

But the magician insists on his catch-22. So reluctantly youmust go along with it. You somehow manage to forget that youhave seen this trick before. He shows it again. This time youchoose card B. He asks you to look under the placemat on thetable. You are amazed to read the words you find written on theunderside of the placemat: "You have chosen card B." However,even though you forgot that you saw this trick before, you feela little uneasy about it. You would like to catch the magician athis game.

This trick shows us that although we spectators seemed tohave no choice at all, we had free will. Yet whatever choicewe made, we would have found that it had been predicted inadvance. To quantum physicists investigating atomicphenomena, the universe appears much like this example of"The Magician's Choice," specifically including the trickster's"catch-22" condition. When physicists make any set of observa-tions, they find that they cannot predict the outcome of theirchoices and yet these choices appear to be related in a cause-effect or predetermined manner. For example, suppose theywish to determine the location of a moving atomic particle.From its past history, which they may have observed as a trackon a film, they may suppose that its future is predetermined. But

if they set their detecting apparatus along the predeterminedpath, they will inevitably be surprised. For their last observationof the particle had so altered the particle's movement that itsnext position along the track became only probable. Like thespectator in "The Magician's Choice," physicists find that eachtime they observe the particle and choose to base its futureposition on its past position they are fooled.

In other words, we never discover God's hidden secret.Our request to see the trick again is like the physicists' continual,experimental study of nature. Each time the physicists ask, Godanswers. But the physicists are not satisfied with the answer.They are plainly disturbed with God's magic show. And theyhave every right to be disturbed, because they insist on a reasonfor such capricious behavior. After all, when they looked at thepast record of the atomic particle, its path appeared predictable.Their minds, like your own, race with thoughts of hidden,controlling factors. "What did we do wrong?" the physicists cry.But in exasperation, they are forced to give up. Their feelingsborder on despair. The more they search for the controllingfactors, the more the factors elude them. Finally, they resignthemselves—they cannot manipulate the universe; they cannotcontrol the universe; they are just victims of the universe.

The role of victims is one that we all can identify with.Victims are not responsible for what happens to them. Those"other guys" did it to them. Victims are not in control of whathappens to their lives. However, if we look closely enough at thecircumstances, a pattern of the victims' past events oftenemerges. We see that the victims, perhaps unwittingly, C£u*efully"made their own beds," so they must lie on them.

Yet victims themselves usually appear to be unconsciousof their actions. With hindsight, they lament their past choices:"If only we could have seen then what we see now." Perhaps thatlament is familiar to you. It certainly is familiar to me. Butthat is just the point. We never could have seen then what we seenow. Our past actions, like the atomic particle's track or themagician's trick, only seem predictable when we look backupon them.

Why can't we see ahead? Why does the world appearpredictable when seen through hindsight? The answer to bothquestions is: we never can see ourselves as we are now. How oftenhave you wondered why your best friends do such seeminglystupid things? It is amazingly easy to see the other fellow'splight. All of us are quite good at being "Dear Abby" and givingadvice to the lovelorn, our friends, even statesmen, umpires, and

presidents. We all know what's wrong with the country, whyour favorite athlete is in a slump, and how to save the world.We all see the other fellow very well.

Yet when it comes to seeing ourselves, we are remarkablyinvisible. We haven't learned to see ourselves as others see us oras we see others. Whenever we observe, our part in thatobservation is seemingly minimized. Or, depending on our egostate, the opposite happens and our part in the process becomesblown out of proportion. While engaged in the act of observing,"we" separate from that which we observe. In that very act ofobservation, the objective, ''real" world appears and thesubjective observer vanishes. We know not how to observeourselves. In the next example, "The Case of the VanishingObserver," we shall look at how we observe the world, as wecontinue our inquiry into the nature of "reality."

The Case of the Vanishing Observer

Quantum physics has taught us that we, the observers of reality,are, at the same time, the participants of reality. In other words,"observation" is not a passive noun; "to observe" is not a passiveverb. However, our classical. Western upbringing has precon-ditioned us to think objectively; to see the world as preexistent.

In a pre-existent world-game, there is no room for players.Like a computer machine, which goes on endlessly doing itsthing and following preset rules, all the game can do is continue.And all we can do is watch, never touching the dials. We aresimply passive, nearly nonexistent observers of that prechosenworld-game.

Objectivity takes its toll; the cost is your awareness ofyour awareness. But objectivity is only an illusion. Consider theparadoxical cube. You chose sides and the cube appeared, butyou lost your awareness of your choosing it. In other words,when the cube appeared, you vanished. At the instant the cubeappeared, you projected the cube's appearance out of your mind.It was an act of sudden creation: "That is a cube!" That actionof choice separated you from "it." Your picture of the cube inyour mind became the real cube out there. All of this happenedvery, very quickly—the instant you "saw" the pattern as a cube.And probably just as quickly, you saw it as an abstract patternagain—or you thought of something else. Your mind was not

entirely fooled. But, if for only an instant, you created the cube"out there" as a solid, three-dimensional object.

Yet suppose you never could see the cube in its comple-mentary guise as an abstract, two-dimensional array of pointsand lines. Suppose you were preconditioned to see it as a solidform, always and forever. I believe that our view of the world isanalogous to such a preconditioned view of the cube. Seenthrough preconditioned eyes, the cube continues to jump fromone "state" to another without continuously passing through anyin-between positions. The more you see it as solid, the less youtake any responsibility for its peregrinations. It jumps wheneverit cares to jump, seemingly at random. After awhile, you mighttry to make sense of its jumpings, seek its hidden mechanism,and thereby continue to make the "matter" worse—for you are nolonger there. You have become a passive point of observation.

To understand this phenomenon, carry it another step. Lookat your hand. Feel your thumb. Each time you sense your thumb'spresence, you objectify your experience. Your thumb is a thing,a part of your body. You feel your thumb "out there." Your thumbis not you, is it? Think about other parts of your body. Each thoughtbrings a sensation to that part. And each sensation makes youvanish. You are not your sensation, are you? Each observationtakes you away from the parts of your body and brings you intoyourself more and more, until you vanish.

But you are there. All you see, hear, smell, touch and tasteis subjected to your mind's pictures of all that you imagine yousee, hear, smell, touch or taste. Reality is constructed from yourthoughts of reality.

Let us look, once again, at the reality of the atomicphysicists as they perform their thought experiment to catchpencil atoms. They see the pencil as atomic particles, tiny pointsof substance, like little ball bearings or itsy-bitsy baseballs.Reality is to them, and probably to most of us, solid. But thelittle baseballs do not behave like little baseballs—they diffractor bend and spread out like waves, producing wave patternswhen collected together and individual marks when seenseparately. If the physicists take the separated view as realityand the collected-together view as a "yet-to-be-explained part"of reality, they become victims of their own preconditionedthoughts: reality is particles of matter, and these particlesbehave in an unpredictable manner, seeming to jump aroundwithout regard to the path they apparently were following inthe past, much like human beings.

Is there another view for the physicists—indeed, for us

148 Is There an "Out There" Out There?

all? I believe there is. We need to see the complementary side. Weneed to see our role in all of this. But this is not an easy task.It is difficult to give up our preconditioning. We are activelychoosing the reality of the world each instant, and during thatsame instant, we are unaware that we are doing it. But ourbecoming aware of this simple truth can enable us to see theworld's complementary side. And once we see this complementaryside of reality, our old prejudices, like the sides of the "cube," willcrumble. The barriers that separate mind and matter willdissolve. God and human will reconcile.

In the ancient Greek schools in Ionia and Elia, the essentialessence of all things, called the "physis," from which our word"physics" is derived, led to the reconciliation of being withchanging. The next example, "Newcomb's Paradox," will bringthe cmcient conflict of a divine being versus objective reality upto our present time. The new "physis" is, however, quantum"physics." We are necessary. We are needed. All we have to do ischange our way of thinking.

IVeivcomb's Paradox

For those who have managed to accept the tenets of quantumphysics, paradox is an old friend. Many theoretical physicistsenjoy playing with and/or creating paradoxes that demonstratehow our prejudices get us into trouble. I don't really know ifWilliEim Newcomb had that in mind when he created thefollowing paradox. I do know that Dr. Newcomb is a goodtheoretical physicist.

I first met Bill Newcomb in 1961, when I chose to spend thesummer of that year at the Lawrence Livermore Laboratorywhere he was working on the problem of Project Sherwood,the peaceful control of thermonuclear fusion. My doctoral thesisdealt with this subject; consequently, I spent many afternoonstalking with Dr. Newcomb. Undoubtedly, during one of thoseafemoons, he must have presented me with this little problem.*

The solution to it, however, did not occur to me until 1977.It is this solution that I wish to share with you. It will provideperspective on how "quantum thinking" resolves the conflictbetween "free will" and "predeterminism." So let us return to theliving room of our old friend, the magician. Only this time we willshrink him and ourselves down to atomic size.

Once again, he enters the room and seats himself before you.He speaks: '*I am an enlightened Being able to witness thefuture, now. I have a gift for you. I shall make you very rich ifyou believe in my powers." He then places before you two smallsafe deposit boxes. The first is labeled "L" and the second islabeled "R." Again he speaks: "In box L, I have placed onethousand dollars; it is yours. In box R, I have placed either onemillion dollars (in large denominational bills, of course) ornothing. You have two choices. Either you choose box R alone oryou choose both boxes." At first, you're surprised. You may haveexpected to have to choose between the boxes. But then you seethat wouldn't really have made any sense. You wonder what thecatch is. The magician says, *'You must have faith in me to getthe million bucks. Remember, I can see into the future. I alreadyknow what you are going to choose. If you choose box R, I willreward your choice, £ind you will find the one million dollars inthe box. On the other hand, if you are greedy and choose bothboxes, you will find box R empty. Your reward will be thecontents of box L only."

He is very confident. Furthermore, as in the earlier trick,"The Magician's Choice," you have heard from others that hedelivers only what he promises. Yet there he sits. He is nottouching the boxes. Either the money is in there, or it's not, or. . . what?

Your thoughts may run, "This Being can really do what hesays he can. He already knows what I'll do. If so, I have no freewill. But how can he really know what I'll choose? Even I don'tknow my choice yet. If I have faith in him, I will choose box Rand get the million. But since he isn't touching the boxes,whatever is done, is done. The money is already in that box orit isn't. So it doesn't matter—I'll choose both boxes and getone million and one thousand dollars. But he knows I'll thinkthat, so he'll have seen ahead and not put the million in box R."On and on, your mind races with the paradox. Your onlyconclusion is that if you accept the Being at his word, you mustchoose R. Destiny rides again and you have no free will.

But you may think, "The Being is an ordinary being. Justfolks like everyone else. He is playing a trick on me. Whetheror not he has loaded box R, there is nothing more he can do. I'llchoose both boxes. Then if I find box R full, I win one million andone thousand dollars. If box R is empty, it would have been soeven if I had chosen R by itself, so I'll have lost nothing." Thus,if the Being is a being, we choose both. Free will is restored.What would you do?

Is There an "Out There" Out There?

The answer is choose box R if you want the million bucks.Your reward isn't caused by the Being's onmipotence or clair-voyance, however. It only appears that way to our Western,preconditioned minds. Since we are atomic size, the milliondollars is in paradox-land, where it is in the box and not in thebox at the same time. Your act of observation creates thechoices—money there or money not there, according to whicheveryou choose. It is your act of observation that resolves theparadox. Choosing both boxes creates box R empty. Choosingbox R creates it one million dollars fuller. Like the paradoxicalcube's front and back sides, your choices create the alternativepossibilities as realities.

"belvedere" by MauritsEschej^ (see detail on page152). CoTnplemerrts andparadox ot the "Co5micHouse."

Complements of the Cosmic House 151

The Principle of Complementarity: A Recap

The quantum is tiny. The world we live in depends on thepictures of that world we paint in our minds. Because of thesmallness of the quantum, these pictures seem quite consistentand continuous, logically connected to our pasts and a reason-able basis for our futures. From our classical heritage, twonaturally occurring pictures of nature have emerged. These arethe wave and particle descriptions of reality.

Physicists thus attempted to interpret all experience interms of these pictures. Their attempts met with failure. Thisfailure was due to the unforeseen and necessary disturbancecreated by the observer when he observed the atomic world.The world appeared paradoxical and discontinuous because wetried to use these pictures and ignored our own presencesin the world.

Both of these schemes—our ignorance of our presence andthe wave-particle picture—work successfully for mechanicaleveryday objects. The reason for their success with these objectsis the smallness of the quantum. But it is finite and not zero.In other words, ultimately and fundamentally we affect theuniverse. Our presence can be felt drastically on the atomic leveland hardly at all on the everyday, macroscopic level. In ourattempts to leave ourselves outside of reality and our insistenceon waves and particles as a description of reality, we are forced toregard the universe as paradoxical and dualistic, consisting ofcomplementary attributes.

Although these ideas appear reasonable and were more orless accepted by most of the physical community, they containa rather disturbing feature. Einstein was referring to this featurewhen he said, "God does not play dice with the universe."Somehow, in Einstein's mind, reality must be real. There must bean "out there" out there. The idea that whatever form realitytakes is dependent upon the whim of the observer was repugnantto Einstein. Even more repugnant was the idea that the observeris powerless to control his fate.

In an effort to disprove the Bohr interpretation and reaffirmthe continuity position, Albert Einstein and two of his associatespresented a very careful and controversial paper in 1935. Thesubject of that paper was later to be called the EPR paradox. Itsaid that quantum mechanics was not the last word on reality.However, it failed to suggest any solution for what might beadded to or substituted for quantum mechanics. It also led toa new and unsuspected connection between all material objects.

Chapter 9

The Case "^

of the MissingUniverse

Nothing is moreimportant about quantumphysics than this: it has

destroyed the concept ofthe world as "sitting outthere J^ The universe willnever afterwards he *^the same.

JOHN A. WHEELER

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The Devil's Advocate

Einstein had been defeated by Bohr's attempts to show that acontinuous mechanical picture of physical reality could not betrue because of the Heisenberg uncertainty principle. Thisprinciple simply refused to give equal status to the positionand the momentum of any object in the universe. Yet Einsteinnever really gave up. During the years following Bohr'spronouncement of the complementarity principle, whichexplained that the universe had to be composed of comple-mentary and contradictory pictures of reality, Einstein labored toshow that the quantum mechanical story was not the last word.He continued to hound Bohr with one thought experimentafter another. These thought experiments put Bohr to the test.However, Bohr successfully defended quantum mechanics, ulti-mately by referring to his own Principle of Complementarity.Einstein, although defeated, was not convinced. He felt that theproblem must lie in the theory itself. Somehow, quantummechanics was not an adequate theory; it had to be incomplete.In 1935, Einstein tried to point out what he felt was missing.This became known as the EPR Paradox.

The EPR Paradox

On May 15th of that year, a gauntlet, presented in the form of aquestion, was hurled to the ground upon which physics stood.The question appeared in the pages of a prestigious journal ofphysics. The Physical Review, in an article entitled, *'CanQuantum-mechanical Description of Physical Reality BeConsidered Complete?"^ The authors of this article were AlbertEinstein, Boris Podolsky, and Nathan Rosen (or EPR, for short).They had been working together at the famous Institute forAdvanced Study at Princeton University since Einstein's exitfrom Berlin in 1931 to escape Hitler.

Einstein was then fifty-six years old. He had the time topursue this question, though many physicists would not consider

153

154 Is There an "Out There" Out There?

it the kind of question likely to lead to new discoveries. Whetheror not it was a matter of their philosophy or even beliefs,physicists were more anxious to play with the new forms ofmathematics and new relationships that quantum mechanicsbrought to bear on physical reality. They had little time forsuch questions as Einstein, Podolsky, and Rosen were to present.The EPR paper was nearly ignored.

The paper simply presented an argument—one that, to thisday, has not been successfully resolved. It began with a simpletest for the reality of any object. That test was given in the formof a condition. Physics is loaded with conditions. There are twokinds: sufficient conditions and necessary conditions.A necessary condition is one that must be fulfilled in order for asecond condition to be met. Children are notorious for givingnecessary conditions to their mothers. "I won't go to bed unlessyou read me a story" is one example of a necessary condition.The child's mother may offer the child all sorts of goodies to gethim to go to bed, and yet he refuses until he gets the story.

A sufficient condition is weaker in its demand. It is aminimal condition. For example, although it is not necessary toeat filet mignon to relieve one's hunger, it is sufficient to do so.The EPR Paradox began with this sufficient condition for thereality of any physical quantity: '*A sufficient condition for thereality of a physical quantity is the possibility of predicting itwith certainty, without disturbing [it]. "^ EPR were concernedwith the probabilistic meaning given to real objects throughquantum mechanics. Specifically, they were concerned with theposition and the momentum of an object. Of course, predictingthe value of a physical quantity with certainty is no problemwhen we are dealing with large objects. We can predict, with totalcertainty, that a coin lying face up on the table will continue tolie there, providing we don't disturb it. Our ability to predictthis, therefore, is a sufficient condition for the reality of the coinshowing heads up.

However, it may not be a necessary condition. If we toss thecoin into the air, we are no longer able to predict with certaintythat it has a face—even though we are no longer disturbing thecoin after we have tossed it into the air. Nevertheless, the coinstill has two sides. It is real, despite our inability to predict thatit has a face as a real attribute of its being a coin.

Classical, everyday objects do not exhibit the bizarreelements of quantum mechanics because of the smallness ofPlanck's constant h. The sufficient condition of reality is clearlynot a necessary one for classical things. But the same may not betrue for the quantum world of objects.

155

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The position and the momentum of any object appear to bereal quantities. Both can be predicted with practical certainty forany classical-sized, macroscopic object. But in the case of atomsand electrons, the uncertainty principle denies reality to bothof these quantities. It is impossible to determine the momentumof an object with absolute certainty if the position of thatobject is determined with absolute certainty. Thus we canconclude, from the EPR condition of sufficiency, that one ofthese two quantities must not be physically real. Which one is tobe denied reedity depends on our choice. When we measure one ofthe two quantities, the other is denied existence.

Even Bohr would agree with this. But Einstein was workingtoward a clever conclusion, one that would show that quantummechanics, if accepted as the last word on reality, leads to acontradiction. Einstein and his friends would use quantummechanics to prove that it is possible to predict either theposition or the momentum of an object without disturbing theobject. In other words, after the object leaves all physicalinfluence that the observer is capable of exerting on that object,either of its two physical attributes can be predicted withcertainty. But the choice depends on the observer, not the object.According to EPR, the object must have had both quantitiesbefore the prediction is made. All the observer does is choosewhich quantity to predict.

Yet EPR would agree that it is not possible to predict bothposition and momentum at the same time. To do so would violatethe uncertainty principle. The EPR argument did not attemptto go that far.

Is There an "Out There" Out There?

The reason for this rather paradoxical situation has to dowith the way in which the observer makes his prediction: hemakes his prediction not by disturbing the object itself, but bydisturbing another object that had a previous encounter withthe first object. The observer learns about the first object byobserving the second object because of something physicists calla correlation between the two objects that have interacted.

For example, take the game of billiards or pocket pool. Whenshooting one ball at another, it is possible to predict the behaviorof the second ball by observing the first one only. Since theseobjects are large or ''classical" size, it is possible to measure theposition and momentum of a ball simultaneously with verygood accuracy. By carefully measuring the position and themomentum of the first ball, both before and after its collisionwith the second ball, both the position and the momentum of thesecond ball can be determined. Once the two balls have collided,they are correlated. In other words, what happens to each of theballs depends on what happened in their past interaction. So ifwe observe one of the balls, we will find we can predict what wewill observe for the other ball.

After the balls have clearly separated from each other,nothing we might care to do to one of them will affect or changethe other. We take this as self-evident, for that's what we meanwhen we say the balls have separated from each other. Thecorrelation that exists between the balls is solely a result oftheir past interaction and cannot be changed by anything we doin the present.

A classical picture of a correlation between two particles-The.observer observes one pcirticle to predict the position andmonnentum otthe other particle.

■Tin

157

The correlation I have described as existing between thetwo balls is a classical mechanical or Newtonian connection. Itarises from Newton's laws of motion. Consequently, it is anindication of the completeness of those laws in dealing with thereality of the collision. If Newton's laws were incomplete indescribing classical mechanics, we could not determine thereality of the ball we did not observe. Yet we know of this ball'spresence because of Newton's second law. After moving withconstant velocity, the first ball underwent an unexpectedacceleration. According to the second law of motion, that meansit had an additional force acting on it, a force produced by thesecond ball. Following Newton's third law—known as the actionand reaction law—we can predict the movement of the secondball by our observation of the first ball. The second ball'sreaction was equal to the first ball's action.

But quantum mechanics is another thing entirely. According

A quantum picture of a correlation between two particles-The observer observes the position of one particle to predict theposition ot a second particle-or he observes the waveier>gth of oneparticle to predict the wovaiervgth of the second par tide. He cannotdo both.

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158 Is There an "Out There" Out There?

to its laws, we cannot know both the position and the momentumof either billiard ball with absolute certainty. Yet the theory isconsidered to be a complete description of that unfortunatesituation. If it is a complete theory of reality, there should be noway to predict both of these quantities without disturbing theobject that possessed them. In other words, there should be noway that the unobserved and therefore unaffected second ballcould have both a position and a momentum unless we actuallyobserve that second ball directly. No observation carried outupon the first ball can, by the condition of the two balls beingseparated from each other, disturb the "reality" of the secondball. Therefore, the second ball's physical attributes—position,momentum, or any compromise between these two—cannot andshould not be determined by any observation performed on thefirst ball. Under no circumstances should the second ball haveboth position and momentum at the same time.

EPR found a way that the second ball would have bothposition and momentum at the same time and yet still beunpredictable. Thus they concluded that quantum mechanicaltheory must be incomplete because it gives these physicalattributes to an object but cannot predict the behavior of theobject.

To understand how quantum mechanics could produce sucha paradoxical situation, EPR devised a clever way to correlatetwo objects: they constructed a wave function that determineda connection between the two objects. This wave function,although not in violation of the uncertainty principle, appearedsomewhat mysterious. Within it, two types of information werecontained. It enabled an observer to determine with certainty therelative distance between the objects and, at the same time, thesum of their momenta.

To understand this physical situation, imagine a beam ofelectrons interacting with a screen containing two parallel slitsthat are some distance apart. Imagine that the electron beam isbeing shined, like a flashlight beam, upon the screen. Picture thescreen as having two long, narrow, horizontal slits, like the slitsin a Venetian blind. Although these slits are extremely narrow,their separation is known. In other words, any two particlespassing through the slits will have, at the moment of passing,a clear, relative separation. Now, keep in mind also that it isperfectly possible to measure the momentum of the screen, bothbefore and after the two particles in the beam pass through it.The narrowness of the slits prevents us from predicting themomentum of either electron. However, by measuring the change

159

in the momentum of the screen, we can determine the totalmomentum given to the pair of electrons at the instant theypassed through the screen.

To recap: EPR had constructed a wave function thatcontained two kinds of information, the total momenta of anypair of electrons that passed through the double-slitted screenand the relative separation between the pair as they passed.Thus, according to quantum physics, both of these physicalquantities were real; they were capable of being measuredsimultaneously. But the location of either electron and themomentum of either electron were still undetermined. Thelocation of a single particle passing through was undeterminedbecause the exact location of the slit was unknown at the time ofpassing. The momentum of just a single particle was unknownbecause the recoil of the double-slitted screen was caused by thepair of particles acting simultaneously. According to quantummechanics, this meant that neither the position nor momentumof a single partner within any pair of particles wasphysically real.

Reality had been denied to these physical attributes becauseof the special way that EPR constructed their wave function.Thus we know something about the particles as a pair, butnothing about them individually. It is like knowing a marriedcouple very well, but never meeting with either partner indi-vidually to learn how each partner feels about the world.

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Is There an "Out There" Out There?

In this manner, the EPR argument found the two particles tobe correlated. But this was no ordinary, classical mechanicalcorrelation. For suppose that after the two electrons are wellseparated, an observer measures the location of one of them.From the observer's earlier knowledge of the relative distancebetween the two electrons, he can state with absolute certaintythe physical location of the second, unobserved electron. Thusthe second electron has the attribute of position because it ispossible to predict the second particle's position withoutdisturbing it.

