QUANTUM MECHANICS IS a branch of physics. There are several branches of physics. Most physicists believe that sooner or later they will construct an overview large enough to incorporate them all.
According to this point of view, we eventually will develop, in principle, a theory which is capable of explaining everything so well that there will be nothing left to explain. This does not mean, of course, that our explanation necessarily will reflect the way that things actually are. We still will not be able to open the watch, as Einstein put it, but every occurrence in the real world (inside the watch) will be accounted for by a corresponding element of our final supertheory. We will have, at last, a theory that is consistent within itself and which explains all observable phenomena. Einstein called this state the “ideal limit of knowledge”.1
This way of thinking runs into quantum mechanics the same way that the car runs into the proverbial brick wall. Einstein spent a large portion of his career arguing against quantum mechanics, even though he himself made major contributions to its development. Why did he do this? To ask this question is to stand at the edge of an abyss, still on the solid ground of Newtonian physics, but looking into the void. To answer it is to leap boldly into the new physics.
Quantum mechanics forced itself upon the scene at the beginning of this century. No convention of physicists voted to start a new branch of physics called “quantum mechanics”. No one had any choice in the matter, except, perhaps, what to call it.
A “quantum” is a quantity of something, a specific amount. “Mechanics” is the study of motion. Therefore, “quantum mechanics” is the study of the motion of quantities. Quantum theory says that nature comes in bits and pieces (quanta), and quantum mechanics is the study of this phenomenon.
Quantum mechanics does not replace Newtonian physics, it includes it. The physics of Newton remains valid within its limits. To say that we have made a major new discovery about nature is one side of a coin. The other side of the coin is to say that we have found the limits of our previous theories. What we actually discover is that the way that we have been looking at nature is no longer comprehensive enough to explain all that we can observe, and we are forced to develop a more inclusive view. In Einstein’s words:
. . . creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.2
Newtonian physics still is applicable to the large-scale world, but it does not work in the subatomic realm. Quantum mechanics resulted from the study of the subatomic realm, that invisible universe underlying, embedded in, and forming the fabric of everything around us.
In Newton’s age (late 1600’s), this realm was entirely speculation. The idea that the atom is the indivisible building block of nature was proposed about four hundred years before Christ, but until the late 1800’s it remained just an idea. Then physicists developed the technology to observe the effects of atomic phenomena, thereby “proving” that atoms exist. Of course, what they really proved was that the theoretical existence of atoms was the best explanation of the experimental data that anyone could invent at the time. They also proved that atoms are not indivisible, but themselves are made of particles smaller yet, such as electrons, protons, and neutrons. These new particles were labeled “elementary particles” because physicists believed that, at last, they really had discovered the ultimate building blocks of the universe.
The elementary particle theory is a recent version of an old Greek idea. To understand the theory of elementary particles, imagine a large city made entirely of bricks. This city is filled with buildings of all shapes and sizes. Every one of them, and the streets as well, have been constructed with only a few different types of brick. If we substitute “universe” for “city” and “particle” for “brick”, we have the theory of elementary particles.
It was the study of elementary particles that brought physicists nose to nose with the most devastating (to a physicist) discovery: Newtonian physics does not work in the realm of the very small! The impact of that earthshaking discovery still is reshaping our world view. Quantum mechanical experiments repeatedly produced results which the physics of Newton could neither predict nor explain. Yet, although Newton’s physics could not account for phenomena in the microscopic realm, it continued to explain macroscopic phenomena very well (even though the macroscopic is made of the microscopic)! This was perhaps the most profound discovery of science.
Newton’s laws are based upon observations of the everyday world. They predict events. These events pertain to real things like baseballs and bicycles. Quantum mechanics is based upon experiments conducted in the subatomic realm. It predicts probabilities. These probabilities pertain to subatomic phenomena. Subatomic phenomena cannot be observed directly. None of our senses can detect them.fn1 Not only has no one ever seen an atom (much less an electron), no one has ever tasted, touched, heard, or smelled one either.
Newton’s laws depict events which are simple to understand and easy to picture. Quantum mechanics depicts the probabilities of phenomena which defy conceptualization and are impossible to visualize. Therefore, these phenomena must be understood in a way that is not more difficult than our usual way of understanding, but different from it. Do not try to make a complete mental picture of quantum mechanical events. (Physicists make partial pictures of quantum phenomena, but even these pictures have a questionable value). Instead, allow yourself to be open without making an effort to visualize anything. Werner Heisenberg, one of the founders of quantum physics, wrote:
The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive concepts cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use them of elementary particles.3
The idea that we do not understand something until we have a picture of it in our heads is a by-product of the Newtonian way of looking at the world. If we want to get past Newton, we have to get past that.
Newton’s first great contribution to science was the laws of motion. If an object, said Newton, is moving in a straight line, it will continue moving in a straight line forever unless it is acted upon by something else (a “force”). At that time its direction and speed will be altered, depending upon the magnitude and direction of the force which it encounters. Furthermore, every action is accompanied by an equal and opposite reaction.
Today, these concepts are quite familiar. However, if we mentally project ourselves three hundred years into the past, we can see how remarkable they really are.
First, Newton’s first law of motion defied the accepted authority of the day, which was Aristotle. According to Aristotle, the natural inclination for a moving object is to return to a state of rest.
Second, Newton’s laws of motion describe events which were unobservable in the 1600’s. In the everyday world, which was all that Newton had to observe, moving objects always do return to a state of rest because of friction. If we put a wagon in motion, it encounters friction from the air through which it passes, from the ground its tires move on, from the axles that its wheels turn around, and, unless it is rolling downhill, sooner or later it comes to rest. We can streamline the wagon, grease the wheels, and use a smooth road, but this only reduces the effect of friction. Eventually the wagon stops moving, apparently on its own.
Newton never had the chance to see a film of astronauts in space, but he predicted what they would encounter. When an astronaut releases a pencil in front of him, nothing happens. It just stays there. If he gives it a push, off it goes in the direction of the push until it bumps into a wall. If the wall were not there, the pencil would continue to move uniformly, in principle, forever. (The astronaut also moves off in the opposite direction, but much more slowly because of his greater mass).
Third, Newton’s premise was