But, hold on. The same argument works for the secondelectron's momentum. By measuring the first particle'smomentum, the second particle's momentum is instantly known,because the earlier measurement of the screen's recoildetermined the sum of the momenta of both electrons.If a H- 6 = 10 and you know that 6 = 3, it is not hard for youto determine that a = 1. Thus, according to the EPR criterionof sufficiency, the second particle's momentum is also physicallyreal because we can predict it without disturbing it.

To make an analogy, suppose that as you stand in linewaiting to buy a theater ticket, two identical thieves race pastyou and grab ten dollars from your outstretched hand. You don'tquite notice which of the two thieves takes the money or ifperhaps both thieves together take it. You do note that they areidentically dressed, but you don't remember what they arewearing.

Later the thieves are caught. They are held in separate

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161

jails, however. Now comes the bizarre part. You go to one jailand you ask the thief to return your money. He gives you $4.00.You tell the jailer at the other jail to ask the second thief foryour money, and he retrieves the missing $6.00. You then askfor a physical description of the unseen prisoner and discoverthat the second prisoner is no longer dressed identically to thefirst. When the prisoner is questioned further, it turns out that he"lost" some clothes or exchanged them along the way.

So far, this is all plausible. But later a crime spree hits thecity. Every person who attended a social event where a $10.00fee was charged was ripped off by a pair of identically dressedthieves. Fortunately, the thieves were all apprehended. But theresults of the catch were a little unusual. Some people got theirmoney back. Others didn't. And some got more money returnedto them than they had lost. In every case where the money wasnot returned in the exact amount of $10.00, the thieves werediscovered to be identically dressed. When the thieves werequestioned about what had happened to the money, their answerswere fuzzy.

On the other hand, in every case where the amount returnedwas exactly $10.00, the thieves were never identically dressed. Infact, it wasn't even clear the two were working as a team. Yetthey always "coughed up" exactly $10.00, even though onethief might have only $1.00 while the other would have $9.00. Inother words, the sum of the amounts contained in both thieves'pockets was exactly $10.00—providing they were not identicallydressed. The amount was never $10.00 in the other cases. But in

The particles are given the same momentum by thewall, but are not the fixed distance L apart.

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162 Is There an "Out There" Out There?

these other cases, each pair of thieves was easy to identifybecause the two thieves dressed identically. No two pairs lookedexactly alike, however.

In this analogy, the identical clothing of the two thievescorresponds to the position measurement of the pair of electrons.The amount of money contained in the thieves' pocketscorresponds to the total momentum given to the two electrons.The example shows a correlation between the thieves. If youcaught them and observed their dress first and did not ask fortheir money, you would find that the thieves were always identi-cally dressed. However, if you demanded money first, you wouldget exactly $10.00 from every pair of thieves you caught, but youwould never find that those thieves who gave you the money firstwere identically dressed. Therefore, the correlation was eitherthat every pair had $10.00 when money was demanded first orevery pair was identically dressed if their clothing was observedfirst. What you observed about the thieves depended on the orderin which you observed their attributes—whether money or dress.

What should we conclude from our analogy? Does the secondelectron really have both a position and a momentum at the sametime? If the answer is yes, then it is obvious we cannot predictboth attributes simultaneously using quantum mechanicsas our theory.

Even more bizarre, suppose that quantum mechanics is acomplete theory. Then the reality of the second electron, by whichI mean its possession of the necessary attributes of position andmomentum, would depend on our choice of measurementperformed upon the first particle. This is extremely odd becausethe two particles need not be anywhere near one another to affecteach other.

Thus EPR attempted to deny quantum mechanics its rulingauthority over reality. The completeness of quantum theorywould mean that objects that had previously interacted couldstill affect each other after they were well separated. Thispossibility was a fly in the ointment of Einstein's special theoryof relativity. Indeed, this objection of EPR later became thecondition of "Einstein separability."

To grasp the seriousness of accepting the completeness ofquantum theory as described by EPR, we shall next considerhow quantum theory could overthrow Einstein's theory of specialrelativity. However, in overthrowing special relativity, we arenot just abandoning another theory. We are abandoning thenecessary basis of any logical and causal understanding ofphysical reality. This is serious business, indeed.

The Case of the Missing Universe

163

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It^s all a dream.Light passing byon a screen.

THE MOODY BLUES

Things That Go Bump m the Mght

The speed of light plays a very special role in modern physics.It is the upper boundary, the highest speed in the universeknown today. All of matter, light, and electromagnetic radiationcan be said to be incarcerated at speeds never exceedinglightspeed.

If, for example, I increase a ball's energy by whacking itwith my first every time it flies by me (like a tether ball on apole), the ball will show an increase in speed. It takes energy tospeed up any object. In the case of ordinary tether balls,baseballs, and even rifle bullets, the energy goes into increasedspeed always, provided that the object is not moving at speedsnear to lightspeed. For if it moves that fast, something strangebegins to take place: the object no longer continues to increaseits speed when given more energy. Instead, it increases its mass!As Einstein put it, "Velocities greater than that of light have . . .no possibility of existence,"^ because it already takes an infiniteamount of energy to accelerate any body to the speed of light.

But what if there were particles that had speeds greaterthan that of light?^ Then these particles would not need to beaccelerated from subluminal to superluminal speed; they wouldsimply exist buzzing around at hyperlight velocity. Physicistshave long been fascinated with these kinds of particles.^ Theyare called tachyons from the Greek word tachy, which means fast.The words tachometer (an instrument used to determine speed)and tachycardia (excessively rapid heartbeat) are also derivedfrom this Greek root word.

Tachyons, if they existed, would turn our world of cause andeffect topsy-turvy. This fact has to do with the Einstein Theoryof Relativity. Let's look at a simple example. Suppose that a rifleis fired at a target. It is obvious that the bullet had to leave therifle and arrive at the target afterwards. But suppose youhappened to be flying by on a supersonic jet at the instant therifle is firing. Your speed would nearly match the speed of thebullet. In fact, you could almost fly side by side with the bulletand watch it from your jet cabin's window. From your vantagepoint, the bullet would seem almost to be standing still. Ofcourse, the target is racing up to it helter-skelter. Is it possible

165

that you could fly by so fast that the bullet would not only stopoutside your window, but would move backwards?

If you are a movie-goer, you have seen that effect manytimes. Just remember the old wagonwheel scenes in any "oldiebut goodie" western. The wheels appear to move backwards,particularly if the wagon is going slowly. That's because thespeed of the film's advance through the projector is greater thanthe speed of the rotating wheels. But still, the wagon is goingforward. Thus it appears that no matter how fast we might flyby, the rifle bullet would continue to advance toward the target—even though, from our speeded vantage point, it might appear tobe traveling backwards.

Relativity theory confirms this apparently obvious obser-vation. But something weird would begin to take place if thebullet could be fired with a speed greater than the speed of light.Suppose the bullet happened to be moving at twice the speed oflight, for example. We would notice nothing unusual about thefiring if we were flying by with any speed less than halflight speed. But the instant we reached half light speed, we wouldwitness the rifle firing and the bullet hitting the target at thesame time! Even weirder, as soon as we were flying by at speedsgreater than half light speed, we would see the whole scene as ifit were a film running backwards; the target would explode,sending the bullet and all of its gases back toward the rifle wherethey would neatly pack themselves into the narrow rifle barreland travel up that small, bored cyclinder until all contents hadrepacked themselves into an undischarged round.

Since relativity successfully predicts the results of obser-vations, we have come to trust it. Thus we would conclude thattachyons cannot exist because of the above example. Thisexample illustrates what we would call a causality violation: thecause comes after the effect.'*

Causality violations are serious crimes in an orderly andlawful universe. Speeding faster than light will always beobserved by some observers as a violation of causality. They willsee events along the trail of the speeding object happening in areverse order. Of course, not every observer will be faced withthis "monkey business." If we all were to observe the sameviolation of causality, we wouldn't think anything of it. We wouldsimply say that the effect was the cause and the cause was theeffect. Running movies backwards makes sense if we never runthem forwards.

But not all of us will see the same thing. The world will seembizarre when it is witnessed by observers who happen to be

167

0^h

A causality violation: A contradiction of facts causedby a tachyon.

moving at any fraction of lightspeed, even at 670 miles per hour,which is only one-millionth the speed of light. For example, if awestbound tachyon were to fly by with a speed of just over amillion times lightspeed, leaving a trail behind it as it flew,observers on the earth would see it heading into the sun. Butpeople in an airplane flying by at 670 m.p.h. would see thetachyon heading eastward away from the sun. Shades of flyingsaucers!

What would the truth be? Where did the tachyon originate?In the east or in the west? With causality violations, truth woulddissolve into a hodge-podge of superstitions. Undoubtedly,Einstein must have felt this instinctively, although he neveractually considered tachyons a reality.

He didn't have to. His theory of special relativity rid scienceof such bizarre objects. All is quite well with causality for objectsthat move at less than the speed of light. For in those cases, noone could ever observe a violation of causality. Things flyingeastward always fly eastward.

But quantum mechanics, as exhibited by the EPR argument,would allow an observation of a physical quantity of one of a pairof previously correlated particles to "create" a similar appearanceof that quantity in the other particle. This sudden appearanceof a physical quantity in the second object would be caused bythe measurement of the similar quantity in the first particle.Since the second particle could not already possess the valuegiven to it by the measurement performed on the first particle,the reality of the second particle must depend on the measuredreality of the first.

That means that "something" had to go from the location ofthe measurement of the first particle to the site of the second.And that "something" was no slowpoke either. There was nothingcontained within quantum mechanics to slow it down, whatever itwas. In fact, quantum mechanics would imply that this"something" was perfectly able to move at lightspeed or evenfaster. However, it was not light that was moving. Light could beexplained and contained within the theory. This "something" wasbeyond such explanation.

The two objects previously correlated could be lightyearsapart. They could be on separate galaxies. Yet as soon as anobservation was performed on one of these objects, the secondwould immediately assume a similar value for whatever wasobserved for the first.

By attempting to dispute quantum mechanics, EPR hadbrought out into the open another of its bizarre features: thesurprising connection between objects that had had a previouscontact. Quantum mechanics indicated that this past contactallowed the objects to be correlated in this special way, eventhough they may have long since been out of any physicalcontact with each other. They were, so to speak, "causality time-bombs," liable to go off at any instant for no apparent reason.To set one off, furthermore, had to be an irresponsible act. Therewas no way to even know that you had done so if the objects wereout of physical contact with each other. All you did was observesomething. If that something was "quantum connected" toanother object, the second object would "feel" the effect of yourobservation. It was like the fabled story of the "CorsicanBrothers," who when separated from each other knew of each

other's love affairs because they had once been Siamese twins.

Although Einstein might have objected, I have called this"quantum connection" between any two past-correlated particlesthe "Einstein connection." Remember that Einstein wasattempting in the EPR argument to disconnect such a connectionby pointing to its unreasonableness. He gets the "honor" becausehe was the first to point out that quantum mechanics could evenproduce such an awkward connection. Yet the fact that anobservation of A could produce a result at B when A and B werelightyears apart is not the main consideration.

The problem with the Einstein connection is that A and Bcould be simultaneous occurrences. Following our previousventure into the tachyonic world of relativity, that would meanthat for some observers who were watching A and B from adifferent vantage point, A could be the cause of B. However, theorder of the events could also be observed in reverse. Someobservers would be able to see B as the cause of A. Simultsineousevents happening in different locations can be observed bymoving observers in opposite time orders. Thus such eventscould not be causally connected. At least not in any ordinarysense of causality.

But quantum mechanics must contain, if it is a completetheory of reality, an extraordinary connection between observersof events. It wasn't even necessary to have two objects to exhibitthis connection. The connection I am referring to dealt with therelationship between all observations occurring simultaneously.This was called synchronistic observations.

According to quantum mechanics, it would be possible tosee that a relationship extended out into space, covering a widerange of possible sites for the observation of an event. But inorder to talk about this synchronistic connection, we will need alanguage, a picture of terms.

QwiffS; Floirs; and Pops

It is difficult to provide a language for this quantumsynchronistic connection. We are still faced with the waves andparticles of our classical experience. Nevertheless, I feel that theattempt will be useful. Let us begin with the idea of a quantumwave function, the kind first described by de Broglie and laterrefined by Schroedinger.

170 Is There an "Out There" Out There?

Though any picture is nearly impossible to imagine, let ustry to imagine a quantum wave function. I shall call the quantumwave function a "qwiff." Think of a qwiff as spreadingthroughout space like ripples on the surface of a pond. I will alsocall the act of observation a qwiff "pop." Thus qwiffs "flow" andqwiffs "pop." Qwiffs flow like moving, undulating waves ofwater. Qwiffs pop like bubbles in a stream. But I want the readerto imagine that a qwiff pop is a destruction of a qwiff flow. Inother words, when the qwiff pops, the qwiff itself vanishes. Whena correlation exists between two particles, it is like a qwiff rubberband stretched between them. The observation of one of theparticles pops the qwiff and instantly affects the other. Althoughthe picture I have painted is a mechanical one, it is not a simpleaction-and-reacton picture. The qwiff is a quantum wave functionthat at best can only describe the probability of the observationand not the actual observation. It is not a real "thing," but itmay be helpful to picture it as a real thing.

The next point that will be helpful in attempting to under-stand synchronistic connections is to realize that qwiff flows aredetermined by a mathematical continuous description. Thisdescription is provided by Schroedinger's equation. SinceSchroedinger's equation describes how the qwiff flows, itdescribes how the qwiff changes in a continuous manner. We arein the curious situation of knowing with certainty how theprobability of things changes.

But Schroedinger's equation cannot tell us what we actuallyobserve. It cannot tell us where or when a qwiff pop will occur.There is no continuous mathematical way of describing a qwiffpop. Each pop is a sudden disruption, a break with the past, aviolation of the law of cause and effect. Let us consider a simpleexample: the quantum mechanics of the nursery rhyme thatbegins, "Starlight, star bright/First star I see tonight. . . ."

The unseen qwiff, in an endless pattern of waves, flows inspacetime in a perfectly logical manner. For example, the qwiffdescribing a photon emitted by a star four lightyears from earthhas a very simple pattern of movement. This pattern takes theform of a spherical wave, endless wave ripples pulsing outwardfrom the center like the layers of an onion. A two-dimensionalversion of this is created whenever you drop a stone into astill pond.

An observer. A, on the earth could be, for example, thinkingabout the possibility of a star existing at some point in space.Imagine that the star is undiscovered and is crying for help.

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seeking to be found. It sends out a single photon qwiff thatspreads throughout all of space. Each point on its wave surface isa possible discovery point. But there is no intelligence in theuniverse to know that. So the wave surface grows, expandingfurther but getting weaker as it goes.Perhaps if it expandsfurther, like a balloon blowing up, it will find intelligence.

Suddenly on earth, something pops in the "mind" of ourthinking observer. In a flash, faster than light, the observer"sees" the light of the star. And at that instant, the qwiff ischanged drastically like a pricked balloon. The photon is said tohave arrived. Intelligence has occurred on the scene. Knowledgehas occurred on the scene. Knowledge has been edtered. The single

Owiff5, flows, and pops: Imagining the unimaginable.Wesee a young persons mind and the universe is qwift-filled.

Is There an "Out There" Out There?

photon qwiff, which had been spread over a four-lightyear radiussphere, has collapsed to a single atomic event at the retina of theobserver. That event—the collapse of the wave function from aneight-lightyear diameter sphere to a single point on the retina ofthe beholder—is an alteration affecting the whole universe forone single instant.

Meanwhile, another observer, B, may have also been seekingthat star's light. Suppose that observer B was waiting for theflash on another planet that also happened to be four lightyearsfrom the star, but on the opposite side from observer A. B wouldmiss the show because A popped the qwiff. When A saw thelight, he altered the probability throughout all space.

But just before A's discovery, both A and B had equalchances to discover the star. In that world inhabited by qwiffs,the photon was potentially in both places—near A and near B at

He has just popped the q\A/ifP.

the same time. Indeed, it was potentially and simultaneouslyat every point on that qwiff sphere. Then A saw the light.

That not only changed A's reality, it also changed B'sreality and just as quickly. It is tempting to say that A actedas the cause and B became the effect in this change. But we mustnot be hasty. We could just as logically say that B'snonobservance of the photon caused A's event to occur. Why?Because at the instant that B knew there was no photon, he alsoinstantly altered the probability from a possibility to nothing.Thus B, as well as A, was responsible for collapsing the qwiff.

The instantaneous qwiff pop does not seem to obey the usuallaws of cause and effect. Because of the instantaneousness of theA and B events, we cannot say who controls whom or whatcontrols what. It's as if minds were eager, hungry children, allout there and waiting to gobble up the first qwiff that passes by.

We see the result: A star's photon has landed on his retina.

174 Is There an "Out There" Out There?

The problem is that the first gobbler leaves nothing for the rest—or else, by his act of not knowing, he creates a feast of knowledgefor another.

In my wild imagination, I picture God in the center of thewhole universe preparing quantum feasts of knowledge, all kindsof magical and tasteful future goodies in the form of magnificentqwiffs. The qwiffs spread throughout the universe faster thanlight, traveling both backwards and forwards in time. And Godcries out, like a good Jewish mother, "Eat, eat, my children.These are wondrous gourmet things, real pearls." But, alas, weare an audience quite fearful of what could be. We watch thesplendor and we moan. We are afraid to laugh at the Great One'sjokes. We are afraid to feast on the new food, for fear ofindigestion.

Even worse, God's qwiffs are popped by any intelligence, nomatter how crude or primitive. Thus great pearls of wisdom arebeing gobbled up by deranged minds and turned into weirdrealities like bad Nazi war movies, starvation of countlesssufferers, and insensitive, unfeeling people. God's timeless jokesare retold again and again as parables, Bible stories, and mysticalinsights. But, alas, they are all hopelessly distorted byinept minds.

Yet not all minds are inept. Science steps in. And then comePlanck and Einstein and all of the rest throughout history pastand history yet to be. An order is perceived. But who is creatingthat order?

Thus, from a certain and perhaps cosmic viewpoint, there isa connection between the two observers, A and B. They maynever know it, however. Before the observations made by A andB, the qwiff was an unbroken whole spread over a vast range ofspace. Before the observation of that single photon by A, therewas no objective separation between A and B. That separationarose when the photon was observed.

Of course, an instant later, another photon qwiff would reachthe two observers. And again, A might see the light. But theqwiff favors neither A nor B. For it is equally likely that B willsee this photon. And if he does see it, he will alter A's reality forjust an instant. Then comes the third photon, and the fourth, andso on. Each photon qwiff is altered from nearly opposite sides ofthe vast spatial universe. In that continual series of observations,the vast distance of space is perceived by both A and B.

By observing the universe, each observer is disturbing theunbroken wholeness of that universe. By observing, each

Faster Than a Speeding Photon

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observer is separating himself or herself from the rest of creation.By observing, the observer is gaining knowledge, but also payinga price. He is becoming more and more alone and isolated.Perhaps this is what is meant by the tree of knowledge in theGarden of Eden. The first bite of the apple is sweet, but costly.Our eyes are opened and we see we are alone.

God creates oJl qwlff tlows,and you create all qwiff pops.SfX VW>i;^^ '^^L^^V ^<4'

Chapter 11

Breakingthe Unbrokenmiole

"To he or not to he""is not the question;it is the answer.

FRED ALAN WOLF

when Tiro Become One

My first real exposure to quantum mechanics came in 1958.I was then a graduate student at the University of California atLos Angeles, pursuing an advanced degree in physics. One of thetextbooks required for our course in quantum mechanics wasDavid Bohm's Quantum Theory.^ It is an unusual college physicstextbook. As you may have discovered, physics textbooks arenormally quite dry and loaded with seemingly undecipherableformulae apparently created by machines rather than people.

Bohm's book was an exception. It had more words thanformulae. It dealt with questions concerning topics that wereapparenty unrelated to physics. "The Indivisible Unity of theWorld," "The Need for a Nonmechanical Description" of nature,"The Uncertainty Principle and Certain Aspects of Our ThoughtProcesses," and "The Paradox of Einstein, Rosen, and Podolsky"were some of the topics that Bohm considered and that were tohave a great influence on my own thinking.

In 1973, I had the opportunity to spend two years as avisiting research fellow with the Department of Physics, Birk-beck College, University of London. During those years, 1973through 1975, I had several discussions with Professor Bohm,who was head of the theoretical physics branch at Birkbeck.

Bohm referred to the synchronistic, causality violatingquantum connection, as "nonlocality." In a paper developed laterwith Basil Hiley at Birkbeck, he wrote:

The essential new quality implied by the quantum theory is non-locality; i.e. that a system cannot be analyzed into parts whosebasic properties do not depend on the . . . whole system. . . . Thisleads to the radically new notion of unbroken wholeness of theentire universe.^

Quantum mechanics stimulates such thoughts. Physicistshave come to realize that the mechanical picture of the universecannot be the whole picture. But the problem still appears to be,"How can we understand the world?" If elements of reality, suchas the location of an object or its path through space and time,are subject to disappearing according to one's choice of obser-vation, we are not left with much. The basis of a reality upon thematerial world is fraught with such paradoxical behavior.

177

178 Is There an "Out There" Out There?

Even what we mean by "space" and "time" must be recon-sidered. Unbroken wholeness means just what it meant to theancient Greeks. You cannot analyze it. You cannot take it apart.For if you do, what you end up with is not contained within theoriginal whole. It is created by the act of analysis. If the wholeuniverse is this way, then the very experience of space and timemust also be continuously created by observational acts.

If we could somehow reach out into the whole withoutbreaking it, what would we find out there? Could we send andreceive signals? Even the concept of a signal deeply involves oneof our most sacred prejudices: the prejudice of space. Bohm andHiley comment:

First of all, we point out that in the theory of relativity, the conceptof a signal plays a basic role in determining what is meant byseparability of different regions of space. In general, if two suchregions, A and B, are separate, it is supposed that they can beconnected by signals. Vice-versa, if there is no clear separation of Aand B, a signal connecting them could have little or no meaning. Sothe possibility of signal implies separation, and separation impliesthe possibility of connection by a signal.^

If the whole universe is one, nonseparable entity, signals wouldmake little sense. To the extent that quantum mechanicsprovides instantaneous communication between all spatial pointson a qwiffian surface, these points cannot be said to be separated.They are all only one point!

To the extent that they can be said to be separated points inspace (and time), signals may be passed between them. Thus ourtwo observers, A and B, from our previous example are bothseparated (they can signal each other by ordinary, slower-than-light means) and not separated (A's observation instantly affectsB's reality as well as A's reality).

It is perhaps difficult to understand how two very differentregions of space can be both separated and unseparated at thesame time. To imagine this situation more clearly, let us returnto the example of "The Paradoxical Cube." As you will remember,the illustration could be seen in two complementary ways: as acube with jumping sides or as an abstract pattern of linesand points.

Suppose now that we have two such cubes in space. Supposethat they are completely independent of each other. Supposethat two observers come along and each observes his or herseparate cube. There is no apparent connection between eitherthe cubes or the observers, so the order of observations willappear completely random when they are compared. For example,

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the first observer might initially see her cube with the lower sidein front. A little later she will see the upper face in front. Andperhaps later she will see it as a pattern of lines and points.Suppose her observations are coded so that U stands for a cubewith the upper face in front, L for a cube with the lower face infront, and P for a pattern with no face at all. This individual'sobservational order over time might be:PPLLULUUUUPULULU.

The second observer would also observe his "cube" in arandom order of P's, L's, and U's. For example,UPPULPULPPPLUUPU. By comparing the two orders ofPUL's, we can determine if there is any correlation, anysimilarity between them. Of course in this case, since we cannotcontrol the observers' choices or when a particular face of thecube will appear in front, there will be no "overlap" in the ordersof observations by the two individuals. Of course there will besome coincidences, but there will be no obvious order to them.

CM'

•

Is There an "Out There" Out There?

But now let us suppose that the two cubes had a past inter-action and thus became correlated. We now have a situationsimilar to the EPR paradox. In fact, Bohm used a similarcorrelation between two spinning particles to explain thecorrelation.'* The observed directions of the spins of the particleswere found to be correlated. Now suppose that the two previouslyinteracted cubes are observed. Again, there is no way to controlthe choices of the observers. Each observer is free to choose toview his or her cube as a cube or as a pattern of points and lines.

Correlated quantum cubes

y^^ /■";:}.. of

However, if both observers just happen to choose to view thecubes as cubes, a similarity in the order of their observations isapparent. For example, suppose that the first observer sees theorder, ULLULLULLUPPLLUULLUULLUUP. The secondobserver will also observe, ULLULLULLUPPLLUU-LLUULLUUP. In other words, both will see the cube in exactlythe same way. Yet neither will feel that the other controls hisor her ability to choose among the U's, L's, and P's.

The order observed by each observer is random: it appearsat the whim of the observer. Neither observer, for example, can"force" an L view of the cube. Yet when the observational ordersare compared, the number of coincidences is overwhelming. It isas if each observer were seeing the same thing. The two observersexist as if they had only one mind and that one mind wasobserving only one cube.

Yet there are two cubes and two separated minds. Their"oneness" appeared only after they compared notes and observedeach other's order of observations.

I Am This Whole Univerae

This "quantum link" between all things could provide a betterunderstanding of how humans come to understand anything atall. Any two points in space and time are both separate and notseparate. Einstein's speed of light sets a clear upper boundary onthe separability of places and times.When points are connectedby signals traveling at speeds slower than the speed of light, thepoints are separate. When they reach the speed of light, signalsbegin to lose meaning. In fact, Einstein's theory predicts thatneither space nor time "appears" for a particle of light. Thiscounter-intuitive conclusion comes directly from Einstein'sspecial theory of relativity. It is due to the observed fact thatthe speed of light is a constant. Any observer watching lightas it moves from a source to a receiver would measure the light'sspeed to be the same. This is true even if the observer is movingrelative to the source and/or receiver, and no matter how fastthe observer travels.

If the speed of light is in fact fixed, the measures of spaceand time we normally think of as fixed are not. Space and timeare relative. This means that any given interval of time, nomatter how set and "frozen" it reasonably appears, can beobserved to be longer or shorter in time by another observer.

Any length or distance suffers an equal embarrassment ofnonrigidity.

Accordingly, moving clocks tick slower and moving rodsshrink. The faster an object moves in relation to the observer, theslower its clock runs and the shorter it becomes. The limit to allthis relativity is the speed of light. A photon's clock, if it had aclock, would be so slowed down that no time at all would pass.The distance it would observe traveling from one point to anotherwould be zero distance. Both points would appear to be the samepoint "now" for the photon of light.

Beyond lightspeed, an object or a consciousness would becompletely free of the shackles of space and time. It could"drop in" at any time, past or future. It could visit anywhere atan instant. All points in the universe would be its home.Quantum mechanics was indicating a meaning for this poeticthought. The universe is not just a collection of separate points.It is what it is according to the observer and what he or she does.By identifying with the "quantum wholeness" of the world, theobserver "becomes" the observed. He is what he sees.

Shortly edter the appearance of the EPR paper, ErwinSchroedinger became deeply concerned with the kind of realitybeing portrayed by quantum mechanics. He had already givenmuch thought to such philosophical considerations.

Remember that Schroedinger was reported to have exclaimedto Niels Bohr: "If one has to stick to this danmed quantumjumping, then I regret having ever been involved in this thing. "^To which Bohr replied: "But we others are very grateful to youthat you were, since your work did so much to promote thistheory."® Later Schroedinger would write "What Is Life?" in anattempt to reconcile quantum physics and biology.'^ In his twolong essays, "My View of the World,"® he revealed himself as amystic much influenced by Eastern views. In his first essay,which he wrote in 1925 before he created his equation, he stated:

This life of yours which you are living is not merely a piece of thisentire existence, but is in a certain sense the "whole"; only thiswhole is not so constituted that it can be surveyed in one singleglance. This, as we know, is what the Brahmins express in thatsacred, mystic formula which is yet really so simple and so clear:TAT TVAM ASI, this is you. Or, again, in such words as "I amin the east and in the west. I am below and above, I AM THISWHOLE WORLD."9

Schroedinger was indeed prophetic, though his prophecymay have been a self-fulfilling one, since he created the

'The Sower" by Vincent Van Goqh-The observer is becoming the observed.

TAT Tl/AM ASL this 15 you I AM THISWHOLE r0U--N(V£R5E.

mathematical means by which quantum physicists have come toview the world in this way. I like to think of this statement, *'Iam this whole universe," as the initial postulate of quantumthinking. I think of it as the one mind seeing itself and acceptingthe paradoxes of its positions. That anything is at all isreconciled with quantum jumps.

The position of wholeness taken by Schroedinger I callquantum solipsism. According to solipsism, the self is the onlything that can be known and verified. Nothing else is for sure.According to quantum solipsism, everything depends on you.You create the whole universe; you are the "you-niverse." How doyou manage this? The answer is: you use your mind. To under-stand the process, we will next look at your mind's architecture—the qwiff.

Imagiiiation's Architecture: The Quiff

The questions raised by such a self-centered view of the world donot have easily understandable answers. Far from it. For if theworld exists and is not objectively solid and preexisting beforeI come on the scene, then what is it? The best answer seems to bethat the world is only a potential and not present without meor you to observe it. It is, in essence, a ghost world that pops intosolid existence each time one of us observes it. All of the world'smany events are potentially present, able to be but not actuallyseen or felt until one of us sees or feels.

If we accept this picture (albeit, it is a strange picture),many events that were previously mysterious appear under-standable. But before we consider some examples, let us examinesome basic concepts. Starting from our present understandingof classical reality, there seem to be two fundamentally differentkinds of reality.

The first reality I will call the "out there." It consists of allexperiences, sensations, and events that you or I agree happenexternally. The leaf fell from the tree. The car stopped at thered light. If you and I agree that any event or series of eventshappened, we usually mean that the event(s) was "out there."I realize that there is a certain "looseness" to my definition; it isintentional and approximate. For according to this definition,any mass hallucination would be an "out there" reality. Muchof "out there" is repeatable and measurable. When a physicisttalks about reality, he or she means the "out there."

But there is also a second reality, one we all know quite well.It is the world of our minds. In this world, much happens thatsimply doesn't fit our common experiences of "out there." I callthis mind world the "in here," and it consists of thoughts,dreams, and pictures, which resemble or symbolize the "outthere." Letters and numerals are symbols of the "out there."They were created in the "in here." In the "in here" world,magic takes place and we hardly give it a second thought. Oftenthere is a direct link or correspondence between events (dreams,thoughts, and symbols) in the "in here" and events (that whichis seen, felt, tasted, smelled, or heard) in the "out there." Again,I am somewhat loose in my definition. A person sleepwalkingmay only sense events as if they were a dream. In this case,sleepwalking would appear as an "in here" reality. When apsychologist talks about the mind's reality, he means the"in here."

And now, according to quantum physics, there is a thirdreality. It has attributes of both the "in here" and "out there"

185

"bonOuixote by Dore*. Quixote projected the "In Here" into the"OutThere^' and found the world of imaqinationcloser to Keality than he imacjined.

realities. I think of this third reality as a bridge between theworld of the mind and the world of matter. Having attributes,of both, it is a paradoxical and magical reality. In it, causalityis strictly behaved. In other words, the laws of cause and effectmanifest. The only problem is that it isn't objects that arefollowing those laws (at least, not the ordinary kinds of objectswe usually refer to), but ghosts! And these ghosts are downrightparadoxical, able to appear in two or more places, even an infinite

number of places, at the same time. When these ghosts are usedto describe matter, they closely resemble waves. And that is whythey were first called "matter waves." In modern usage, they arecalled "quantum wave functions" or, as I have chosen to labelthem, qwiffs. They are called functions because they arefunctional, which means they depend on things for theiroperation. The things that the qwiffs depend on are space andtime. Qwiffs change. They change in very orderly, causal wayswhenever they are not observed. They are much likemischievous elves.

If we could somehow watch qwiffs without really watching atall—because our observations disturb these quantum elves —we would see some marvelous adventures. One qwiffian elf might,for example, divide into two, each elf replicating the other asthey both do their pranks. Furthermore, they are addable orcountable, but like ghosts that you can see through, adding themup sometimes produces nothing at all!

All or IVothing at All: How to Add Qwiffs

Let's imagine that we are able to "see" what goes on in the thirdreality. Remember that we aren't really seeing or observing, forif we were, we would only see what we normally see. This isjust like "The Paradoxical Cube." Seeing the "cube" as a solidcube corresponds to our "normal" way of seeing matter; thereare no ghosts—just weird, popping, quantum-jumping particles.But "seeing" the "cube" in the third reality would be seeing itas a pattern of points and lines. In a certain sense, "seeing" inthe third reality is seeing a superimposition of the two usualways of seeing the cube in the "out there" reality.

Physicists call this way of seeing the SuperpositionPrinciple. We have already come across this principle in ourdiscussion of interfering wave ripples. This principle was alsoused by de Broglie in constructing his "snake swallowing its tail"wave form for the electron in the Bohr atom. Schroedinger'swaves were another example of the idea of wave superposition—that is, the addition of one wave to another. And we came acrossthe same idea in Bohr's concept of the wave-particle duality.The key feature of superposition is that one plus one can equalzero, two, or any number in-between!

Now here we will add or superimpose two qwiffs. In thenext two illustrations, the Buddhalike figures wearing pointed

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hats appear upside down and right side up. Think of the upside-down Buddhas as the opposite of the right-side-up ones.Whenever an upside-down Buddha and a right-side-up Buddhacome together, they cancel each other out. We say that theydestructively interfere with each other. But two right-side-upBuddhas or two upside-down Buddhas reinforce each other. Wesay they constructively interfere with each other.

^^L

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how to add qwiffs

In the first illustration, the two qwiffs add together, orsuperimpose, to give nothing. In the second illustration, theysuperimpose to produce a qwiff with twice the magnitude ofeither one. If you think of the top qwiff in each drawing as athought and the bottom qwiff as an opposite thought, then youmight look at the first qwiff illustration as the canceling effectof a negative thought, while in the second qwiff illustration, wehave the reinforcement effect of reaffirming an original thought.For thoughts behave like qwiffs. Since qwiffs exist in your mindas well as in space and time, we may begin to see how ourthoughts actually manifest in the physical universe. It is thethought that creates the qwiff. Because the qwiff is ourknowledge of the world, positive thoughts about the world createthe world as a positive place to be. And, of course, negativethoughts work the opposite way, creating a negative world.Qwiffs obey the laws of cause and effect. They follow amathematical description. Schroedinger's equation was inventedto give us that description.

And qwiffs have a second magical property, not only canthey be added together and vanish, but they can also bemultiplied and in two or more places at the same time!

Two Places at the Same Time: Entangling Qwiffs

The second feature of qwiff magic is so strange that even itsfounders resisted the fact that qwiffs can entangle or multiply,producing a product that appears in more than one place at anyinstant. Each product may appear as an identical copy of itsoriginator. How do qwiffs entangle? By entering into physicalinteraction with each other. Why do they entangle? To learnabout each other.

Schroedinger's concern with qwiff magic and the EPRparadox led him to write an unusual paper describing theentanglement and multiplication element in qwiffs. Like most ofhis papers, this one was filled with vivid metaphors. He wasconcerned with what happens when two objects—two realobjects, that is—interact with each other. What happens to theirqwiffs? Schroedinger called the qwiffs representatives of theobjects, in much the same sense that an ambassador is arepresentative of a country. What happens when two objectsbump into each other? Like the wrestling representatives of the

United States and the Soviet Union in the film, Dr. Strangelove,the representatives of these two objects entangle. AsSchroedinger put it:

When two systems of which we know the states by their respectiverepresentatives, enter into temporary physical interaction due toknown forces between them, and when after a time of mutual influencethe systems separate again, then they can no longer be described inthe same way as before, viz. by endowing each with a representativeof its own. I would not call that the ONE but rather THE characteristictrait of quantum mechanics, the one that enforces its entire departurefrom classical ideas of thought. By the interaction the two repre-sentatives [or qwiffs] have become entangled. To disentangle themwe must gather further information . . . although we know as muchas anybody could possibly know about all that happened.^<^

What does Schroedinger mean when he says that although we knowall that we can possibly know about the system, we must gatherfurther information? How can we add further information to allthat we can possibly know?

Schroedinger^s Gat in a Gage

The only way we can add further information to all that we canpossibly know is by observing the system. For our actionsdisturb the system. The system depends on what kind ofquestion we ask it. Schroedinger made the analogy that aquantum system was like a tired but very bright student. Thestudent would invariably give a correct answer to the firstquestion you asked him, but he would become so tired after theeffort that he would invariably give an incorrect answer to thesecond question. The order in which you presented the questionsmade no difference.

Schroedinger's questions to the student were like thequestions of position and momentum put to nature by aphysicist. The momentum of the system would correspond toyour expectations, provided you measured momentum first.Similarly, the position of the system would correspond to yourexpectations, provided you measured position first. But in eithercase, the second quantity measured would never correspond toexpectation. In the example that follows, the life of a cat in acage will be at stake.

190 Is There an "Out There" Out There?

Imagine a closed steel cage containing one radioactive atom.This atom is said to have a half-life of one hour. That means in asample of material containing a large number of such atoms,only one-half of them would remain after the passing of onehour. The other half would have "decayed" or transpired byemitting radiation into the environment. Thus after the passingof an hour, we have an equal chance of finding the atom intact.

Further imagine that the radiation emitted by the singleatom strikes a sensitive photocell tripping a circuit that allowsa poisonous gas to fill the cage. This gas will kill any livingthing that has the misfortune to be in the cage at the instant theradiation hits the photocell. And now imagine that we place inthe cage an unsuspecting cat. (All cat lovers, please forgive me—the example is Schroedinger's.) If we then wait one hour, whatwill we find in the cage? A living cat or a dead one?

What controls the fate of the cat? According to quantummechanics, you do—if you are the one who is to open the cageand discover the cat. At first, you and the cat are quiteindependent of each other. But as time goes on, two possibleqwiff editions of the cat appear in the cage; one dead and theother alive. The dead cat edition appears more and more probableas time wears on, while the live cat edition appears increasinglyless probable. After one hour, there are two equally likely cateditions present in the cage.

Discovering a dead cat in a cage is not a pleasant prospect.Thus you are of "two minds" while waiting to open the cage.One mind is happy at seeing a live cat and the other is sad atfinding a dead cat. Just a mild case of schizophrenia. In a certainsense, the universe has become two universes. In one, there isa living cat and a happy you, and in the other, there is a deadcat and a sad you. You at this time had nothing to do with thissplitting of the universe. It came about because the cat interactedwith the atom in the closed cage. The cat-atom interactioncreated the split. As far as you are concerned, there is only oneuniverse, and you are in it!

But what happens when you open the cage? It is at thisjuncture that quantum mechanics appears to falter. While it iscertain that you will know the fate of the cat instantly, it is notclear how you come to know it! Remarkably, it is not possible toexplain the simple discovery of a fact using the new physics.There is no mathematical way to predict the cat's statis. Toknow, you must reach in and disturb the cage. That is whatSchroedinger meant by gathering further information. Thoughthe mathematical description told all that it could, it wasincomplete.

Breaking the Unbroken Whole

191

But the question still rings in our ears: what does it taketo complete quantum mechanics? Bohr and Heisenberg saynothing. It is as complete a theory as possible. We are respon-sible for its incompleteness. We play a vital role. Or do we?

Perhaps the role we play is overestimated. Perhaps thereare, instead, hidden variables controlling the mysterious behaviorof quantum objects. Perhaps there are other explanations. In thenext chapter, we will examine a range of differing explanations.These explanations all arose from EPR's earlier considerations.The continuists have not yet given up.

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Chapter 12

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There may be no suchthing as the "glitteringcentral mechanism o^jthe universe!' ^Not machinery hutmagic may he the hetterdescription of thetreasure that is waiting

JOHN A. WHEELER

A scene from Luis Bunuel's brilliant film, The Phantom ofLiberty, presents the French Revolution with a novel twist:the revolutionaries cry, "Down with freedom! Give us tyranny orgive us death!" Indeed, the price of freedom is high. That oldneed for security invades our dreams of Utopia. Don't we allwant to know that there is something controlling us? Don't weall seek something bigger than we mere mortals, perhapssomething hidden, something responsible for it all?

No surprise then that quantum physicists sought hiddenvariables that would return quantum physics from the world ofmagic to the objective universe of cheap tricks. Is there a hiddenorder? Were Einstein and his friends, Podolsky and Rosen,correct in assuming that quantum mechanics is incomplete? Ifthey're wrong, what is this thing called "reality"? Is it—as thetitle of Robin Williams' record album, Reality/What a Concept,suggests—just a concept, just something we imagine?

Up until around 1965, the answer seemed to be: no oneknows. In fact, no one even knew how to ask the question in asensible way. Several debatable "hidden variable" theories^appeared, notably the theory of David Bohm and later co-workers.^ Ingenious though they were, they only attracted mildinterest from physicists who were already too busy applyingquantum mechanics to everyday concerns like nuclear physics.But then came John Bell.

John S. Bell, a physicist working at the Stanford LinearAccelerator (SLAC) and the European Center for NuclearResearch (CERN) on leave from the University of Wisconsin,published a paper in the first issue of a new journal calledPhysics,^ The paper was entitled "On the Einstein PodolskyRosen Paradox." Thirty years had passed since the EPR paperhad appeared. Bell presented his argument in the form of atheorem and showed that any attempt to produce a hiddenvariable understructure to quantum mechanics was doomed. Inother words, there is no hidden message—this is it. We live in aZen world and, like Pinocchio, there are no strings on us.

Our search for hidden, controlling strings, the hidden orderswe all must obey, is part of our human nature. The first torealize its connection to quantum mechanics was Richard

193

Feynman. He found that a particle could still be a particle if itcould follow two or more paths at the same time.

The Search for the Unseen Order

When I first saw Man of La Mancha, the musical based uponCervantes' Don Quixote, I was deeply moved. I, too, had myimpossible dream. I, too, felt I was destined to greatness. Idreamed of making my life count in the universe. Perhaps theNobel Prize, a cure for cancer. The dream was to right the world'swrongs. My mind soared into fantasy.

It still does. I seek the hidden order of the universe; I wantto know how God does it. I am not satisfied with my mortallimitations. Jonathan Livingston Seagull has nothing on me."I want to know, I want to know, my God," laments the superstarJesus Christ. And so must we all, as we evolve into super-conscious beings.

I have an "I." Even worse (or better, perhaps), I am aphysicist. I have been taught to *'see" the world in terms of itsseparate parts, cause and effect-wise, pushing and pulling on oneanother. Everything must have a reason, to my order-seekingmind. I am in the game of right and wrong, good and evil, and —most important, because I am a scientist—the world of orderand chaos.

If only my dreams made sense! The concept of sense is basedon our collective and individual need for the cause-effect world,the world of objective realism. Long live my fantasies, say usall! Objective reality is a dream. This dream (or perhaps, as somewould say, this nightmare) has not lasted very long. We are justbeginning to wake up collectively from it. But is the nextexperience the real reality? Or is it just another dream, justanother world of our dreams?

Imagination is that drive, that dream, that search for theunseen order we all suspect lies beyond the reality we all havegrown accustomed to, the facade of life.

The vision of an unseen order has been with us for a very longtime. Hero of Alexandria, around A.D. 100, wondered about order.^Perhaps one day he wandered with a friend by a sunlit reflectingchannel. Watching her reflection in the water may have alsoraised a question in his mind. Why does the light of my friend'simage in the channel appear to come from under the water, at

195

'Enchanted Sleep' by Dore- Is life but a dream^ If so,who is thedrean-^eK?

exactly the same position as my friend? He traced the path of thelight rays in his mind and discovered an interesting and far-reaching order: the universe is economical; the light rays alwaystook the shortest path upon reflection to reach his eye.

Fifteen hundred years later, Pierre de Fermat was amusinghimself by playing with bits of glass and our economicalmedium—light.^ Light is bent as it passes from air through glassor from air into any other medium. Everyone has observed theold bent-straw trick, whenever a drinking straw is placed in atransparent glass of water.

Fermat wondered why the light took a bending path.He soon found the answer. Not only was light economical, itwas also speedy. Light always took the shortest time pathbetween its source and the eye, even when passing throughdifferent layers of differing media. Thus the straw's light reachesour eyes appearing bent and distorted in order to be cheap andefficient. How reassuring!

Around the same time period, A.D. 1650, ChristiaanHuygens, a Dutch physicist, pondered God's opening gesture. Hehad devised an improved telescope with which he could seeSaturn's rings clearly.^ Perhaps he, too, marveled at light's

economy. But if light was really economical, how did it know itwas? In other words, how did light know, once it was on the path,that the next step it took was in the right direction?

Huygens saw light differently from his predecessors. Heimagined light progressing outward in waves, each wave frontcarefully duplicating the one just before it, like ripples on a pond.But Huygens saw more. He imagined that each wave frontconsisted of thousands, even millions, of little transmittingstations, all lined up along the wave front like a rank of soldiers,each soldier in line emitting a pulse, a battle cry, and eachminuscule cry, a tiny yelp hardly heard, but all together makinga gigantic roar.

Each tiny yelp sends out a little circular wave ripple of tinycrests and troughs traveling through space and time. Togetherwith a neighbor's yelp, that itsy-bitsy cry is reinforced only inthe direction perpendicular to the line of the front. All otherdirections create confusion and the sounds come togetherrandomly and disordered. The soldiers must go forward along theleast time path, along the path that can be heard, the one justahead.

Huygens used his imagination, and even today, in everyoptics class, his wave construction technique is taught. What arelief—it's just a mechanical trick. The light doesn't really haveto know something in order to proceed. It follows the least timepaths along the shortest routes by going along all possible pathsfrom start to finish. It does this by sending out little waveletsthat bob and weave along their paths in all possible directions.But it is only the least time path that reveals itself; all otherpaths cancel out in confusion and noise, as the troughs and crestsof the light waves slosh together.

The idea is a powerful one. Good thing that light is a wave.For if it wasn't—if light was particles after all—how could weexplain its behavior? Such were the thoughts of RichardFeynman, an American physicist in the 1940s, working on hisdoctoral thesis nearly three hundred years later. Feynman hadnoticed something magical.

Feynman noticed that classical particles, like baseballs andbilliard balls, also follow a least-something path. That somethingturned out to be action, the same quantity that makes upPlanck's quantum constant. In every interaction, a whole amountof action units must be passed from one thing to the other.Feynman noticed that classical particles follow a least-actionpath through the universe. No matter how an object moved, itbalanced out energies so as to use as little action as possible.

Nothing Up My Sleeve 197

All physical things move economically, disturbing and disruptingthe balance between kinetic energy and potential energy as littleas possible.

Hero's least or shortest path for light rays, Fermat's leasttime paths for bending light, and even Huygen's wavelets allmust follow the path of hidden orders. Light follows orders.Feynman found that everything follows the same orders, be itlight or be it baseballs.

To create a physical reality is simple. Learn to move bystaying as close as possible to a balance of energies. Yet if thingswere in perfect balance, nothing would or could move at all, orelse the universe would be totally bananas (very crazy).

Have we found the hidden orders? Is the search over? Theworld is a giant machine run by an economical, albeit somewhatcheap, God. In other words, a lawful universe is an economicaluniverse, a balanced universe.

It was turning out that this principle of least action was evenmore powerful than Newton's laws, for later discoveries revealedthat even the laws of electricity and magnetism as well as lightfollowed it. But then, as Feynman puts it:

How does the particle find the right path? ... all your instinctson cause and effect go haywire when you say that the particledecides to take the path that is going to give the minimum action.Does it "smell" the neighboring paths to find out whether or notthey have more action?"^

reynman- How does theparticle findthe right path?

What happens if we fool light into taking the wrong paths?Can we do this? The answer is yes. When we fool light, weobserve the phenomenon called diffraction, the bending andinterfering of light with itself. The way we accomplish this isby blocking the natural light paths. Feynman states:

When we put blocks in the way so that the photons could not testall the paths, we found out that they couldn't figure out whichway to go. . . .^

It may seem strange to think of light particles losing their way.But what about ordinary particles like baseballs? Feynmancontinues:

Is it true that the particle doesn't just "take the right path" butthat it looks at all the other possible trajectories? And if by havingthings in the way, we don't let it look, that [it will do somethinglike light does?] . . . The miracle of it all is, of course, that it doesjust that. That's what the laws of quantum mechanics say.^

In other words, we can make matter behave like light. Wecan block some of the natural paths that matter takes in gettingfrom here to there and cause it to interfere with itself, cancelingitself out as light waves would. The world follows all possiblepaths open to it.

Feynman hoped to find how God gave orders to matter. Hefound that all possible paths, including the least action paths,contribute to the history of an atomic particle. The particlemagically follows as many paths from its present to its futureas it finds open to it. This discovery would later stimulate HughEverett to formulate a bizarre, parallel universe theory ofquantum mechanics. By blocking out the natural or least actionpath, the quantum interference effects could be observed. Byusing the idea of a "sum over the paths" available to a particle,Feynman could rid us of any picture regarding quantum wavefunctions.

But somehow this wasn't enough. Interfering paths or wavesstill were a mystery.

Bell's Theorem: Separate Housesnith a Common Basement

Physicists are human. They, too, have fears and likes, just likeeveryone else. Their needs for warmth, security, and the pursuit

All possible futures.

Nothing Up My Sleeve 199

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of happiness are no different than those of anyone else. Butquantum mechanics seems to pull the carpet out from under allour traditional beliefs regarding security and predictability.Quantum physics is not "nice.'* It is not simple and straight-forward. Thus physicists traditionally brought up with the niceformalities of classical Newtonian physics are often outragedor at least disturbed that quantum physics offers no solace toseekers of a deterministic universe.

Classical physics concepts, like all physics concepts, aieunfortunately not immune to the slings and arrows of experience.A theory may be beautiful and elegant, but if it doesn't fit thefacts, it's just plain wrong. A photon emitted many years ago froma distant star makes its way to my eye. Does it exist if my eye isnot there to see it? The question is reminiscent of the age-oldpuzzle, "If a tree falls in the forest and no one is there to hear it,does it make any noise?" The answer appears so obvious: ofcourse it exists. The photon must be there, like the sound wavesfrom the falling tree, whether or not anyone experiences it.At least, that's the answer if you believe in classical physics.

But alas, quantum mechanics does not seem to agree.Accordingly, the photon comes into existence as a spot on myretina only when I see it. Physicists have been more or less"forced" to accept this mystical position because of the uncer-tainty principle, which denies existence to objects having bothspatial locations and well-definied paths of motion simul-taneously. But suppose that the uncertainty principle is simplya sign of our ineptness. Suppose there is a real physical world outthere, but we haplessly mess things up as we go about the worlddiscovering it. To our insensitive methods, a whole world remainshidden. Quantum physics does not deny that we play a role inevery measurement procedure. Could there be an underlying,unrevealed order to quantum mechanics?

Such may have been the thoughts of David Bohm in theearly fifties.^^ Bohm led the chorus of those who followedEinstein's dream of a nongambling God in a revival of the searchfor hidden variables. By rewriting Schroedinger's equation in aform more familiar to the workers in the field of statisticalmechanics, Bohm was able to point to the key difference betweenclassical and quantum mechanics. This difference appeared as asingle term in the equations and was given the name thequantum potential.

This quantum potential acted upon the real classical particlein much the same way that any field of force would act. Thus the

potential was capable of accelerating and slowing the motion ofthe particle. In this, it was like the gravitational potential thatacts upon an automobile coasting along a hilly highway. But thequantum potential was also different, for it depended on thedistribution of an infinite number of possible locations of theparticle. No matter—the particle had only one position and oneunique path. However, it was practically impossible for us todetermine that uniqueness because we did not quite know whichof its infinitely possible positions the single particle had.

Though the Russian physicist Vladimir Fock felt thatBohm's position was "philosophically incorrect,"^^ no one reallyargued with Bohm and his followers in a convincing manner. Yetthe followers of Bohr would soon rise to the occasion. The Bohr-Einstein debate would live again.

The date was April of 1957. It was the Ninth Symposium ofthe Colston Research Society, held at the University of Bristol,England.^2 Bohm presented his Einstein-inspired uncertaintyprinciple position, while Leon Rosenfeld, a contemporary ofBohr, argued for Bohr's complementarity.

Bohm's position was that the underlying assumptions ofthe uncertainty principle (there cannot be a more deterministictheory than quantum theory) are contradicted by the possibleexistence of a hidden level of reality. Moreover, Bohm stated, itmay be totally impossible to detect this level of reality.Rosenfeld, on the other hand, argued that the world is as weexperience it. All hidden veiriables, if they exist, must beconnected to our experiences. They must show themselves. It isthe peculiar wholeness of the quantum process, the indivisibilityof the quantum of action that must be transferred in anyobservable process, that denies existence to a hidden, moreorderly level of reality. We simply cannot help but disturb theuniverse whenever we observe it.

It might seem that if we cemnot observe anything withoutchanging what we observe, we should perhaps drop the idea thatanything exists without our observing it. But then gdong cameJohn S. Bell and his strange theorem. Bell offered a proof thatthe hidden variable interpretation sought after by thosephysicists desiring a deeper, more mechanical, cause-effect basisof reality could reveal an even worse kind of order. Real particlesmay exist according to Bell, but they follow very strange orders.These orders border on what we now call psychic phenomeneu

How did we get to such a strange world view? The heart ofthe problem for John Stewart Bell was the arbitrary division of

the world into things and observers of things. Quantummechanics did not really tell us where this dividing line was to bedrawn and who was observing what? Bell felt that a study ofthe problem of hidden variables would shed some light. He hadbecome fascinated with the chapter on indeterministic physics inMax Horn's book, Natural Philosophy of Cause and Chance,^^and he had read Bohm's 1952 papers on hidden variables. Hedecided then to present his thoughts in the Reviews of ModernPhysicsy^^ but due to an editorial error, Bell's paper, written in1964, was not published until 1966.

In this review paper, Bell expressed his view that earliermathematical proofs by the eminent mathematician John vonNeumann (who decided that hidden variables were not possiblebecause they were inconsistent with quantum mechanics) weretoo stringent. He successfully constructed a hidden variabletheory describing particles that were spinning like tops.

Paradoxically, while he was writing his review, he was alsoworking on a second paper that contradicted the conclusionsof the first paper. He had become obsessed with the Einstein-Podolsky-Rosen argument, and it was the content of this secondpaper that became known as "Bell's Theorem."^^ There, Bellproved that any "local" hidden variable theory cannot reproduceall of the statistical predictions of quantum mechanics.

The key word in his paper is locals and it means "on thespot," happening at a precise location. A local hidden variable issomething that only affects things at a particular location. Forexample, a bottle of champagne awaits me. I open it and itexplodes, popping the cork to the ceiling. That explosiondepended on the state of the bubbly in the bottle, locally there infront of me. While it is true that the bottler prepsired theshipment of wine bottles, all containing champagne from thesame barrel, the condition of the champagne upon arrivaldepended strictly on the environment within each bottle. Thoseclods who left their bottles in the sun before they opened themhave no excuse for the spoilage that resulted. Certainly, theircarelessness cannot affect my bottle, which has been carefullypreserved in my cool cellar. Thus local variables arequite reasonable.

Nonlocal variables are not at all reasonable. Change any oneof them here and something happens elsewhere instantly. Inother words, nonlocal variables are our old friend, the EinsteinConnection. Bell's proof showed that hidden variables onlyaffiBCting the immediate environment would produce observable

results that contradict the predictions of quantum mechanics.In other words, if there were hidden variables that behavedreasonably, there would be observable consequences that wereentirely unreasonable. How could they be unreasonable? Theywould alter the "crap" tables of reality.

And now we come to the second part of Bell's theorem:that local hidden variables cannot reproduce all of the statisticalpredictions of quantum mechanics. The key word here isstatistical. All of us are conditioned by statistics. We literallylive in a statistical world. Statistics tell us that people only liveseventy years, dogs less than twenty. They also tell us how fastwe can drive safely, how much we can eat, and what we shouldpay for life and medical insurance. They even govern what we willbe able to watch on television or in cinemas.

Statistics enable us to discern the underlying laws thatgovern behavior. Whether the subject is baseballs, rocket ships,atoms, or people, statistics describe normal behavior, what weshould expect to observe. Consequently, whenever we observeand label something an abnormality or a deviation we meanthat what we observed is not statistically predicted to occur.

Take the famous Nielsen rating system for determiningwhat Americans are watching on television, for example. Fromjust over one thousand television sets, the raters can determinewhat the whole nation is watching. Why? Because the peoplewatching those Nielsen sets are typical Americans in homesaround the United States. They are a sample. If seven hundredsets are tuned to "Happy Days" on a given night, the ratersexpect that 70 percent of all television sets in the country aretuned to that program. But suppose that the people in the samplesystem decided to have a conspiracy? In other words, supposethey all decided to watch "I, Claudius" on PBS instead of"Happy Days." Since it is highly unlikely that 70 percent of thenation as a whole would be watching the PBS program, wewould have quite a deviation from the statistic norm.

And indeed. Bell's theorem showed that local hiddenvariables, like the hypothetical hidden conspiracy of theNielsen sample system, would create results that would deviatefrom those predicted by quantum physics. So far, no one has everobserved any phenomenon that deviated from that predictedby quantum mechanics. Thus, if there are hidden variables, therules they follow are not local.

Nonlocal hidden variables or parameters are, therefore,the only kinds admitted to provide the substructure for a

deterministic world. To have an orderly house, you need acollective network basement, one that is common to all of thehouses on the block. For nonlocal means just the opposite oflocal. Whenever a nonlocal parameter varies, it instantly affectsobjects that are not in its immediate environment. If there were,for example, nonlocal hidden variables governing the openingof my champagne bottle, they would affect the conditions ofall champagne bottles processed at the same time as mine. Thuswhen I pop my cork, the other bottles would also lose somecarbonation. And that disagreeable flattening of all those otherbottles would occur instantly, at the moment I opened my bottle.While such a deterministic world would give us a kind of cause-effect basis for reality, we would all be victimized by theinstantaneous whims of those we happened to have interactedwith in the past. Bell concluded:

In a theory in which parameters are added to quantum mechanicsto determine the results of individual measurements, withoutchanging the statistical predictions, there must be a mechanismwhereby the setting of one measuring device can influence thereading of another instrument, however remote. Moreover, thesignal involved must propagate instantaneously, so that such atheory could not . . . [satisfy Einstein's objections in the EPRParadox].^6

Clearly, the price of determinism is too high. We soughthidden variables in the first place to rid us of those tachyonic(faster than light) ghosts. But if we insist on a well-ordered worldof observation, the underworld is indeed magical.

The rules followed by hidden variables are far more unrulythan the laws of observed variables. The deeper we go in oursearch for law and order, the more we find ghosts and goblins,monsters and boogeymen. Is there any hope? cry the classicalrealists. Yes, provided that someone can prove that quantummechanics yields the wrong predictions about the world. So far,however, quantum physics has given excellent results.^"^

Probing the depths of reality is much like probing our owndepths in a psychological study. I am reminded of Carl Jung'sarchetypesy forms of what now is called the ''collectiveunconscious mind." These forms are, in some sense, buried in adeep pool called **the unconscious." They are said to exist inall of us. But do they? I think not. Furthermore, I don't believethere is any collective unconsciousness at all. We create it whenwe seek it, in much the same way that physicists create "hiddenvariables" when they seek an underlying order to reality.

Thus, there are no "hidden variables." Why not? Because,simply, we don't need them to explain anything. The world isalready paradoxical and fundamentally uncertain. Further digslead not to anthropological discoveries, but to human's creativeability to form from that which is not, that which is. Since thereis nothing out there until we find it, we are discovering nothingmore than ourselves. No wonder we find paradox whereverwe look.

We are that nothing we seek. Just as zero is both plus 10 andminus 10 at the same time, we are composed of complementaryproperties. If we seek ultimate order or ultimate chaos, we createa monster. What we seek already preexists as imagination or canexist because of imagination. Our imaginations are constantlychanging. Nothing is forbidden to them. If quantum physicscontinues to give a correct picture of reality, then perhaps littleis impossible. As one physicist put it: that which is not forbiddenis compulsory.

We Has Found the Hidden Variables: They Is Us!

A few years ago I visited physicist John Clauser in his laboratoryat the University of California, Berkeley. We had been attendinga series of discussions concerning Bell's theorem. Clauser was oneof the first physicists to attempt an experiment measuring thelimits set by Bell's mathematical theorem. His results confirmedquantum mechanics; the hidden variables, if they existed, werenonlocal. As I entered Clauser's lab, I was amused to see,attached to his door, the words that introduce this part of thechapter. They are adapted from these immortal words of Pogo,Walt Kelley's comic character: *'We has found the enemy, andthey is us!"

Clauser's experiment tested what we meant by physicalreality —specifically, objectivity and locality, which heabbreviated as O H- L or simply OL. Objectivity is what wehave been talking about up to now in this book. It means theexistence of a physical universe independent of the actions ofmy thoughts. The opposite of objectivity is subjectivity—theworld as it appears through my eyes. Colors for a color-blindindividual are subjectively influenced. So are likes and dislikes ofpeople's personalities.

A world without objectivity and locality would be a verysubjective world. It would consist of one element: me. This is theworld of the quantum solipsist.

The world of the quantum solipsist bears some resemblanceto Descartes' "I think, therefore I am." A quantum solipsist says:I am the only reality. Everything out there is in my mind. Tochange reality—that is, to change objects into different objects—I need to change my mind. To the extent that I am able to dothis, so appears the world as I see it. My failures to achievedramatic results, such as floating off the ground or travelingbackwards and forwards in time as easily as I do so in space, areperhaps due to my lack of imagination.

Similar to solipsism, we have a way of thinking calledpositivism. Positivism denies everything except senseperceptions as the only admissible basis for human knowledge.What we know is simply what we sense. In contrast, let us addthe two ingredients, objectivity and locality. Objectivity meansmaterial reality, and locality means that whatever happens hereand now can only be caused or affected by past events thatwere materially connected to the here and now.

And now let us look at a letter written by philosopher KarlPopper to physicist John Clauser, whose experiments confirmedthat both objectivity and locality were impossible. Clauser'sexperiments showed that a world that is both objective andlocal—attributes we normally take for granted as the basis forour own world—is not our world. Our world conforms to the rulesof quantum mechanics, and quantum mechanics (QM) deniesmaterial reality and locality. Clauser and Home describe theirresults in the conclusion of their 1974 paper in the PhysicalReview D:

Physicists have consistently attempted to model microscopicphenomena in terms of objective entities, preferably with somedefinable structure. The present paper has addressed the questionof whether or not the existing formalism of quantum mechanics canbe recast or perhaps reinterpreted in a manner which restoresthe objectivity of nature, and thus allows such models (deter-ministic or not) to be made. We have found that it is not possibleto do so in a natural way, consistent with locality, without anobservable change of the experimental predictions.^^

Popper's letter to Clauser is dated August, 1974. He wrote:

Many thanks for your immensely interesting paper. I still cannotbelieve that Objectivity + Locality is untenable. In fact, I do not

Nothing Up My Sleeve 207

think that Bohr would have expected it, in spite of the fact thathe rejected Einstein's pleading for OL. It is only now, due to Belland to your group, that the implications of QM become clear;though it is also clear that Bohr discerned them, if somewhatdimly. (Still, should Wigner too be right in discerning that QMimplies solipsism, then QM must be false, in spite of your andFreedman's shattering results. Do not forget that positivism(Mach) rejected atomism.)

I am more than puzzled. If positivism is objectively right, whyshould I accept objectivity "thus far, and no fathef'l^^

Clauser's experiments went against objectivity and locality (OL).But in supporting quantum mechanics (QM), they tended toindicate that positivism gmd solipsism are closer to truth.And that is a very strange situation, indeed. Suddenly everyoneout there is you. Popper's last remarks are a play on theparadox of objectively knowing that there is no objectivityor fathers.

Let's look at an exemiple of quantum solipsism in action. Lifeis a great teacher. But too often we confuse its messages. Haveyou ever noticed how stubborn some people are? Perhaps oneday not too long ago, you may have said to someone, "You arevery fixed in your attitude about that." Or you may haveobserved that your spouse kept belaboring a point that youwould gladly have given up. Why do others behave that way?In a world of objectivity and locality, what you see about theworld outside of yourself is what is. The other person is stupidand pig-headed. You have merely been the observer of that factand been kind enough to point it out to the stupid person youare dealing with. Perhaps the person benefits from yourobservation. He might say, "Thank you for pointing that outto me. It's just that lately I have been worried about the pricesof Japanese kumquats."

Your observation of that person's quality of obstinacy is anexample of objectivity. His admitted worry about kumquat pricesis an example of locality. The problem that occurred between youand him, then, was not influenced by you. He was at fault. Doesthis little scenario seem familiar to you? Does its explanationin terms of objectivity and locality make sense?

But let's look again, this time through the eyes of a quantumsolipsist. That other person is you. His pig-headedness is nothis quality but a projection of your thoughts. If he appearsstupid, you are looking at what you see as stupid. In other words,you Eire looking at your own stupidity, your own pig-headedness.

208 Is There an "Out There" Out There?

That other fellow is nothing more than a mirror of you. He doeswhat he does as you see it for you to learn about yourself. Yourexperience of his feelings and attitudes are your own feelingsand attitudes.

The quantum solipsist is a powerful individual, for after allhe or she is the whole universe. He uses his power in magical,beneficial ways. He uses his mind. Perhaps the hidden variableis the mind?

Part Four

Losing Our Minds

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Consciousness

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Parallel Universes

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What Kind of Machine Am I?

If there are no strings attached to us, why do we experience theworld as if there were? Eugene Wigner, Nobel Prize winner inphysics, believes that our consciousness alters the world itselfbecause it alters how we appraise the future. That is, weexperience the world the way we do because we choose toexperience it that way. In an amusing example, now called"Wigner's Friend," we see how it is that a friend's consciousnessalters reality and leads to a disagreement.

But what is this thing called consciousness? What is itsplace in quantum mechanics? Hugh Everett III completed hisgraduate studies in mathematical physics at PrincetonUniversity in 1957. He offered in his doctoral thesis anoutrageous solution to this question: no consciousness isnecessary in quantum physics. The future is not altered byconsciousness. Rather, all possible futures reedly happen!Instead of a single universe proceeding in a haphazard, conscious-ness-altering "drunkard's walk," there are an infinite number of"parallel universes," all proceeding on well-ordered qwiffianflows into the future. And we are on all of those universe layers!

By their nature, all these universes are parallel and noneoverlap. Therefore, we are only aware of the universe layer wehappen to be on and not the others. Every action taken is aninteraction that acts like a fork in the road for a wayfaringtraveler. Only the traveler need not make up his mind; he is onboth forks simultaneously but aware of only one of them.

Every observer, in Everett's view, is nothing more than amachine with a memory. The apparent freshness of experienceon any single universe layer is due to the uncertainty principle.Consciousness is the quantum connection between the numerouslayers making up the quantum machine. In other words, we arequantum mechanical "golems."

The Golem: A Machine nith Consciousness?

The roots of the story of "The Golem" can be traced to the Jewishghettos of medieval Germany.^ A pious spiritual leader, Rabbi

211

Loew, known to be a master of the deeply mystical, magicalCabala (or Kabbeda), created a "practical" use for his magic.He created the golem, an attendant who would serve his peoplein their sufferings and struggles, bringing aid to the oppressedcommunity. "He shaped it from clay, endowed it with spiritualbreath, and made it a doer of wonders." Can we repeat theRabbi's miracle today?

My first encounter with golems came in the fall of 1973. Ihad been given a small grant from the University of London,Birkbeck College, Department of Physics, to make a computer-generated motion picture of the interaction between ions andmolecules. As a result, I decided to submit the film to a computerarts festival being held in Edinburgh, Scotland. There I metProfessor Ed Ihnatowitz from the Department of MechanicalEngineering at the University of London. Professor Ihnatowitzhas a remarkably inventive mind. Even more remarkable, he isalso a renowned artist and sculptor. But before I tell you abouthis work, let me tell you about the festival.

Every year, in the fall, the city of Edinburgh hosts an artsfestival. It is a week-long gala event that celebrates much that isnew in European art, including the performing arts. Recentlycomputers have come into their own as an art medium. Oneingenious creator even composed a computer ballet with theperformers wearing the most unusual costumes.

Professor Ihnatowitz was exhibiting, among several of hisworks, a film of one of his "sculptures." At the time, the actual"sculpture" was on exhibition at the Eindhoven Museum inHolland. It consisted of a large, tinker-toylike constructionin the form of a prehistoric beast. It was bigger than an elephant,perhaps shaped more like a giraffe. Furthermore, it moved. Theprofessor included in its mechanical design a sensitive soundreceptor, one that would respond differently to sounds of varyingpitch and loudness. The receptors were attached to the creature'shead, much like ears.

To the delight of children, who were ceaselessly enthralledwith its antics, the "beast" would respond to their squeals bylowering its head from its lofty height to the level of thechildren's mouths. It was listening to them and wanted to bringits "ear" closer. That is, it would listen until the child happenedto make an unpleasant noise. Then it would jolt its head upward,away from the unpleasantness and return to its haughty position.

I was quite impressed with the film and the inventivenessof the beast's creator. But the way the creature entertainedchildren wasn't the amazing part of this invention, althoughthat is what it had been designed to do. It seems that each

morning, when they opened the museum, the attendants wereperplexed to find that the beast had laid its head on the groundas if it were asleep. As soon as it "heard" them, it would, as ifawakening from its sleep, turn its head toward the pleasantsounds of the attendants' low, morning voices. Since thisbehavior had not been programed into the device, it was at firstdifficult to see just why it was "going to sleep at night." Could ithave gotten bored? For many days, this uncanny "lifelike"behavior created quite a stir.

But soon enough the reason for its behavior becameapparent. Can you guess what it was? It turns out that, in asense, it was getting bored. Once the museum had closed,shutting out voices, only the sounds generated by other machineswithin the well-insulated building broke the silence. One ofthose machines was the air conditioner housed on the floor belowthe beast. The beast, like a child listening to its mother's heart-beat, was listening to the pleasant hum of the air conditioner.With no other voices to keep it company, the creature soughtout the only "living" companion around it—another machine.

For some reason, I was quite moved by the behavior of thebeast. Later I asked the professor how the unexpected behaviorof his creation affected him. He responded by telling me thatthis was quite a usual case among his inventions: the things didthe unexpected. Is it possible we may build a sophisticated,thinking device that will surprise us by exhibiting self-generated,intelligent behavior? What then constitutes the differencebetween living things and machines?

The possibility of creating an intelligent mechanical device,a golem, is greater today than ever. This is undoubtedly due tothe great advances in microminiaturization of electronic circuitscalled "chips."2 According to a recent article in Future Life,what formerly required 400 cubic feet of hardware to store onemillion characters in computer "memory" now takes only .03cubic feet, about the size of an American baseball.^ As ourhardware technology becomes smaller and smaller, we shallultimately be faced with quantum physics. Perhaps we arequantum machines.

The Mind of Professor Wigner

Einstein once remarked that the only incomprehensible thingabout the universe was that it was comprehensible. We are

214 Losing Our Minds

able to understand and find meaning in our lives and in theworld we all expect to see each morning when we rise from ourslumbers. But how does that happen? How is it that you and Ican agree and find meaning in the world? From a quantumpoint of view, this is a real question. The evolving future "seems"to be attached to the past. We "seem" to be governed by ourpast conditioning. We are much like puppets with someoneelse holding the strings. Why?

Eugene Wigner offers us an answer. This Nobel Prize winnerin physics suggests that our consciousness alters the world byaltering us. It affects how we appraise the future. And it doesthis by altering our own quantum wave functions, our qwiffs.Since our qwiffs contain all possible futures, it is our wills thatchange those probable futures into an actual present. Thishaopens as a result of the impressions we gain whenever weinteract with anything. Wigner describes the process:

The impression which one gains at an interaction may, and ingeneral does, modify the probabilities with which one gains thevarious possible impressions at later interactions. In other words,the impression . . . called also the result of an observation, modifiesthe wave function of the system. The modified wave function is . . .unpredictable before the impression . . . has entered our conscious-ness: It is the entering of an impression into our consciousnesswhich . . . modifies our appraisal ... for different impressionswhich we expect to receive in the future. It is at this point that theconsciousness enters the theory unavoidably and unalterably.*

So we experience the world as if it were on strings and tiedto the past or to a "heavenly manipulator" because we cannotprecisely control the results of our choices. Ultimately, each of usis the source of our own joys and sorrows, through such choices,our own wealth and poverty, and all that we experience. Butthe impressions we gain are unpredictable. They modify our wavefunctions just as the fiddler's fingers on a violin change thewaves on the strings. You are the fiddler. It's time to leave thesecurity of the inside "past" of your "time" house and climb ontothe "future" roof. It is because these impressions areundetermined that you have this power. You are the "fiddler onthe roof." But the tune may not come out exactly as you wish.

What I am pointing to is our power, as individuals, to influenceevents in our everyday lives. Quantum mechanics clearly showsthat nothing can be predetermined, no matter how events mayappear. Not only is ours a small world, it is a Zen world after all.You may object and claim that you can't change because peopleremember how you are, that you are powerless to change

anything. But the indivisible quantum of shapable actionproves you wrong.

Even our concept of memory needs revision. The unrelentlessquantum shows that the past as well as the future, is created.There is no past. There is no future. We create both, continuouslyand in unpredictable ways. This is it. There are no hiddenmessages. If, for only an instant, you sense this overwhelmingfact of your existence, it will alter your future now as you holdthis book in your hands. You can't help but sense a feeling ofpower. No one knows you. You know no one.

''But hold on," you say. "Of course, I know my daughter.Why, she is right here before me. What do you mean?" Youwant to know how we can experience the same things and knowby our communication that we are doing so. Surprisingly,quantimi physics can provide a solution to this puzzle.

How is it that we share a common reality? We shall answerthis question in two ways. First, we will look at an amusingexample provided by Professor Wigner. It has been given thename, "The Paradox of Wigner's Friend." We shall then extendthis example into the following section, which concerns what Ithink is the most outrageous idea of reality ever to hit the fansof consciousness. Whereas Wigner's friend creates realitythrough acts of consciousness, the parallel universes theory ridsus of consciousness altogether! However, be prepared for a shock.What replaces consciousness is a far more mystical and magicalenterprise, for we live in an infinite number of continuallyinteracting universes.

The Parado:i[ of Wigner's Friend

Consciousness is the creative element in the universe. Withoutit, nothing would appear. There is no sound without ears, andthere is no Schroedinger cat, living or dead, without you to openthe cage. Quantum mechanics does not expledn this; EugeneWigner simply postulates that it is true. Although some readerswill undoubtedly object that I should use the word consciousnessin this manner, I feel justified in defining consciousness as "thatelement outside of the physical universe that collapses the qwiff,producing the observed result from its range of possiblesituations."

Professor Wigner appears to agree with me.^ Here is how he

Losing Our Minds

approaches the problem. Just before you open the cage, thereare two cat editions superimposed in the cage. But the instantyou open the cage one of those editions becomes the real catand the other edition vanishes. That is, the buck stops in yourmind the moment you know the cat is alive (or dead). Toemphasize the point, Wigner has us consider the amusingparadox of his friend.^ It goes like this:

Wigner's friend is carrying out an experiment. He hasplaced a particle in a box and closed the box. According toquantum physics, the bound-in particle no longer has a well-defined position, but now assumes the form of a standing wavepattern inside the box. This wave pattern tells where the particleis likely to be found but not where it actually is. Furthermore,because the particle is contained, its momentum is alsoindeterminant. It could be moving toward either the left side orthe right side of the box.

To find out what is happening inside the box, Wigner'sfriend decides to open two sides opposite each other at the sametime. The removal of the two opposing walls causes the standingwave pattern to split into two opposite, moving wave pulses.After awhile, both pulses will pass through their respective

The parable of Wignet^'s friend.

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217

openings. The friend then sees the particle on the left (right) sideof the box and records his observation.

At this point the professor appears. He explains to hisfriend that he was carrying out an unusual experiment thatinvolved both the friend and the particle. The professor hadplaced both in a very large box. Thus, according to quantumlaws, even the friend's observation of the particle was split intotwo possible editions. In one edition, the friend sees the particleon the right of the box, and in the other edition, he sees it on theleft side of the opened box. The professor points out that itwas his kind observation of the friend and the particle that"created" the friend observing the particle when he (theprofessor) had opened his bigger box! In other words, the friendand the particle owe their very existence to the professor's kindobservation.

Wigner answers the paradox by stopping the observational

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buck with the friend in the first place. Accordingly, his friend'smind created the particle's position, so when the professoropened the larger box, he only saw what was already there.But is this really a solution to the problem? Wigner felt it wasthe only acceptable solution. We know that consciousness ormind is affected by physicochemical conditions, so why shouldn'tthe mind, in turn, affect those very same conditions? ThusWigner is forced to go beyond quantum mechanics to find themeans by which consciousness collapses the qwiff and producesreality as observed from the unobserved, potential quantumworld. So far no one knows how to do this in a completelytestable mathematical model.'' But do we need to go beyond thealready outrageous postulates of quantum physics to createthe world? Hugh Everett III doesn't think so.® However, thealternative he offers is perhaps even stranger. He asks us toaccept quantum mechanics at its word. The world is not just inour minds until we create it—it is really out there and in allof its editions at the same time.

An Infinite IVumber of Parallel Universes

Everett added an amusing aside to the paradox of Wigner'sfriend.^ When the professor reveals that he "created" the friendand the particle, the friend does not respond with gratitude.Instead, he points out that yet another observer may have placedall three of them—the professor, his friend, and the particle —in an even larger box. Thus, they may not have any independent,objective existence until this third observer opens his box.

Do we exist in a nest of Chinese boxes, wherein each boxowes its existence to a larger box in which it happens to benested? Who opens the last box? Is there a last box, or doesthe series of boxes go on forever to infinity, all of them waitingfor God to observe his or her own dream? If reality is just adream, who is the dreamer? If there is only one dreamer and I amthat dreamer, then nothing exists but me. This is the solipsist'sposition, and it is not a very popular philosophy. It is, however,logically consistent. To get out of the nested boxes, Everettposed another solution: all possible editions of realityreally exist.

Jorge Luis Borges, in The Garden of the Forking Paths,described such an outrageous world as

an infinite series of times, in a dizzily growing, ever spreadingnetwork of diverging, converging and parallel times. This web oftime—the strands of which approach one another, bifurcate,intersect or ignore each other through the centuries—embraceevery possibility. We do not exist in most of them. In some youexist and not I, while in others I do, and you do not, and in yetothers both of us exist. In this one, in which chance has favoredme, you have come to my gate. In another, you, crossing thegarden, have found me dead. In yet another, I say these very samewords, but am an error, a phantom.^^

To grasp the idea of parallel universes, we need to review thepossible alternative explanations of reality provided by theinterpretations of quantum physics.^^ The problem is how toexplain the universe with more than one observer in it. Further-more, we need to understand how it is that we—all of usobservers—can come to any agreement at all about what weobserve.

Why is there a problem? The most common interpretationpostulates that the world changes in two fundamentally differentways: it pops and it flows. A pop is a sudden, discontinuouschange brought on by any observer's act of observation. Thischange is sudden and noncausal. It cannot be predicted even byquantum mechanics. Therefore it is outside the ability ofquantum physics to predict the capricious behavior of nature.Whenever the world "pops," someone has observed something.Until the "pop," the world remains unobserved.

The world also changes in a continuous, flowing manner.But it is not the objects of the world that change in this way.Rather, it is the qwiffs, which represent those objects, thatchange in a continuous, flowing, and causal manner. The qwiffs,however, only represent reality; they are not reality any morethan the oil-tongued ambassador who represents a country is thecountry he represents. His country may be undergoing revolutionwhile the ambassador appears quite calm and smoothly tells usthat all is well back home.

Qwiffs represent what could take place in reality. Quantummechanics predicts with certainty the behavior of qwiffs.Qwiffs predict with uncertainty the behavior of matter. If theworld was somehow totally represented by the qwiff (or, in thecase of the ambassador, if a representative could be found for

each person in the country), the world would then flow andnot pop. The world would then be totally predictable.

But the world is not predictable in principle. The problemis the magical ingredient that pops the qwiff. Who decides whenthe world is to flow (remain unobserved) and when it is to pop (beobserved by someone)? Einstein expressed the dilemma morecolorfully when he said that he could not believe a mouse couldbring about drastic changes in the universe simply by looking atit.^2 If the mouse doesn't pop qwiffs, who does? Can only humanbeings pop qwiffs? Does the mouse live in a qwiffian ghost worldof all possibilities happening at once? Perhaps it is better to be amouse than a human being!

From this perspective, the paradox of Wigner's friendseems more realistic. For instead of there being a series of nestedobservers, each observing another observer, you yourself arethat nested series. Your electrons are observed by your atoms,who are, in turn, observed by your molecules, which are watchedby your cells, which are seen by your organs, which aremonitored by your nervous system, which is willed into action byyour brain, which is observed by you, and you, in turn, arewatched by . . . where does the buck stop? At what point doesreality finally and totally exist? Quantum mechanics does nottell us where consciousness enters to record the event. Instead,it tells us in principle how all of the above interact. It predictsthat, at each level of interaction, a bifurcation or sometimeseven a multifurcation takes place. It says that, at each level,equally likely possible paths come into existence as a result ofinteraction, just as in the example of "Schroedinger's Cat."Quantum mechanics never says when a single cat appears. Asfar as quantum mechanics is concerned, all possible paths arerepresented by the qwiff.

But if one postulates that consciousness exists outsideof the physical world, where does it enter? There does not appearto be any convenient entering port for the mind to reach in andpop the qwiff. We may never discover a way that is consistentwith the world as we observe it. So far all attempts to modifyquantum mechanics to include consciousness have fallenshort of explanation.^3

Everett listed five alternatives by which the paradox ofthe observer may be resolved.^"^ The first alternative we havealready mentioned. There is only one observer in the entireuniverse, and each reader may rejoice because—you are it! Allother people follow the laws of quantum flow. They remain in astate of suspended animation, or however you wish to think

of them, until you come along. Only you pop the qwiff.Congratulations! I thank you for creating this book and thewriter who is writing these words. But then you knew thesewords all along.

The second, third, and fourth alternatives limit the validityof quantum physics.^^ Each of them, in a sense, states thatsomething must be added to quantum mechanics. Yet, as wehave seen in this book, it is not easy to do this in a consistentmanner without making quantum mechanics weirder than italready is. At this point, what you add to the recipe ruinsthe cake.

Thus we come to the fifth and final alternative. It simplystates that the world does not pop. All observations by allobservers are interactions and therefore governed by the causallaws of the quantum universe. All is flow. The world iscontinually changing in a smooth fashion. However, it is a bizarreworld consisting of all possible worlds. There is only one qwiff—the master qwiff, with all of its branches spread out in space-timelike a network of the grandest design. There is no consciousness.None is needed.

The mouse does not change the universe; it is changed bythe universe. Multiple copies of itself are formed with its everyobservation, and each copy follows along like an automaton.However, each copy remembers what it saw in the previousinteraction, and each copy is sensitive to changes that takeplace in its environment. In one mouse universe, white cheese isremembered; in another, parallel universe, the cheese is red.Each time there is an interaction of the mouse and the cheesethe mouse-cheese branch of the one qwiff splits into as manybranches as there are varieties of the taste sensitivity of themouse and tastability of the cheese. If the mouse has a highlysensitive tasting apparatus, it notices what kind of cheese it iseating. Thus each copy of the mouse tastes a different cheese. Onthe other hand, if the mouse is insensitive to the differencebetween cheddar and swiss, no split takes place. But in eithercase, the mouse is only aware of its one experience—its individualexistence as a single mouse.

"All well and good for mice," you may say, "but what aboutpeople? Surely you're not saying that we, too, are automatons?"Yes, indeed, I am. For we are nothing more than the qwiff'sbranches. Everything that is possible is actually occurring onsome universal layer parallel to this one. "But I am conscious!"you cry. "I am more than a machine!" And yes, you are. You are aqwiff branch. You are in every branch of the universal wave

function. And in every branch of the Big Qwiff you are onlyaware of that single branch. Why? Because that is what abranch is: an offshoot from an interaction between the variouspossible things that could interact. And since all things caninteract, they do.

"But why can't I get what I want when I want it?" youmay ask. The answer is that some things can occur in more waysthan others—in other words, there are more branches. The worldbranch you happen to be on, and where you are reading thisbook, is one of many branches that happen to occur more oftenthan other branches where you are not reading this book.

Let's look at an example. In it we shall explain how it isthat each of us is only conscious of the layer we happen to beon and how it is that we all are aware of each other. We shallalso see how it is that we can come to any kind of agreementabout what we each observe. Furthermore, this example willhelp us to understand how it is that we can have disagreementsabout what takes place in our lives. Thus, from this point ofview, we shall learn how it is that several people can witness anaccident and come up with entirely different stories about whattook place.

People are sensitive creatures. They are able to respond tovarious kinds of stimuli in remarkably sensitive ways. Considerthe sense of smell. Just a few molecules whiffed tells us thatthe potatoes are burning! Indeed, sensitivity is an importantingredient for living things. And we can use human sensitivityto help us understand how we can exist on several layers oruniversal branches of the Big Qwiff and yet only be aware of theedition we are on.

We have all heard the expression, "Boy, is she sharp!"We know that the speaker means the lady is quite intelligent.Sharpness can be defined as "the ability to discern differencesor make differences where none were perceived before," as whenone uses a sharp instrument to cut something. In fact, the rootword skeriy meaning "to cut," is the Indo-European root for theword certain. Thus a sharp mind "cuts" or separates oneobservation from another.

Now let us imagine that we have found such an individual,a person who is able to tell the differences between cheddar andSwiss cheese. The cheese has been ground up, so no obviousvisual clues as to the identity of the cheese are available. To tellwhat variety of cheese we have, the cheese must be sniffed ortasted. According to the many-worlds version of quantummechanics, once the discerning lady tastes the cheese, she

immediately splits into a large number of duplicate copies ofherself, one edition for each possible variety of cheese imaginablein the untasted batch. In each universal layer, she knows justwhat she tasted. The layers are quite distinct, as distinct as theability of her taste buds and intelligence to perceive theremarkable differences in the taste of cheese. Then along comesa friend.

Now there are two possible kinds of friends. One kindincludes equally observant cheese-tasters and the other kindincludes clods who cannot tell the difference between"liederkranz" and "mozzarella." But let us suppose that thisfriend is the discerning kind of friend. The lady offers her frienda sample of the cheese. Of course, he does not know what is instore for him—namely, that as soon as he tastes the cheese, hewill split into a billion replicas of himself, each replica blessedlyunaware of the split. But our unknowing but game friend tastesthe cheese. If he is as sensitive to the taste of cheese as thelady, he will share his worlds with her. So on each layer that thelady tastes cheddar, we will find her friend as well, alsotasting cheddar.

However, our story is not over yet. Does the friend knowthat what he tasted is the same as what our discerning ladytasted? Can the two of them find happiness together in theirbranch of the Big Qwiff? Well, yes, if they agree that they havetasted the same thing. And for that to happen, the friend has toobserve the lady as well as the cheese. Did she taste the samething he did?

To be certain she tasted the same thing that he tasted, it isnot enough to just ask. Cheese tasting is quite an art. It requiresdiscernment beyond words. And that is where he can run intotrouble. If he is too sensitive to her, he will find that not only ishe on a different branch corresponding to the different possiblecheeses of the Big Qwiff, but each of these branches also has abillion or more fine branches corresponding to all of her tastebud differences. For example, the cheese may indeed byMozzarella #324, Batch #867. Yet although he knows this, hisextreme sensitivity to her tastes will cause him to be on adifferent fine branch corresponding to her description. Thus shemay say that the cheese is bittersweet and tacky, with a slightaroma of Kentucky bluegrass. As a result, her friend's experienceof the cheese and of her will be different than if she said thecheese has "a slight aroma of morning bluegrass."

This could lead to confusion because, while he is notequipped to sense those differences in the cheese, he is equipped

224 Losing Our Minds

to sense those differences in her. And, therefore, for the two ofthem to have complete agreement, he must be insensitive to herwhims of tasting, her fine structure. Let's suppose that he hasthe required insensitivity to her and the required sensitivity tocheese. Then they will be in agreement about what they eachtaste no matter which layer of the splitting-cheese part ofBig Qwiff they are on. In other words, they are on all of thelayers and not aware of any but the one they are on. She tastesCheddar #1 on Layer #1; he tastes Cheddar #1 on Layer #1;and he sees that she tastes Cheddar #1. Now repeat the precedingsentence, substituting 2, 3, ... on to infinity. Then go backand repeat it for Mozzarella #1, #2, #3, and so forth.

Disagreements are due to different sensitivities. Learningto get along sometimes means not getting too specific. Atother times, it means getting specific and enjoying life's manyuniversal branches. You are enjoying them even if you don'tknow that you are. So you might as well start to enjoy life; youwill anyway.

Of course, there is more that we could say about the paralleluniverses interpretation of quantum mechanics. I must admitthat I find it reassuring that reality as a whole is completelydeterministic, all of it flowing while my little piece of theBig Qwiff appears to suffer from indeterminism and theuncertainty principle. What is remarkable about this interpre-tation is that it shows that the mathematical formalism is capableof determining its own interpretation. In short, it is what itsays it is.

It was this observation that led Everett to write his thesisin the first place. Bryce S. Dewitt and Neill Graham have puttogether Everett's original papers and the comments of otherphysicists in a remarkable little volume entitled The Many-Worlds Interpretation of Quantum Mechanics,^^ Dewitt alsoincluded his own exposition on the subject, which I foundparticularly clear. ^"^ One of the most important ideas in Everett'swork is that the normal worlds occur in greater abundances thanthe maverick worlds where everything goes crazy. This is becausethe relative frequencies of occurrences of events taking placeon any one branch are matched almost exactly by the numberof branches in which a single occurrence takes place. Thus,an experiment in which 50,000 coins are flipped in the air givesthe same probability of a single head occurring as an experimentin which just one coin is flipped.

Finally, can we jump from one branch to another? The

Consciousness and Parallel Universes 225

answer depends on your interpretation. Since you are on allbranches in which you exist, there is no need to jump, for wherewould you jump to when you are already there? But if you don'tlike parallel universes, then you can't help but jump becauseyou are popping the qwiff every time you choose to do anything.The only reason you can't do what appears to be impossible,like flying or floating in the air, is that the worlds in which youcan do such things may be maverick worlds in which you don'texist as you.

So what can you do? Anything you want to. You are doingit. To get to any branch of the multiple-branching, universalqwiff is simple. Just become aware of what you want to do. Fromany branch there is a pathway leading to any other branch. Timeis all you need, and time is really all you have to work with.So it becomes clear. Time is the necessary medium for change.Consciousness is the awareness of any particular branch youhappen to be aware of. If you were aware of all of the branchesat one time, you would know all there is to know, sense allthere is to sense. You would also see the whole universal qwiff,for you would be able to see with certainty how all of thebranches began and how they must end.

When this moment occurs, you are free. Until it occurs,keep making the impossible possible. Keep choosing whichbranch you wish to sample life on. Remember that you are on allbranches that you can exist on. It's up to you which branchyou happen to be sampling now. And since joy for all people isdesired, eventually all will be joyful if that is the branch weall wish to be aware on.

Think of the branches as branches of a tree and of the senseof self you now feel as the sap or lifeblood of the tree. Feed thegood branches.

Chapter 14

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The universe begins tolook more like a greatthought than a machine

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Queerer Than We Can Imagine

What an imagination! No doubt you have said that aboutsomeone or have had it said about you. Usually, when we thinkof someone with a vivid imagination, we think of a person whois able to put together things or concepts that were previouslyunthinkable. Paper milk bottles. Air-sailing. Skydiving.Mini-card computers. The list is endless. Who thinks up suchthings? How do people do it? Well, if Professor Richard Feynmanis correct, imagination is as natural for man and nature asbreathing. He describes it as wonder. He wrote:

For instance, I stand at the seashore, alone, and start to think . . .There are the rushing waves . . . Mountains of molecules, eachstupidly minding its own business . . . Trillions apart . . . Yetforming white surf in unison . . . Ages on ages . . . Before any eyescould see . . . Year after year . . . Thunderously pounding the shoreas now. For whom, for what? ... On a dead planet, with no life toentertain . . . Never at rest . . . Tortured by energy . . . Wastedprodigiously by the sun . . . Poured into space ... A mite makesthe sea roar . . . Deep in the sea, all molecules repeat the patternsof one another till complex new ones are formed. They make otherslike themselves . . . and a new dance starts . . . Growing in size andcomplexity . . . Living things, masses of atoms, DNA, protein . . .Dancing a pattern ever more intricate . . . Out of the cradle ontothe dry land . . . Here it is standing . . . Atoms with consciousness. . . Matter with curiosity . . . Stands at the sea . . . Wonders atwondering ... I ... A universe of atoms . . . An atom in theuniverse.^

Atoms with consciousness, matter with curiosity? Are thesepeculiar statements for a physicist? I don't think so. They aresimply recognitions of undeniable facts. That particularrecognition, the perspective that allows mind to imagine that it,mind itself, exists as mind, I call consciousness. Consciousnesswithout imagination is a contradiction. Mind that lacks wonderis mindless.

But what is "mind"? Perhaps the best definition I can giveis that mind is "the metaphor of all possible metaphors."For example, we see ourselves in our "mind's eye." Mind isstuffed with metaphors, is itself a metaphor. Mind looks atitself in order to know that it exists. As you read this, perhaps

227

it becomes evident that anything we say about anything is ametaphor, the substitution of one experience for another. Everydefinition is always, "in other words." In other words, "in otherwords" is a substitute. Writing or talking about the process islike holding up a mirror to a mirror to see what a mirrorlooks like.

Mind looking at mind is a similar process. Since atoms withconsciousness are looking at atoms with consciousness, we havethe same experience of wonder and mystery whenever we lookat the universe. We are looking at ourselves. It is this processthat we call the universe. Professor Feynman goes on to say:

So what is this mind, what are these atoms with consciousness?Last week's potatoes! That is what now can remember what wasgoing on in my mind a year ago—a mind which has long ago beenreplaced.

That is what it means when one discovers how long it takesfor the atoms of the brain to be replaced by other atoms, to notethat the thing which I call my individuality is only a pattern ordance. The atoms come into my brain, dance a dance, then go out;always new atoms but always doing the same dance, rememberingwhat the dance was yesterday.^

If it is true that the universe is nothing more than mindlooking at itself, then what is self?

The Quantum Mechanics of Human Consciousness

What am I? I'm sure the question has crossed your mind as oftenas it has crossed mine. Am I simply a machine? Is my mind anillusion, a simple construction that arises out of my mechanicalbrain? Am I, as John Lilly put it, "a human liquidbio-computer"? Somehow, deep inside of me, I feel that I ammore than that. At least, I think I must be. If I am more thana mechanical device, then what distinguishes me from a canopener or a washing machine?

The answer appears to be my consciousness, my mind.But this is not an easy answer to understand, for what do Imean by my consciousness, my mind? In this chapter, I hopeto define consciousness by showing what it does rather thanwhat it is. As a physicist, I learned a long time ago that younever can really say what anything is, only what it does. When Isay that an electron is a particle carrying a negative charge of

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electricity and a magnetic moment, I am only describing how anelectron behaves.

Similarly, consciousness is what consciousness does. Andwhat does it do? It performs a dual role in the universe. In theworld of the quantum, it is both the awareness and the creationof experience. It is the being and the knowing of experience.With the stroke of the twentieth-century quantum eraser, thedividing line between ontology (theory of being) andepistemology (theory of knowing) is rubbed out.

In short, knowing is mind and being is matter. Just how thetwo separate is the magical process we call consciousness.Professor L. Bass of the Department of Mathematics at theUniversity of Queensland, Australia, has studied theirconnection, and he sees them in continual interaction. Thisinteraction between mind and matter, or knowing and being,has perplexed philosophers for centuries and is called the"mind-body problem." Bass's paper, "A Quantum MechanicalMind-Body Interaction," published in Foundations of Physics,^offers us a solution, one based upon quantum physics, to thisancient perplexity.

The problem has to do with will. Just getting the job doneis not sufficient. Any old machine will do that. It's knowingthat the job is being done that is the grabber. In other words,when I choose to do something, how does it get done and howdo I know that I am doing it? Surprisingly, it is quantumindeterminacy that leads to deterministic choices on the normallevel of perceived experience. If this indeterminacy was to vanishsomehow, my will would not be done. I would have no choice,none at all.

All of this choosing takes place inside of me because specialchannels open in the walls of my neurons.^ Neurons are highlyadapted, electrochemical, excitable, elongated cells that makeup my central nervous system (CNS).^ Bass suggests that wehave created, through the process of evolution, a device withinour CNS. I like to compare this device to an agency, such as theCentral Intelligence Agency (CIA). This device, much like theCIA, gathers information.

This device exists as an independently operating agent ineach and every neuron, perhaps in each and every molecule, oreven in each and every atom. Each agent is free to choose whathe or she wants, where he or she wants, and when he or shewants. But the choice is somewhat limited: it is to note or not tonote reality. And at these levels of reality, reality noticed isreality created. In a single act of noticing by one of my CNSagents, a pure qwiff pops and a dream becomes a reality.

230 Losing Our Minds

Bass's model directly connects will with qwiff reality. Thisreality takes place inside of single neuron. As a result of anencounter of the cell's membrane (substrate) with an active groupof atoms on an enzyme molecule inside the cell, the neuron isleft in an indeterminate state. The qwiff describes the cell asbeing in a state in which it cannot be said to have fired a definitenumber of times. This indeterminate reality may persist overseveral time cycles (milliseconds).

But then an unusual event happens. This event cannot bepredicted. It is the conscious noting of the positionalconfiguration of the active atomic group on the enzyme molecule.It is this sudden and unpredicted event that I call the "act ofconsciousness." When this event occurs, the neuron is no longerin an indeterminate state. Suddenly it has fired a definite numberof times. Furthermore, I am aware of it.

In the next part of this chapter, we shall look at a very shortperiod of time—short, that is, in comparison to our normal timeperception. The period of time is five thousandths of one second.It corresponds to the period between pulses or firings of a singleneuron. As we shall see, much goes on in the human nervoussystem during this time.

A Quantum Mechanical Mind-BodyInteraction: Bass's Model

How do you will something to happen? For example, when youchoose to bend down and pick up a pencil, what is going on?Why is it that we sometimes do things with much apparentwillful thought, while at other times, after much practice,we just do the same things without thinking at all? An initiallydirected and conscious action becomes a habit, an unconsciousact. Our ability to learn is dependent on our acquiring of habits—for example, the habit of listening. Learning, it appears, is theability to turn initially conscious acts into unconscious habits,good or bad.

According to Bass, this ability we have is due to thedevelopment of the above-mentioned magical device, one thatpops the qwiff in our nervous systems. Bass has us place thedevice right smack in the central nervous system itself. Thedevice was not present in early humans. Conscious direction

of muscular movements confers an advantage in natural selectionthat might have taken ten million or perhaps one hundred millionyears to evolve. This device is capable of choice, depending onwhether the qwiff has just been popped. Bass argues: "Onlythe long evolutionary process could justify the introduction ofsuch a device, the construction of which is at present entirelybeyond the practical capabilities of science."® In other words,the device would produce different results, depending on thebehavior of the qwiff, not the matter.

Let us look more closely at the CNS. It is made up of nervecells. These cells are excitable, capable of undergoing atransformation that involves their ability to transmit electricedimpulses along their elongated bodies. These impulses can cause,by minute chemical reactions, contractions of small muscle fibersconnected to the nerve cells. It would appear that if this deviceis anywhere within us, it must be in our nerve cells. Nervecells control us. But what determines whether a nerve cell fires —that is, undergoes electrical transformation?

Now Bass points out that it is the act of noticing, the eventin the consciousness of a suitably located observer, that causesthe cell to fire. I call such an event a qwiff popping. When a qwiffpops, the wave function has been changed or modified. From theinstant the event is noted, the moment it becomes an event ofconsciousness, the world is a different place. This is because theappraisal of possibilities now available to the observer has alsochanged. Thus I notice a pencil on the floor and I reach topick it up.

This whole process is not simply mechanical. I have a choice.However, the choice is very subtle. It is to note or not notethe event. I can make the event part of my consciousness or not.For a pencil lying on the floor, this appears clear enough. Butwe are now dealing with events at the level of individual nervecells. The taking note of the event is, in fact, the event we aretalking about. The situation is analogous to an observer watchinghimself in a mirror. The instant the observer notices that he isobserving himself, a new awEireness occurs. At that moment, heis no longer observing himself in the mirror. Instead, he isobserving himself in the process of observing himself. As soonas he stops observing himself engaged in observing himself,he can once again simply observe himself in the mirror.

The concept is elusive because it is self-referring. To notice,you have to notice that you notice. It is a mirror facing anothermirror and asking, "Who is the fairer, you or me?" But what is

Losing Our Minds

the event we are talking about? Is it the nerve cell firing itself?No. It is even further down the scale of events: We need to lookat a smaller part of the nerve cell. This smaller subsystemconsists of one complex molecule. It is part of an active group ofatoms on an enzyme molecule inside the nerve cell and lying veryclose to the wall of the cell.

Several kinds of enzymes actively operate within humancells. For example, proteolytic enzymes introduced into a nervecell can modify the ability of that cell to fire. Apparently, theenzyme attacks the protein gates to specific channels connectingthe cell to other nerve cells. Depending on the configuration ofthe enzyme, the gate opens or closes, and the cell firesor it doesn't.

We might think of the enzyme as a kind of gatekeeper.How does the enzyme do it? It appears that it has tails, andthat it lies attached to the cell wall (membrane) so close to thechannel that a mere encounter of one of its tails with the channelgate occurs whenever the cell fires.

The small subsystem we are interested in lies at the endof one of these tails. Bass cites a specific example. It is calledmethylamine and it is a molecule that terminates the side chainthat composes the tail. It is a part of this tiny molecule, which

Molecules vjith tails surrounding a protein gate.

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233

consists of two hydrogen atoms and one nitrogen atom forminga triangle configuration, that determines the activity of someimportant enzymes, such as the aldolases. To this little moleculartriangle we shall pay a great deal of attention in what follows,for the device we are seeking operates on its atomic level ofbehavior.

The scenario goes something like this:

The nerve cell fires. The protein gate undergoes a changein conformation appropriate for a channel gate. The tail entersthe gate. The two hydrogen atoms form a baseline on the tinytaiPs tip, with the nitrogen atom above or below that line. If thenitrogen (N) atom is above the baseline, the tail fits into the gatemuch like a key fits a lock, and the gate stays open to fire againafter the tail leaves the gate.

If, on the other hand, the N-atom is below the baseline,the tail again fits the gate, but like a good boy, it closes thegate after its encounter with it. These are the only two fits ofthe tail's "key" tip into the gate "lock." So far, so good. An "up"triangle keeps the gate open. A "down" triangle closes the gate.So, what happens? Well, it depends on whether or not you notice.You see we are in quantum land. Thy will is about to be done.

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The Impossible Mission:The Exercise of Human Will

In chapter 11, we looked at the example of Schroedinger*s cat.Perhaps you wondered how the cat could be existing in twocontradictory realities at the same time. Certainly real cats donot exhibit such bizarre features. But if we descend to themolecular level of reality, we shall find our own examples ofSchroedinger's cat. They are the molecules and atoms that makeup our nervous systems.

For the cat in the cage, it was the interaction of a radioactiveatom with the cat that caused the double reality of a live cat anddead cat existing side by side within the cage. If the atomradiated, the cat was dead. If, on the other hand, the atom didnot radiate, the cat was still alive. The atom was an analogy tothe actual behavior of the triangular NHg molecule. This moleculelooks just like an isosceles triangle with two equal sides. Butbecause of its tiny size, the triangular molecule participates inquantum reality in order to remain stable.

Molecules are curious things. Each is made up of atomsthat stick together by electrical forces. But it seems these forcesare not enough to keep the molecule stable. If the forces becometoo attractive or too repulsive, the molecule shakes andsometimes flies apart. Quantum magic glue comes to the rescueand keeps all molecular families of atoms together. However,the price is high: the family members must give up theirindividual selves. They must live in a qwiff world that has twoor more places at the same time. The moment any of the atomsthat make up the molecule become located in one spot,the molecule begins to shake and dance. It radiates away excessenergy in its attempt to stabilize itself. The little triangle isno exception to the rule.

In other words, the H-atoms do not exist separately when-ever they are part of a molecule. All we have are their remnants,their qwiffian ghosts to remind us that they are potentiallypresent. Their actual presence comes into being only when theyare noticed. At that instant, the molecule shakes. The radioactiveatom in the Schroedinger cat cage is analogous to the dualpositions of the H-atoms in the molecular triangle. To find asingle position, the little triangle encounters the gate. In the caseof Schroedinger's cat, the cat plays the role of the protein gate.

After the interaction of the triangle with the gate, we havetwo gate positions—open and closed at the same time. Again,

this is completely analogous to what happened to the cat afterit interacted with the radioactive atom. The gate's qwiff isdouble positioned. Now, if the gate is open, the cell continuesto fire. A neighboring neuron responds to that signal. If itreceives two or more blips, telling it that the gate is still open,it transmits a high-frequency signal, alerting the neural networkof which it is a small piece.

On the other hand, if the gate is closed, the neighbor onlytransmits a low-frequency signal to the rest of the CNS net ofwhich it is a piece. Which does it do? That depends on you or,more specifically, on your agency. The agent must pay attentionto that frequency, listen to its melody. Since the triangle wasin two places (like the radioactive atom that may or may nothave radiated) at the time of interaction with the gate, thegate (like the cat that is, at once, alive and dead) is both openand closed, potentially, at the same time. Thus it is simul-taneously firing to its neighbor and not firing. Following alongthe logical chain of possible events, that means the agent issensing both a high-frequency and a low-frequency signal at thesame time, and yet the agent is not really sensing anything at all(like the cat's observer who has not yet opened the box). Why?Because these signals are only potentially present in yournervous system; they are in the qwiff world.

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The agent must choose to notice that there is a low-frequencyor a high-frequency signal on his line. All it takes is for himto choose it. Once he has, it becomes part of your agency'sagenda. Suppose he notices the high frequency. And down at themolecular level, the gate is open and the little triangular tailpoints upward. Of course, if he noticed a low frequency, thenfollowing the chain of logic back to the little triangle, it wouldbe pointing downward.

In either case, something has been noticed. A choice wasmade. The original cell itself now undergoes another kind oftransformation: it transmits, at the instant notice is taken, atrain of microwave frequency pulses to a nearby muscle fiber,which then contracts mechanically. The agent was completelyfree to notice the signal at any time. There was nothing causinghim to take note at that particular time. He was also free not tonote it.

What happens if he simply does not pay attention to thepotential reality sharing reality with your nervous system?Suppose he ignores those ghosts from your qwiffian world?Then, nothing happens. The original cell relaxes in its ownrandom thermal bath and does not alert the muscle fiber.The little triangular tail maintains its previous uncertainconfiguration and remains stable.

Taking note of its position shakes the tail. It then dancesinside the cell emitting the microwave frequency that, in turn,induces the cell to signal the muscle. This is the essential featureof the model: it uses quantum uncertainty as a basis for willfulaction. It is the lack of knowing that gives each agent his freewill. He chooses in order to know.

The agent tunes into the world of imagination. Suppose he"hears" a high-frequency buzz. This means that the cell signaleda second time, but hold on—did it really signal twice? Thisquestion arises as soon as we begin to consider the time elapsedbetween the supposed second signal and the taking note of thehigh frequency. That brief time interval is about five thousandthsof a second. It is hardly worth noticing anything on such a tinytime scale, yet this is the scale on which our nervous systemsnormally functions.*

* We can experience such a small time scale quite simply. It corresponds tosomething moving to and fro two hundred times a second. If you pronouncethe letter 2 as in the word eat, and hold the e sound, you will be producinga sound vibration of about two to three hundred vibrations a second. Ofcourse, you will also be producing other sounds as well. Five thousandthsof a second is the time between two successive vibrations of your letter e.

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The fact is that this small time interval separates two verydifferent kinds of events. About the latter event, there is littlequestion. The high frequency was definitely noticed by a singleagent of the CNS. But what actually took place at the firstevent, when the tail entered the gate? Did it leave the gate open,thus producing the ultimate high-frequency buzz noticed bythe agent? Or did it close the gate after its encounter, causing alow-frequency buzz to be felt? The answer is, paradoxically,neither and both. The gate is open and closed and it is alsoneither open nor closed. Like the observer of Schroedinger's cat,the gate exists in the third reality.

Now perhaps an objection arises in your thinking. Whyis it necessary for the cell's gate to behave in this paradoxicalmanner? Why is it necessary that there be a time intervalbetween these two events? Why can't the two events happenat the same time? Indeed, why aren't the two events one singleevent? The answer is: if these events did not occur as they do,free will would vanish. We would become total machines. Withoutthis tiny, precious time interval, we would all be simple stimulus-response engines, behaving much like thermostat-controlledhouse heaters.

The initial stimulus causes the interaction between the tailand the gate to take place. From nothing, two potentiallyrealizable events occur. You might say that a kind of dynamictension takes place. The closest I can come to describing this"sense" is to call it psychic. Your agent is alert to what canpossibly occur. He has a choice now. That choice did not existuntil the stimulus was "sensed," until the tail encountered thegate. The little triangular molecule has been changed by theencounter, but it is still quite stable. Although it is now in anexcited state, its atomic constituents are still quite blissfullyuncertain as to their locations. Consequently, the molecule doesnot shake the tail to which it is connected. The alert agent stillhas a choice: to note the position of the H-atoms after theencounter or to ignore them. Without this period of respite,this contemplation time on the neuronal scale of temporal events,we would become nervous wrecks. Our muscles would beresponding to every neuronal signal, continuously twitching.Quantum mechanics is necessary for life as we know it. Out ofuncertainty comes freedom. From the uncertain atom comesfree will.

But suppose that the agency noticed a low-frequency buzz.The tail's tip points downward, thus closing the gate after theencounter. Again, the H-atoms' positions are noticed and the

tail shakes. Up or down, so long as it is noticed, the enzymewill be alerted by its tail. The neuron, in turn, becomes alertedby the enzyme and signeds the muscle fiber to contract. Thechoice is to note or to ignore. In either case, thy will be done.But, we have left something out of the discussion. Whatdevice pops the qwiff in the first place? Where does the deviceexist? The answer seems to be nowhere. The device may be whatwe mean when we say the magical word, "I." The device is ourawareness of our own existence. "I" exist because I chooseto exist.

The Atom and "'I'*: Are Atoms Conscious?

Bass's model offers us an answer. Consciousness is choice. Thischoice, however, is not among the already chosen and preexistentforms known to us as matter. This choice comes to us fromqwiff land, the land of our imaginations. Before we choose (whichis the same thing as saying, before we are aware of anything),the universe is paradoxical and not *'out there." Something called"mind" is present. Mind is in the world of quantum reality.

The exciting feature of Bass's model is that it ties togetheror correlates a single quantum event (the localization of the singletiny molecule's position) with a macroscopic event (the excitationof the whole neuron). Bass cautions us, however:

While examples of neuronal excitation triggered by single quantumevents are well established and explained ... it would not sufficefor the present purpose to trigger the macroscopic event by anyone of many possible quantum events (such as a one-photoninteraction with any one of many pigment molecules). It isapparent that here the impression entering the consciousness ofthe observer must pertain to a single unique quantum systemdescribed by a wave function [qwiff].''

Do human beings possess this unique ability? Can a personcorrelate macroscopic events with single quantum systemsdescribable by a qwiff (such as the methylamine molecule)? Forthis ability to be present, a close coupling between the wholeneuron and its individual ionic channels would be necessary.This coupling would appear as a "kind of enhanced sensitivity"or heightened awareness. Bass suggests that

a detailed model of the requisite close coupling between a uniqueionic channel and the excitation of the neuron would be too

speculative. In order to see how such a coupling might have beenevolved for some special neurons, it should be noted that groupsof some 100 normal ionic channels . . . are known to suffice forexcitation by electrodes, but a lesser number is hkely to sufficeon the known specialized parts of any neuron (the so-called axonhillock), where firing is initiated in normal functioning of theneuron because of the locally high membrane excitability. Theextension of these existing local features of neuronal membranes tothe limit required in the present model in a set of specializedneurons would seem to be within the scope of natural selection.^

Bass's device changes the qwiff; it pops the wave function.But where is it located? It has no location. It is the living neuronitself. It is the enzyme operating within the neuron. It is themolecule operating at the end of the tail of the enzyme withinthe neuron. It is the atom operating within the molecule thatlies at the end of the tail of the enzyme that is attached to thewall of the neuron. It is the conscious atom noticing itself andthus creating itself. Consciousness is the process whereinpotential reedity become actual reality. It is the qwiff popping.It is the wave function collapsing.

At the atomic level, consciousness is primitive, butnecessarily so. Neurons contain possibly several billion atomic"consciousnesses." We might call each such consciousness amind. All together they are the agents that make up yourintelligence agency. At the molecular level, each agent performsa single task: that of noticing itself. It is like one potentialreality noticing another potential reality within the same pureqwiff. In that sudden mysterious event, one of those potentialrealities just "appears." That act of consciousness is the creationof reality at the atomic and molecular level. Now the neuron isalerted to signal the muscle. Now the neuron is signalingthe muscle.

Perhaps several billion minds are acting in that neuronor in other neurons. Some minds notice the high buzz and otherschoose the low buzz. Together these minds, these countlessminds, functioning in quasi independence, often unaware of eachother's presence, and sometimes even making choices detrimentalto your life, act on your behalf. In fact, they act as your behalf,by choosing what you experience as reality. Together these minds"make up" your mind. They are your own CIA. And when anoutside event stimulates a quantum encounter between yourneuron's gates and enzymes, these simple minds join in randomfashion, some seeing H-atoms up and the others seeing H-atoms

down. They are your normal mind, your normal waking (orpossibly sleeping) mind.

Taken randomly, they form a kind of net of unknowing, apool of unconsciousness. In this way, your individual mindsknow what's going on, while your collective consciousness hasn'tthe foggiest idea of why you bent over to scratch the cat.Your action becomes an unconscious, habitual act, like riding abicycle. When you were first learning to ride, you had to mindyour minds; you had to listen to them as they all screamed theirpitiful, tiny discoveries of up H's or down H's to no one, as thewhole ensemble that is called "you" tipped and fell out of balanceand hit the street.

But you got up again. "You" took over. You rode the bike.Imagine climbing on that bike for a moment. Remember howyou felt as your parent or sibling pushed you out solo? You werein a pure state, your qwiffs unpopped. You did not know how toride. Then you began to tip. You became alert. Your neurons hadfired alerting NH2's to encounter the gates, to find out whatwas going on. The NHg molecules tasted the gates and snappedback. They were excited, but stable. The gates had doubled;they were in qwiffland. Your qwiff was still pure and unpoppedafter the encounter, and you were falling over.

Each agent looked at himself, inspecting for possibledamage. And each agent saw the two possible positions. So eachagent chose. The qwiff popped. The gates were then open orclosed—nothing in-between. Each mind knew, and all of themtogether presented a sum of their knowledge. They were "you."You knew. You acted. You chose to do something. You stopped oryou leaned the other way or you pedaled faster.

This integrated consciousness is your consciousness ofconsciousnesses. It is a kind of overseer. It observes theobservers. For it, all of the other acts of consciousness forma mixed state of popped qwiffs. That mixture of states is thusphysiologically identical to billions of molecules, each of whichis in one of the two possible states, up or down H's. Your firstconscious acts while learning to ride a bike where conscious toyour collective consciousness, which was observing all the waydown to your atoms. In this manner, you correlated your fallingoff the bike with your atomic feelings. You were of "one mind."But after all those qwiffs popped, you became "many-minded."And that made a big difference. The individual "minds" werethen trained; they were noticing. Together they formed theunconscious random pool of atomic minds acting independently.

An imaginary view of t\)w we learn to "make up' our minds.havingobserved the scrambled data of the world, one mind becomes manyatomic minds,they observe ench other, and then they become one mind

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All for One and One for All: Where Is My Mind?

Wilder Penfield, the well-known neurosurgeon and mindresearcher, discovered through many exhaustive case studiesthat the mind has no unique location within the body. As hestated in his book, The Mystery of the Mind: "To suppose thatconsciousness or the mind has location is a failure to understandneurophysiology."^ But if the mind does not have a location, thenwhere is it?

The mind appears to be everywhere. It is observing on thescale of atoms and molecules, neurons, cells, tissues, muscles,bones, organs—in other words, it is observing on all scales ofphysical existence. It sees all, from your NHg's to your socks. Itis one mind that is capable of acting as several atomic minds.

There is an intentional, subtle difference between the onemind and the individual atomic minds. The atomic minds popqwiffs. They operate at the level of quantum mechanics. Theydeal in the bizarre world of choice among qwiff possibilities. Andtheir choices have not been decided upon until they choose. Eachaction of an atomic mind is a popping of a qwiff. When an atomicmind operates, the gate is observed to be open.

The one mind does not normally deal with atomic realities.In fact, it deals only with atomic minds, and it deals with whathas been created by the choices made by the atomic minds. Itacts as a data-saver. In the example of the paradoxical cube,the atomic mind "sees" the cube with one face in front. The onemind adds up all of the pictures of the cube gathered together byall of the atomic minds that are acting.

By summing up the experiences of the atomic minds, the onemind makes up its mind. It literally creates a one-mindedness. Indoing this automatically, it transforms new experiences into oldexperiences and creates habits. In the case of the firing of theneuron, it didn't make any difference which position of themolecule of NHg was noted by any individual atomic mind. Solong as a position was noted—up or down for the moleculartriangle—the neuron fired. Thus, even though the atomic mindcould not predict nor determine what it would observe, thebehavior of the whole person became determined. Bass remindsus that "an initially consciously directed action graduallybecomes automatic through frequent repetitions; yet the processof fading from consciousness leaves the actual muscularmovements entirely unchanged. "^°

The unique freedom of the one mind is that it is all of theatomic minds and any one of them at the same time. There areno clear dividing lines between the one mind and any other

consciousness within the body. This freedom arises because themind has no location in space. It operates psychically in just thesame manner as the two observers observing the two previouslycorrelated paradoxical cubes (p. 181). Each mind saw a cube with aparticular face forward. No mind could predict which face wasforward. Yet both saw the same face forward. It was as if eachsaw the same cube or each was part of one mind only.

If this idea is correct, then consciousness is able to sensethings on an atomic scale. The possibility is mind-boggling.It means that new or novel events can be accepted at the atomiclevel, the level where potential reality becomes real reality.

Julian Jaynes, in his book. The Origin of Consciousnessin the Breakdown of the Bicameral Mind.^^ postulated thatintrospected volition—the ability to know that one is controllingone's own destiny—has been a recent addition on the evolutionaryscale. Jaynes also points out that today's schizophrenic is a''throwback," a return to the time before humans acquired their"willing" minds. Was it the ''one mind" communicating with themany minds? Was the event of the bicameral breakdown thatof a human being acquiring Bass's device? Did that event, threethousand years ago, occur because that person's neurons had atlast evolved the necessary close coupling with their unique firingchannels?

I suggest that this was the case. Humans had found out whothey were when they became atomically conscious. Or perhaps,better said, they had learned how to live in quantum reality.

The first documented case of quantum consciousness mayhave been Moses. When he asked, "Who are You?" of thePresence felt at the burning bush, the answer came: "I AMTHAT I AM." Moses then recognized that, within him, the GodVoice now spoke as Moses. And from that moment onward,humans began to control their destiny. When I picture the"one mind" piercing the individual atomic minds, I am remindedof the words of my teacher of the Cabala, Carlo Suares. Whenasked whether one must seek for one's soul, he replied, "No,don't worry, it will find you."^^ \iy higher self is seeking me.My "one mind" seeks to find my many scattered minds.

Is there evidence for this many-minded theory? Split-brainresearch indicates that we do indeed have many minds, eachacting in a complementary fashion with all the others.^^ WilliamJames, in Principles of Psychology, noted that

in certain persons the total possible consciousness may be split intoparts which coexist but mutually ignore each other, and share theobjects of knowledge between them. More remarkable still, theyare complementary.^^

If these split minds function atomically, perhaps thecomplementarity spoken of by James is the same comple-mentarity referred to and identified by Neils Bohr on the levelof atomic phenomena. Following this line of thinking, allmetaphors become nonmetaphorical; they are simply describingreality on several levels of perception at the same time. Forexample, your feeling of excitement is your atoms in excitedstates. Since we are clearly of the world, that complementarity ofatomic phenomena should also exist within ourselves. The sumtotal of all the complementary consciousnesses make up ournormally perceived world, that world of classical cause-effectreality.

But what about the quantum world? Do the various atomicminds that make up a person*s one mind communicate with eachother? Can you align your atomic minds in some coherentfashion? If so, the effect would be fantastic and quite magical.^^

Imagine your one mind as the chief of your CNS. Pictureyour individual atomic minds as agents acting independently.Remember that it makes no difference whether or not themolecule is "observed" pointing upward (t) or downward (i).In either case, as long as it is "observed," action is taken and amuscle fiber is contracted. Suppose that an atomic agent, actingalone, observes the following pattern over time:

time

►

Such a random mixture of up and down H's, although sufficientfor producing the necessary muscle contraction, hardly causesthe "chief," the "one mind" to stir. It is free to explore otherthings, other ideas, or other neuronal realities. As a result,that once-directed choice fades from consciousness; yet themuscle, now trained, contracts. Things happen more or lessmechanically. That random chain of arrows, corresponding to arandom mixture of high- and low-frequency buzzes on the line ofthe CNS, produces a quantum washout, a series of classical,objective experiences.

The integrated effect is sometimes my "H" is up, sometimesit's not. In other words, nothing unusual is happening. But that'sjust one agent acting alone. Suppose that now there are severalatomic minds acting and observing. Let's look at three typicalminds, each observing a particular chain of signals as before.

Let's label them minds 1, 2, and 3. Since we have three mindsacting, they are acting in different places. Their pattern ofobservations might appear as:

time

TTTiiTTiiiitnTTiiiiTTTiitimiiTTTiTiiTi (mind i)iiiTTiiTiTTiiiiTiTiiiiTtintitTiitmtiTi (mind 2)irnTiTiiTiTntiitiiTTnTiTiiiTTnTiTiiTT (mind 3)

Such a random sequence of sequences would appear to wash outall quantum experiences. These signals are also distributedspatially as well as temporally. Again, nothing to excite the chief.But now, the will participates. The atomic minds must noticeeach other. Not just a breakdown of bicamerality, but of atomicseparability is taking place. The atomic minds arecommunicating with each other. The effect would be startling,perhaps appear cosmic, to the mind filled with voices.And perhaps Moses saw the burning bush. The pattern of theindividual minds would be partially coherent; they would berepeating each other's patterns. It might appear something like:

time

TttiimiiittiTTiiiiTTTiinniiittnTiiti (mind d

II TtniTniimiTtiiiittnititiiiitttitiiti (mind2)

TtnmiiiittimiiittTiititiiiiTttitiin (mind 3)

Each mind senses the same pattern of arrows, each "hears"the same "drummer." Such a spatial correlation would benoticeable to "the boss," and a new awareness would be "felt."Suddenly, "I think, therefore I am."

Today we are edready familiar with such a spatial correlationexisting in several minds at once. Only the minds are in differentbodies. The rock concert experience is, I believe, such anexample. Group mediation produces a similar result, but so does"team spirit." Perhaps this is what we mean when we say thereare "good vibes" between people—their consciousness patternsare matching. Spatial correlation makes us of "one mind."

But how do we do it? How is an individual mind able toresonate its pattern to another mind? The answer is throughthe qwiff, that psychic conduit that ties us all together as one.And what happens if there is temporal as well as spatial

correlation? For example, suppose we had our three atomic mindsobserving this pattern:

time

TTTTTTTTTTTTTTTimiiimiiiiiTTTTTTTTrTTTTTT (mind i)TTTTTTTTTTTTTTTiiiiimmiiiiTTTTTTTTTTTTTTT (mind 2)TTTTTTTTTTTTTTTiiiimiiiiUiiTTTTTTTTTTTTTTT (mind 3)

Again, such a combination could not or would not be ignoredby the chief. It would be of extreme significance, a kind of"seeing" with an atomic magnifying glass. One would certainlyfeel a new awareness. Is this cosmic consciousness?

Is this what happened to a few individuals in the past,such as Buddha, Jesus, and others? Is this what is happeningnow to so many? I believe that the answer is yes. We arebeginning a new age of awareness, the age of quantum conscious-ness, the age of the conscious atom. By looking within ourselves,we may be able to solve the problems facing us on the finalfrontier—the frontier of the human spirit.

God's Will and Human Will

Some very old questions are still around. These questions concernhuman behavior, thoughts, and will. Can quantum mechanicsshed some light on such questions as: Am I just a machine? Howdoes my will act? What is God's will? Is there a God?

Most of these questions and others, I'm sure, regardingmind and matter have never been satisfactorily answered. Thesequestions all relate to human power to control and determinedestiny. Just how far do our human powers extend? Quantummechanics seems to point to the limits of human power. Theselimits refer to our knowledge and our ability to gain knowledge.The qwiff or quantum wave function is unobservable. Yet we feelthat it is an adequate model for determining the probabilities ofevents. Qwiffs flow in a perfectly orderly fashion. But then anobservation takes place. The orderly flow becomes a disorderlypop. A probability becomes an actuality. We humans seem tohave some control over our lives and yet we also seem to bepowerless victims to another will, another order.

Human Will and Human Consciousness 249

In this chapter, I have offered mostly speculative thoughts,models, and ideas about how quantum mechanics, God, humanthought, and will are related. I view quantum mechanics as verynecessary in human development and psychology. I feel that theunderlying order of the qwiff, the quantum mechanics of theuniverse, is God's will being done. Yet to us, this order appearsrandom and often without any meaning. In an earlier chapter, wesaw how the paradoxical cube appeared to have no special orderto its appearance. Sometimes the upper face of the cube seemedto pop out in front and sometimes the lower face. By letting twocubes have a past interaction, two separated observers observingseparated cubes later discovered that the order of theirobservations were identical. Yet each observer had in fact seenonly a random pattern without any meaning.

This example gives us a small glimpse of the unity of theuniverse. The observers' wills could not control the cubes. Yet thetwo observers found an order in their observations. This ordercould not be used for communication or manipulation. Eachobserver was free to choose what he or she wished. And yet eachsaw in the other's order of observation his or her own order.Perhaps this is the unique form of human communication. We areone to the extent that we stop manipulating each other. We aremany to the extent that our individual wills be done.

The cubes were analogies for quantum particles such aselectrons and atoms. But can the analogy go any farther? Canquantum mechanics help us to understand our own limits ofpower? If it can, perhaps the world could become a safer andmore enjoyable place to live in. Perhaps if people saw that therewas no way to break the uncertainty principle, wars would stop.Certainly, if people became aware that a power over anotherhuman being was impossible because of quantum physics, theworld would be a different place for all of us.

Quantum mechanics, perhaps more clearly than any religion,points to the unity of the world. It also points to somethingbeyond the physical world. It matters little which interpretationyou choose—parallel universes, Feynman paths of action, qwiffsthat flow and pop, or consciousness as the creator. All of theseinterpretations point to the mystery of the physical world from anonphysical perspective.

We might say that God's will is exercised in the world of theqwiff, the quantum wave function. It is a causal world of exactmathematical accuracy, but there is no matter present. It is aworld of paradox and utter confusion for human, limited

250 Losing Our Minds

intelligence. For it is a world where a thing both occupies a singleplace at a single time and occupies an infinite number of places atthe same time. Yet there is an explicit order to the paradox.There is a pattern to the many positions, a symmetry.

But we, who exist in the world of matter, can only disruptthat perfection of paradox by attempting to observe the pattern.We pay a large price for a material world. The price involves oursanity. We cannot make total order of our observations. Therealways appears to be something missing. This disruption ofGod's order appears to us as the Principle of Uncertainty. Thuswe become helpless, feel inadequate, and long for the order weare helpless to create in the universe. All we can do is go alongwith it.

On the other hand, we are free to choose. Our veryhelplessness to create a perfect order allows us to create. Youmight say that the uncertainty principle is a two-edged sword.It frees us from the past because nothing can be predetermined.It gives us the freedom to choose how we go about in theuniverse. But we cannot predict the results of our choices.We can choose, but we cannot know if our choices will besuccessful.

The alternative to this uncertain world is a certain world.In such a world, particles would follow well-determined pathswith exact locations at each and every point. But this alternativeis known to be unworkable. The tiny electron inside of everyatom would have to radiate each and every instant in such adetermined world. It would lose all of its energy and quickly fallinto the nucleus. All atoms would disappear. All electromagneticenergy would vanish. All nervous systems would cease theiractivity. All life would stop. For life as we know it can only existthrough the blessing of uncertainty, and security is a myth.

Yet security is there. We feel its presence. It is the longingfor the perfection of universal order that we all feel. It is felt asthe desire to crawl back into the universal womb. But, alas, wecannot do so and still remain in human bodies. We must acceptthe uncertainty of our positions. Without that uncertainty,there is no world.

Perhaps if we come to understand how modern physics,particularly quantum mechanics, can make us aware of the limitsof human will, we will learn to get along with each other. Evenbetter, we may realize our cosmic heritage as part of the greaterwill. I hope so.

IVotes

251

Chapter 1

1. J. Jaynes, The Origin of Consciousnessin the Breakdown of the Bicameral Mind(Boston: Houghton Mifflin Co., 1976),chaps. 3, 6.

2. F. Capra, The Tao of Physics (Berke-ley: Shambhala Publications, 1975),p. 21.

3. T. Dantzig, Number. The Language ofScience (New York: Doubleday & Co.,1956), pp. 125-129.

Chapter 2

1. R. March, Physics ^orPoets (New York:McGraw-Hill Book Co., 1970), p. 22.

2. K. Greider, Invitation to Physics (NewYork: Harcourt Brace Jovanovich,1973), p. 24.

3. Ibid., p. 32.

4. Ibid., p. 65.

5. L. Cooper, An Introduction to the Mean-ing and Structure of Physics (New York:Harper & Row, 1968), p. 9 (quote).

6. G. Holton and S. G. Brush, Introduc-tion to Concepts and Theories in Physi-cal Science, 2nd ed. (Reading, Mass.:Addison-Wesley Publishing Co., 1973),pp. 64-66.

7. R. March, Physics for Poets, p. 6.

8. K. Greider, Invitation to Physics,p. 73.

9. G. Holton and S. G. Brush, Conceptsand Theories, pp. 110-111.

10. F. Rutherford, G. Holton, and F. G.Watson, dirs.. The Project PhysicsCourse (New York: Holt, Rinehart &Winston, 1970), unit 2, chap. 8, p. 120.

11. R. March, Physics for Poets, p. 95.

12. Ibid.

13. C. G. Jung, ed., Man and His Symbols(New York: Dell Pubhshing Co., 1968),p. 9.

14. J. R. Burr and M. Goldinger, eds..Philosophy and Contemporary Issues(New York: The MacMillan Co., 1972),p. 254.

15. Ibid., p. 255.

16. Ibid., p. 259.

17. G. Holton and S. G. Brush, Conceptsand Theories, p. 345.

18. Ibid., p. 392.

19. Ibid., p. 420.

20. Ibid., p. 422.

21. M. Jammer, The Conceptual Develop-ment of Quantum Mechanics (NewYork: McGraw-Hill Book Co., 1966),pp. 14-22.

Chapter 3

1. M. Jammer, The Conceptual Develop-ment of Quantum Mechanics (NewYork: McGraw-Hill Book Co., 1966),p. 21. See also R. March, Physics forPoets (New York: McGraw-Hill BookCo., 1970), p. 190.

2. O. Theimer, A Gentleman's Guide toModem Physics (Belmont, Calif.: Wads-worth Publishing Co., 1973), p. 234.

3. M. Jammer, Conceptual Development,p. 19.

4. Ibid.

5. Ibid., p. 21.

6. A. Einstein, Podolsky, and Rosen, "CanQuantum-Mechanical Description ofPhysical Reality Be Considered Com-plete?" T/iePhysica/Kefiei/; 47 (1935): 37.

7. M. Jammer. Conceptual Development,p. 28.

8. A. B. Arons and M. B. Peppard, "Ein-stein's Proposal of the Photon Con-cept— A Translation of the Annalender Physik Paper of 1905," AmericanJournal of Physics 33 {1965): 368.

9. Ibid.

Chapter 4

1. R. March, Physics/"orPoets (New York:McGraw-Hill Book Co., 1970), p. 194.

Chapter 5

1. R. March, Physics for Poets {New York:McGraw-Hill Book Co., 1970), p. 207.

2. M. Jammer, The Conceptual Develop-ment of Quantum Mechanics (NewYork: McGraw-Hill Book Co., 1966),p. 243.

Notes

3. Ibid., p. 244.

4. Ibid., p. 251.

5. Ibid., p. 249.

6. Ibid., p. 257.

Chapter 6

1. M. Jammer, The Conceptual Develop-ment of Quantum Mechanics (NewYork: McGraw-Hill Book Co., 1966),p. 283.

2. Ibid.

3. W. Heisenberg, Physics and Beyond(New York: Harper & Row, 1971), p. 38.

4. M. Jammer, Conceptual Development,p. 329.

Chapter 7

1. M. Jammer, The Philosophy of Quan-tum Mechanics (New York: John Wiley& Sons, 1974), p. 86.

2. Ibid., p. 115.

3. Ibid.

4. Ibid., p. 116.

Chapter 8

1. E. Wigner, "The Problem of Measure-ment," American Journal of Physics31 (1963): 6. See also E. Witmer, "Inter-pretation of Quantum Mechanics andthefutureof Physics," American Jour-nal of Physics 35 (1962): 40; W.Wootters and W. Zurek, "Complemen-tarity in the double-slit experiment:Quantum nonseparability and a quan-titative statement of Bohr's principle,"Physical Review D 19 (1979): 473; H.Stapp, "Mind, Matter and QuantumMechanics," talk given at a Joint Psy-chology, Philosophy, and Physics Col-loquium, University of Nevada, Reno(October 20, 1967); H. Stapp, "TheCopenhagen Interpretation and theNature of Space-Time," American Jour-nal of Physics 40 (1972), p. 1098.

2. M. Jammer, The Philosophy of Quan-tum Mechanics (New York: John Wiley& Sons, 1974), p. 44.

3. See, for example, M. Gardiner, "Mathe-matical Games," Scientific American(May, 1979): 22.

4. P. Watzlawick, How Real is Real? (NewYork: Vintage Books, 1977), p. 208.Here Watzlawick discusses Newcomb'sparadox in the light of communicationparadoxes and relates this to our notionsof causality.

Chapter 9

1. A. Einstein, Podolsky, and Rosen, "CanQuantum-Mechanical Description ofPhysical Reality Be Considered Com-plete?" The Physical Review 47 (1935):777.

2. Ibid.

Chapter 10

1. A. Einstein, H. A. Lorentz, H. Weyl,and H. Minkowski, The Principle ofRelativity (New York: Dover Publica-tions, 1923), p. 63.

2. G. Feinberg, "Possibility of Faster-Than-Light Particles," Physical Review159(1967): 1089. Gerald Feinberg wasone of the first physicists to considertachyons seriously.

3. G. Benford, D. Book, and W. Newcomb,"The Tachyonic Antitelephone," Physi-cal Review D 2 (1970): 263. Benford,Book, and Newcomb discuss the amus-ing situation created by tachyons thatallow people to communicate with them-selves in their pasts. See also O.Bilaniuk, V. Deshpande, and E. Sudar-shan, " 'Meta' Relativity," AmericanJournal of Physics 30 (1962): 718.

4. Y. Terletskii, Paradoxes in the Theoryof Relativity (New York: Plenum Press,1968), p. 71.

Chapter 11

D. Bohm, Quantum T/ieory (EnglewoodCliffs, N.J.: Prentice-Hall, 1951).D. Bohm and B. Hiley, "On the Intui-tive Understanding of Non-locality asImplied by Quantum Theory," Founda-tions of Physics 5 (1975): 94.

3. Ibid.

4. D. Bohm and Y. Aharanov, "Discus-sion of Experimental Proof for the Para-dox of Einstein, Rosen, and Podolsky,"Physical Review D 108 (1957): 1070.

5. M. Jammer, The Conceptual Develop-ment of Quantum Mechanics (NewYork: McGraw-Hill Book Co., 1966),p. 324.

6. Ibid.

7. J. Bernstein, "I am This Whole World:Erwin Schroedinger," in Project PhysicsReader 5 (New York: Holt, Rinehart &Winston, 1968-69), p. 178 (quote).

8. Ibid.

9. Ibid., p. 179 (quote).

10. E. Schroedinger, "Discussions of Prob-ability Relations Between Separated

Notes

253

Systems," Cambridge PhilosophicalSociety Proceedings 31 (1935): 555.

Chapter 12

1. B. DeWitt and N, Graham, "ResourceLetter IQM-1 on the Interpretation ofQuantum Mechanics," American Jour-nal of Physics 39/7 (1971): 737. Thisarticle contains twelve references tothe EPR paradox and several refer-ences to hidden variables research.

2. D. Bohm, "A Suggested Interpreta-tion of the Quantum Theory in Termsof 'Hidden' Variables I," PhysicalReview 85 {1952): 166; D. Bohm and J.Bub, "A Refutation of the Proof byJauch and Piron that Hidden VariablesCan Be Excluded in Quantum Mechan-ics," Review of Modern Physics 38(1966): 470; D. Bohm and J. Bub, "AProposed Solution of the MeasurementProblem in Quantum Mechanics by aHidden Variable Theory," Reviews ofModern Physics 38 (1966): 453.

3. J. S. Bell, "On the Einstein PodolskyRosen Paradox," Physics 1 (1964):195-200.

4. R. Feynman, R. Leighton, and M.Sands, The Feynman Lectures on Phys-ics, vol. 1 (Reading, Mass.: Addison-Wesley Publishing Co., 1965), chap.26, p. 3.

5. Ibid.

6. F. Rutherford, G. Holton, and F. G.Watson, dirs.. The Project PhysicsCourse (New York: Holt, Rinehart &Winston, 1970), unit 2, chap. 9, p. 21.

7. R. Feynman, R. Leighton, and M.Sands, Feynman Lectures, vol. 2, chap.19, p. 9.

8. Ibid.

9. Ibid.

10. D. Bohm, "Suggested Interpretationof the Quantum Theory," p. 166.

11. M. Jammer, The Philosophy of Quan-tum Mechanics (New York: John Wiley& Sons, 1974), p. 291.

12. Ibid., p. 294.

13. M. Born. Natural Philosophy of Causeand Chance (London: Oxford Univer-sity Press, 1949), p. 93.

14. J. S. Bell, "On the Problem of HiddenVariables in Quantum Mechanics,"Reviews of Modern Physics 38 (1966):447.

15. J. S. Bell, "On the EPR Paradox," p.195-200.

16. Ibid., p. 199.

17. H. Stapp, "Are Superluminal Connec-tions Necessary?" II Nuovo Cimento40B (1977): 191; H. Stapp, "Bell'sTheorem and World Process," II NuovoCimento 29B/2 (1975): 270; H. Stapp,"Mind, Matter and Quantum Mechan-ics," talk given at a Joint Psychology,Philosophy, and Physics Colloquium,University of Nevada, Reno (October20, 1967); H. Stapp, "The CopenhagenInterpretation and the Nature of Space-Time," American Journal of Physics40 (1972): 1098; H. Stapp, "Theory ofReality," Foundations of Physics 7(1977): 313; H. Stapp, "WhiteheadianApproach to Quantum Theory and theGeneralized Bell's Theorem," Founda-tions of Physics 9 (1979): 1. The weird-ness of these results still causes con-cern among physicists; Stapp addresseshimself to Bell's results in these refer-ences. See also N. Herbert, "Crypto-graphic Approach to Hidden Variables,"American Journal of Physics 43 (1975):315; E. Wigner, "On Hidden Variablesand Quantum Mechanical Probabili-ties," American Journal of Physics 38(1970): 1005; Bernard d'Espagnat, "TheQuantum Theory and Reality," Scien-tific American (No-vemher, 1979): 158.

18. J. Clauser and M. Home, "ExperimentalConsequences of Objective Local Theo-ries," Physical Review D 10 (1974):532.

19. J. Clauser, Personal correspondence be-tween Karl Popper and John Clauser(August 30, 1974).

Chapter 13

1. C. Bloch, The Golem (New York: RudolfSteiner Publications, 1972), p. 1.

2. T. Johnston, "Will Your Next HomeAppliance Be a Mini-Computer?" NewWest (March 4, 1977), pp. 50-59.

3. K. O'Quinn, "The Whole World in YourHands!" Future Life 13 (1979): 52.

4. L. Bass, "A Quantum Mechanical Mind-Body Interaction," Foundations ofPhysics 5 (1975): 160 (quote).

5. M. Jammer, The Philosophy of Quan-tum Mechanics (New York: John Wiley& Sons, 1974), p. 499.

6. Ibid.

7. J. Mehra, "Quantum Mechanics andthe Explanation of Life," AmericanScientist 61 (1973): 722-728. Wigner's

Notes

9.10.

11.

12.

13.

14,

15.

16.

17.

ideas for extending quantum mechanicsto include consciousness are given inthis reference. For Wigner's views onconsciousness and quantum physics,see also E. Wigner, "The Problem ofMeasurement," American Journal ofPhysics 31 (1963): 6.B. DeWitt and N. Graham, eds., TheMany—Worlds Interpretation of Quan-tum Mechanics (Princeton: PrincetonUniversity Press, 1973), p. 3. This ref-erence contains Everett's thesis.M. Jammer, Philosophy, p. 500.B. DeWitt and N. Graham, eds., Many-Worlds Interpretation, quote in frontis-piece.

B. DeWitt, "Quantum Mechanics andReality," Physics Today (September,1970): 30; L. E. Ballentineet al., "Quan-tum Mechanics Debate," Physics Today(April, 1971): 36. These two articlescontain DeWitt's explanation of themany-worlds interpretation of quEintummechanics and the resultant rebuttalof reluctant physicists.B. DeWitt and N. Graham, "ResourceLetter IQM-1 on the Interpretation ofQuantum Mechanics," American Jour-nal of Physics S9/7 (1911): 116.L. Oteri, ed., "Quantum Physics andParapsychology," parts I and II, pro-ceedings of an international conference,Geneva, Switzerland, 1974 (New York:Parapsychology Foundation, 1975), pp.1-53. E. H. Walker, the author of thisarticle and one of the pioneers in thephysics of consciousness, follows Wig-ner's approach and Bohm's hiddenvariable approach.

B. DeWitt and N. Graham, "ResourceLetter IQM-1," pp. 110-119.Ibid., p. 114. Also see L. E. Ballentine,"The Statistical Interpretation of Quan-tum Mechanics," Reviews of ModernPhysics 42 (1970): 358.B. DeWitt and N. Graham, "ResourceLetter IQM-1," p. 151.Ibid.

R. Keynes, "Ion Channels in the Nerve-Cell Membrane," Scientific American(March, 1979): 126.C. Stevens, "The Neuron," ScientificAmerican (September, 1979): 55.L. Bass, "Mind-Body Interaction,"p. 161.Ibid., p. 167.Ibid., p. 168.

W. Penfield, The Mystery of the Mind(Princeton: Princeton University Press,1975), p. 109.

L. Bass, "Mind-Body Interaction,"p. 171.

J. Jaynes, The Origin of Consciousnessin the Breakdown of the Bicameral Mind(Boston: Houghton Mifflin Co., 1976).12. C. Suares, Personal Communication(Fall, 1974).

R. Ornstein, ed., The Nature of HumanConsciousness (New York: The VikingPress, 1974), part 2.M. Jammer, The Conceptual Develop-ment of Quantum Mechanics (NewYork: McGraw-Hill Book Co., 1966),p. 350.

R. M. Bucke, Cosmic Consciousness(New York: E. P. Dutton & Co., 1969);M. H. Chase, "The MatriculatingBrain," Psychology Today (June, 1973):82. Chase discusses the possibility ofthe willful control of a single neuron inthe human body. See also J. V. Bas-majian, "Control and Training of Indi-vidual Motor Units," Science 141 (1963):440-441. Basmajian discusses how themind singles out and controls the firingof a neuron through the technique ofbiofeedback.

Chapter 14

R. Feynman, "The Value of Science,"Project Physics Reader 1, AuthorizedInterim Version (1968-69), p. 3.Ibid., p. 4.

L. Bass, "A Quantum Mechanical Mind-Body Interaction," Foundations ofPhysics 5 (1975): 159.

255

Arons, A. B., and Peppard, M. B. "Ein-stein's Proposal of the Photon Concept—A Translation of the Annalen der PhysikPaper of 1905." American Journal ofPhysics 33 (1965), pp. 367-374.

Ballentine, L. E. "The Statistical Interpre-tation of Quantum Mechanics." Reviewsof Modern Physics 42 (1970), p. 358.

Ballentine, L. E.; Pearle, P.; Walker, E. H.;Sachs, M.; Koga, T.; Gerver, J.; andDeWitt, B. "Quantum MechanicsDebate." Physics Today (April, 1971),p. 36.

Basmajian, J. V. "Control and Training ofIndividual Motor Units." Science 141(1963), pp. 440-441.

Bass, L. "A Quantum Mechanical Mind-Body Interaction." Foundations of Phys-ics 5 (1975), p. 159.

Bell, J. S. "On the Einstein Podolsky RosenParadox." Physics 1 (1964), pp. 195-200.

Bell, J. S. "On the Problem of HiddenVariables in Quantum Mechanics." Re-views of Modern Physics 38 (1966), p. 447.

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Index

Acceleration, 43; Galileo'sexperiment on, 36

Achilles and the tortoise, 16, 21

Action: defined, 79; principle of leastaction, 196-98; and reaction law,39, 157

Active observation, 25-56; exemplifiedby Gahleo, 33, 36-37; interpreted byI. Newton, 37

Age of Certainty, 25, 28

Age of Reason, 28-29, 32

Air, sound waves in, 48, 49

Angular momentum, 79-80, 87, 88

Aristotle, 23, 29, 33, 46, 59; concept ofmotion, 13, 20-22, 36; and Galileo'sconcept of acceleration, 36; physicsof, 22

Arrows, motion of 17, 20, 21, 117

Atomic minds, 240-48

Atoms: colors of light determined by,48; with consciousness, 227, 228,239—48; existence based on observa-tion of, 6; in experiment on wave-particle duality, 134-37, 139-40;influenced by observation andthought, 2, 3, 6, 60; light emitted by,60, 79, 82, 85; methods to viewstructure of, 74-75, 108-11; nucleiof, 75, 79; size of, 73-74, 75, 78, 80

Atoms, structural models of, 73-81;Bohr's quantum model, 78-85, 111;J. J. Thompson's model, 74, 78;planetary model, 74, 75, 78; Schroe-dinger's theory, 94-97, 101, 102

Avogadro, Amadeo, 47

Balmer, Johann, 82

Bass, L,, 229; mind-body modelconceived by, 230-33, 239-43, 244

Being and change: in Cartesian

philosophy, 32; in Greek philosophy,11-12, 22, 32, 148

Bell, John Stewart, 193; local hiddenvariable theory of, 204-5

Bell's Theorem, 202-4, 205

Birkbeck College, 177, 212

Bohm, David, 177, 178, 193; quantumpotential conceived by, 200-201

Bohr, Niels, 59, 182, 191; collaborationwith Heisenberg, 105; comple-mentarity concept of, 118, 123, 127,130, 133-41, 150, 153, 201, 246;correspondence principle of, 128;debate with Einstein, 20, 61, 117,118-24, 151, 153, 201; discontinuityof atomic light discovered by, 60, 79,82, 85; early career of, 75, 78; orbitsof electrons studied by, 79-85, 87-88;

Planck's constant used by, 79, 80, 82;

quantum atomic model of, 78-85, 101,

111Bohr orbits, 82, 87; explanation of,

88-91Born, Max, 107, 117; on indeterministic

physics, 202; on wave-particle duality,

118-19; wave probability theory of,

101-5, 112Boyle, Robert, 47Brahe, Tycho, 29Brougham, Henry, 47Bruno, Giordano 25, 29

Cabala, 212, 245

Calculus, 27, 37

Causality violations, 166-68, 177

Cause and effect, 143; in Newtonian

physics, 42, 43; and reality, 185, 188Cavendish Laboratory, 74, 75Celestial mechanics, 43Central nervous system, 229-30; and

human will, 234-41, 247; and the

quantum mechanical mind-body

interpretation, 230-33. See also MindChoice: and the central nervous system,

231, 238; and consciousness, 239, 245;

freedom of, 250; in reality, 141, 144-45,

146, 150, 155, 177Clauser, John, 205Collapse of the wave function, 172;

debate on, 121-22; defined, 119Collective unconsciousness, 204Colors of light, 28; emitted by hot

objects, 28, 52-55, 59, 61Colston Research Society, 201"Complements of the Cosmic House,"

129,134Conditions for reality, 154—55Consciousness: acts of, 230, 241; of

atoms, 227, 228, 239-48; cosmic, 248;

and creation, 215-218; development

of, 10-11; future affected by, 211,

214, 215; interpretation of, 215, 225,

227, 228-29, 239; in quantum

mechanics, 220, 228-30, 245-48Continuists vs. discontinuists, 101,

117-24, 151, 153Continuity: desire for, 128; of

mechanics, 37-38, 59Continuity of motion: compared to

Bohr's studies of motion by electrons,

83-85; in Greek philosophy, 13, 20-22;

Heisenberg's attitude toward, 106;

in Newtonian physics, 38—39, 59Copenhagen interpretation of quantum

mechanics, 122, 127Copernicus, Nicolaus, 25, 28-29

259

Correlation: in classical mechanics,156—57; described in the EPR paper,158-63, 168-69; in quantummechanics, 157-58, 168-69, 179-81

Crime, and Newtonian physics, 38-39

Darrow, Clarence, 44-45

Davisson, Clinton, 92

De Broglie, Louis Victor, 117, 169;mathematical formula created by,91, 92, 101, 109, 140; matter wavesconceived by, 87-94, 101, 118

Descartes, Ren^, 25, 29-30; and

Newtonian physics, 46; and quantumsolipsism, 206

Destiny, 141; control of, 245, 248

Determinism, 118; defined, 42; andhidden variables, 204; and Newtonianphysics, 42-46; problems of, 43-46

Dewitt, Bryce S., 224

Dialectical materialism, 44

Discontinuity of motion, 23; of energyand light emitted by electrons, 78-79,85; Greek observations of, 13-17,18-20; of light waves, 63, 65-67, 68;opposed by continuists, 101, 117-24,151, 153

Double slit experiment, 3—5, 158-59.See also Wave-particle duality

Earth, position of in theuniverse, 28-29

E = hf formula, 87, 88, 101; in Bohr'stheory of atomic light, 79; creation of,65-67; Einstein's use of, 67, 68, 70;and Newtonian classical physics, 73

Einstein, Albert, 10, 62, 105; debatewith Bohr, 20, 61, 117, 118-24, 151,153, 201; on de Broglie's wave-particletheory, 91; EPR paper of, 151, 153-69,168-69, 193, 202, 204; Heisenberginfluenced by, 106-7; on observationof reality, 151; Planck's formula usedby, 67, 68, 70, 79; quanta theory oflight by, 68-71, 79, 81; on the speedof light, 165, 181; thought experi-ments of, 119, 153

"Einstein connection," 169, 202

"Einstein separability," 162

Einstein's Theory of Relativity, 46, 87,106-7, 162; and light speed, 165-68,181

Electricity, 25, 50, 73

Electromagnetic waves, theoreticaldiscovery of, 50-51

Electromagnetism, 50

Electronics industry, 113-14

Electrons, 73-85, 87; defined, 2, 228-29;discovery of, 73; and Einstein'squanta theory of light, 69-70; energyand light emitted by, 78-79, 82-85,87; observation of, 108-14, 118, 128;position and momentum of, 158-63;

"quantized" orbits of, 80, 82; quantumjumps by, 82, 83, 84-85; reflectionpatterns of, 92; stable orbits of, 78,80, 82

Elliot, Hugh, materialist philosophyof, 45-46

Elsasser, Walter, 92

Energy: radiated by electrons, 78-79,82-85; relative to the frequency oflight produced by, 65-66

Enzymes, 232-33, 239, 240

EPR Paradox, 151; described, 153-63;and the hidden variables in quantummechanics, 193, 202, 204; and obser-vation of correlation, 158-63, 168-69

Escher, Maurits, 129, 132, 150

"Ether," 22, 49-50, 51, 52, 54

Everett III, Hugh, 198; theory ofobservation, 211, 220-24

Existence of physical reality: conscious-ness of, 215—18; dependent on observa-vation, 184, 200, 216-18; objectivityand locality theory of, 205-7

Experimental physicists, 32, 37

Faraday, Michael, 25, 50Fermat, Pierre de, 195, 197Feynman, Richard, 194; on the human

mind, 228; imagination interpreted

by, 227; paths of particles studied

by, 196-98Flows, 169-75Fock, Vladimir, 201Franck, James, 92

Freedom, human, 44, 225, 244-45, 250Freud, Sigmund, and Newtonian

physics, 45Future, effect of consciousness on,

211, 214, 215

Galileo Galilei, 25, 33, 36-37

Gas: electrical discharges in, 73; role inthe development of heat and lighttheories, 47

Gay-Lussac, Joseph Louis, 47, 53

German Physical Society, 62

God, 11, 12, 37, 145; and Moses, 245;and quantum knowledge, 174; willof, 248-50

"Golems," 211-13

Graham, Neill, 224

Gravity, Newton's theory of, 29, 39, 43

Greeks, early observations by, 11-23,27, 29; on being and change, 11-12,22, 32, 148; on continuity of motion,20-22, 121; on discontinuity ofmotion, 13-17, 20, 121; wholenessconcept of, 11-12, 59, 61, 121

Heat: colors emitted by hot objects, 28,52-55, 59, 61; and Einstein's theory oflight, 68, 69; frequency of light wavesgenerated by, 65; nineteenth-centuryexplanations of, 47, 49

Index

Heisenberg, Werner, 21, 59, 118, 191;

on reality, 141. See also Principle of

UncertaintyHelium ions, 74, 75Hero of Alexandria, 194-195, 197Hertz, Heinrich, 51, 73Hidden variables, 121, 193; human

minds as, 205, 208; local and nonlocal,

202-4, 205; search for, 200, 201;

theories based on, 193, 202—5Hiley, Basil, 177, 178Human behavior, and Newtonian

physics, 44-45, 46Human beings: power of, 214-15, 225,

248; will of, 229, 230, 233, 234-41,

247, 248-50Hydrogen atoms, 73, 74, 234; Bohr's

model of, 78-80; light spectrum of, 82Huygens, Christiaan, 195-96

"I" awareness, 10-11, 12Ihnatowitz, Ed, 212-13Imagination, 184-86, 194, 196; power

and value of, 206, 227Impossibility, human capacity for, 225Infinity, 20, 21, 38Intermediate reality, 141Ions, 74

James, William, 245-46Jaynes, Julian, 11, 245Jeans, James, 227Jordan, Pascual, 107Jung, Carl, 204

Kelvin, Lord, 46, 51, 61Kepler, Johannes, 25, 29Knowledge, 174, 175, 225; and furtherinformation, 189, 190

Laplace, Pierre Simon, 43, 44

Laws of physics, 1; of conservation,27; determinism based on, 42-46; inNewtonian concepts, 38-39, 42, 157,197. See also Principles

Light, 25, 28; bulbs, 53; diffraction of,139, 198; discovery of the quantumnature of, 60, 63, 65-71; early explana-tions of, 46-52; economy of, 195—96;Einstein's theory of, 68-71, 87;emitted by electrons, 78-79, 82-85;Newton's theory of, 47; spectrum,53, 82, 83

Light speed, 174; constancy of, 52;particles moving faster than, 165—68;in space and time, 181-82

Light waves, 59; relationship betweenenergy and high-frequency waves of,65-66; relationship between lengthand frequency of, 54, 61; theory of,47-50, 62, 68, 196; wave-particleconcept of, 60, 68-71, 73, 87-94

Lilly, John, 228

Locality and objectivity, 205—7Loew, Rabbi, 212Lorentz, Hendrik, A., 118

Machines: with consciousness, 211-13;

universe viewed as, 42, 43"Magician's Choice," 130, 142-45, 149Magnetic field, discovery of, 50Magnetism, and electricity, 25, 50Marsden, Ernest, 75Marx, Karl, and Newtonian

physics, 44, 45Materialist philosophy, 44, 45-46Mathematics, 26-27, 29, 37; ofcontinuity, 27; formula on wave-particle relationships, 89, 91, 92;of operators, 107-8; Planck's formulaon light, 62, 64-67, 68, 70, 79;Schroedinger's wave equation, 94-96,101, 102, 112, 118-19, 170Matrix mechanics, 108Matter: Aristotle's concept of, 22; wavesand particles in, 3—5. See also Mind-body problem; Wave-particle duality"Matter waves," 88-93, 118, 186Maxwell, James Clerk, 25, 61; theoryof electromagnetic waves developedby, 50-51, 54Mechanical Age, 25, 27; end of, 56, 59Mechanical clocks, discovery of, 33Mechanical models, end of, 105-15Mechanical universe, interpreted by

Einstein, 68Methylamine, 232Michelson, A. A., 46, 51, 52, 61Microscopes, observation of electrons

in, 108-11, 114Mind: body perceived by, 10-11; defined,227-28; and hidden variables, 208;location of, 244-45; and Newtonianphysics, 45; observation influenced by,146-48, 150-51, 171, 183-86, 206,208, 218; relationship between atomicand human minds, 240-48Mind-body problem, 229; quantum

mechanical model of, 230-33, 239-43Molecules, 234Morley, E. W., 51, 52, 61Motion, 9-10; Cartesian theory of, 32;Galileo's theory of, 37; Newtoniantheory of, 38-39, 42; in quantummechanics, 1, 3. See also Continuityof motion; Discontinuity of motion

Neon signs, 73

Neutrons, discovery of, 92

Neutron stars, 78

Newcomb's Paradox, 130, 148-50

Newcomb, William, 148

New physics, 1. See also Quantum

mechanicsNewtonian classical physics: compared

to Bohr's theory of atomic light.

Index

261

83-85; compared to quantummechanics, 200; and conflictingexplanations of heat and light, 46-56passim; correlation in, 156—57, 160;impact of the Planck-Einstein formulaon, 73; laws of, 27, 29, 38-39, 42, 157,197; and matter waves, 93; scientificassumptions of, 56; social impactof, 42-46

Newton, Isaac, 37-39, 42; attitude

towards observation, 37, 38; scientificheritage of, 25, 28-29, 32-33, 36-37

Nobel Prize in physics: to M. Born, 102;to de Broglie, 91; to Einstein, 71; toHeisenberg, 21; to Planck, 63; toE. Wigner, 211, 214

Nonlocality, 177

Objectivity: and locality, 205-7; andobservation, 146

Observation: active, 25-26; atoms andmatter influenced by, 2, 3, 6, 9, 21; bychildren, 10; construction of realityby mental acts, 128; contradictoryperceptions of, 127-51, 222-24;disturbance caused by, 60, 117, 128,172, 174-75, 186, 201; of electrons,108-14, 118; passive, 8-23; predictionsbased on, 155, 158, 160; and predeter-minism, 144-45; in quantummechanics, 170-75, 178-81; role of theobserver's mind in, 146-48, 171,183-86, 206, 208, 219; synchronistic,169-75, 178-81

Observers: "case of the vanishingobserver," 130, 146-48; choices of,178-81; disagreement and agreementamong, 221-24; and existence ofphysical reality, 184, 200, 216-18;first active observer, 33, 36-37; identi-fication with the universe, 182-83;as machines with memory, 211-13

Paradoxical Cube, 129, 130-33, 137,146-47; and atomic minds, 244; andcorrelation, 178-81; and reality inquantum physics, 186

Parallel universes, 211, 218-25

Particles: correlation of, 156-60; experi-ments on wave-particle duality, 305,119-21, 134-37, 158-59; movingfaster than light, 165-68; paths of,196-98. See also Wave-particle duality

Pencil atoms, 134-37, 147

Penfield, Wilder, 244

p = h/L formula, 91, 92, 101, 140

Photoelectric effect, 70-71

Photons, 70, 87; development of thetheory of, 68-71; and observation ofelectrons, 109-11; and observation ofstarlight, 170-74, 200

"Physis," Greek concept of, 22, 148

Planck, Max, 58, 61, 105, 117; discon-tinuity of light waves discovered by,62-67; Einstein influenced by, 67,68, 70, 71; mathematical formulacreated by, 62, 64-67, 68, 70, 79, 82,87, 88, 91

Planck's constant, 65, 88, 89, 91; inBohr's atomic model, 79, 80, 82;smallness of, 122, 154

Podolsky, Boris, 153, 154, 193

Popper, Karl, 206-7

Pops, 169-75; defined, 170, 219

Positivism, 206-7

Predeterminism, 144-45; vs. freewill,148-50; in quantum mechanics, 214

Prediction, 219-20

Princeton University, 153

Principle of Complementarity, 118, 123,127, 130, 153, 201, 246; in brainfunctions, 245-46; defined, 132;impact of, 139; and wave-particleduality, 133-41, 150

Principle of Correspondence, 85,107-8, 128

Principle of Indeterminism. See Principleof Uncertainty

Principle of least action, 196-98

Principle of Uncertainty (Heisenberg'sPrinciple of Indeterminism), 1, 21,141, 153, 211; described, 105-15;and existence of objects, 200, 201;and God's order, 250; interpretationof, 117, 122, 123, 124

Probability interpretation, 61; in Bom'swave theory, 102-4, 118

Quanta, in Einstein's theory oflight, 68-70

"Quantized" orbits of electrons, 80, 82

Quantum: connection, 168-69, 211; link,181; potential, 200-201; solipsism,183, 206, 207-8; wave functions,169-70, 186

"Quantum leap": defined, 1; by elec-trons, 82,83,84-85

Quantum mechanics: challenges to thecompleteness of, 153-63, 191, 193,202, 204, 221; concept of correlationin, 157-63, 168-69, 179-81; debate oncontinuity vs. discontinuity of motion,117-24, 151, 153; defined, 1; discoveryof 1, 2, 9, 25, 28, 68-70; Einstein'scriticism of, 153-63, 168-69; of humanconsciousness, 220, 228-30, 245-48;paradoxes in, 2-6, 148-50, 215-18;relativity of continuous and discon-tinuous motion in, 85

Quantum physics, 1. See also Quantummechanics

Quantum: the, defined, 66; discovery of,60, 62, 66, 70; smallness of, 150

Quantum Theory (David Bohm), 177

Index

Qwiffs: the Big Qwiff, 22, 223, 224; andthe central nervous system, 231;defined, 170, 186; entanglement andmultiplication of, 188-89; flows andpops, 169-75; future influenced by,214; and God's will, 248-50; andmatter waves, 186; reality representedby, 219-220; superimposition of,186-88 . .

Rayleigh, Lord, 54, 61

Reality: conditions for, 154-55; contra-dictory perceptions of, 127-51;objectivity and locality in, 205—8;"out there" and "in there," 184-85,186; potential, 140-41; in quantummechanics, 184-91, 200, 205-8,214-18, 219-25; role of choice in, 141,144-45, 146, 150, 155, 177; search foran unseen order in, 194-98, 200, 201,204-5, 250

Relativity theory. See Einstein's Theoryof Relativity

Rosenfeld, Leon, 201

Rosen, Nathan, 153, 154, 193

Running, and discontinuity of motion,15-16, 20-21

Rutherford, Ernest: and Bohr's atomicmodel, 78; planetary model of atomspresented by, 75

Rutherford nuclear atom, 75

Schroedinger, Erwin, 117, 169; on

knowledge and information, 189-90;

on representatives of objects, 188-89;

universe interpreted by, 182-83; wave

equation and theory conceived by,

94-97, 101, 102, 112, 118-19, 170, 183,

188,200Schroedinger pulse, 97-99, 102, 112,

114, 118"Schroedinger's Cat," 189-91, 215, 216,

220, 234-35Scientist-analysts, 25-26, 28-29Solvay conference, 117Sound waves, 48-49; harmony and beats

in, 48, 88, 94, 101; in sculpture,

212-13; speed of, 52Space: Newtonian concept of, 38;

separability of, 178, 181; and

time, 181-82Spreading time, 114Standing waves, 88-91Stanford Linear Accelerator, 193Starlight, observation of, 170-73, 200Statistical predictions of quantum

mechanics, 203Suares, Carlo, 245Subject-object distinction, 10-11Sunlight: colors in, 47; travel to

earth, 47, 49Superposition of qwiffs, 186—88Superposition Principle, 186Synchronistic quantum connections,

169-75; and nonlocality, 177

Tachyons, 204; defined, 165; and light-speed, 165-67

Theoretical physics, precedents of,14, 37

Thomson, J. J.: atomic model of, 74,78; electrons discovered by, 73; andNiels Bohr, 75-76

Thought experiments, 119, 129, 153;defined, 132-33

Thoughts, qwiffs created by, 188. Seealso Mind

Time: in the central nervous system,236; in early Greek philosophy, 12, 20;and human aspirations, 225; interpre-tation of, 178; in Newtonian physics,27-28, 38; in quantum mechanics, 186,215. See also Future

"Ultraviolet catastrophe," 52-55, 62

Uncertainty Principle. See Principleof Uncertainty

Units, in physics, 79

Universe: affected by observation, 6,150, 172, 174, 219, 220; Cartesiantheory of, 32; location of the earth in,28-29; materialist views of, 44, 45-46;mechanical model of, 25, 42, 43, 59,68; order of, 6, 184-98; parallel, 211,218-25; wholeness and unity of,177-91 passim, 249

University of London, 212

University of Queensland, 229

Vaserely, Victor, 129, 132, 133

Wave-particle duality, 129; debate on118-24; de Broglie's theory of, 91-92;defined, 132; in the EPR model,158-63; experiments on, 3-5, 119-21,134-37, 139-40, 158-59; and thePrinciple of Complementarity, 132,133-41, 150; probability interpretationof, 61, 101-4, 118

Waves: bending of, 139, 198; Bom'stheory of probability of, 101-4, 112;in early theories of light and heat,47-52; electromagnetic, 50-51; inter-ference patterns, 48-49, 139, 140;length and frequency of, 54; of"matter," 87-93, 118; quantum wavefunction, 169-70, 186; Schroedinger'stheory of, 94-99, 101, 112, 114, 118;standing, 88-91

Wheeler, John A., 152, 192

Wigner, Eugene, consciousness theoryof, 211, 214-15

"Wigner's Friend," paradox of, 211,215-18, 220

Young, Thomas, wave theory of lightconceived by, 47-49, 50, 51, 62

Zeno, 59, 61, 117, 121; discontinuity ofmotion interpreted by, 3-17, 20-22,23; as a theoretical physicist, 14, 63

SCIENCE

A FASCINATING JOURNEY FROMFUNDAMENTAL CONCEPTS OF PHYSICS TOTHE FURTHEST LIMITS OF SCIENCEAND IMAGINATION

TAKING THE QUANTUM LEAP traces the history of physics from theobservations of the early Greeks, through the discoveries of GaHleo andNewton, to the dazzling theories of such scientists as Planck, Einstein,Bohr, and Bohm. Tl;iis blend of history, conceptual understanding, andspeculation carries the reader from a solid, nontechnical grasp of con-temporary physics to mindstretching visions of how quantum mechanics,God, human thought, and will are related.

Entertaining, informative, and witty, TAKING THE QUANTUM LEAPmakes modern theoretical physics accessible to the general reader. Itpresents a humanized view of science that is historically accurate, wellresearched and documented, and rich in profound implications for ourunderstanding of the nature of reality and our relationship to the cosmos.Author/physicist Fred Wolf provides clear explanations and generousillustrations to make comprehensible such concepts as quantum mechanics,telepathy, relativity, parallel universes, faster-than-light communication,and the connections between human psychology and modern physics.

The new physics, as outlined in TAKING THE QUANTUM LEAP,appears to describe a universe that includes us in a very special way: itmay well be that the order of the universe is the order of our own minds.Challenging and exhilarating, TAKIN(} THE QUANTUM LEAP givesus a solid grasp on the latest crucial—but often intimidating—findingsin science and technology, reveals the previously unexpected Hnksbetween the person and the cosmos, and offers startling new insightsinto the nature and potential of human consciousness.

Fred Alan Wolf, formerlyProfessor of Physics at San DiegoState University, is a scienceconsultant working with giftedchildren in California schools andco-author of the best-sellingSpace -Time and Beyond. He isthe author of numerous scientificarticles published in variousperiodicals and has lecturedextensivelv around the world.

HARPER & ROW, PUBLISHERS

Cover design: Design Office

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Photo: Scot Sothern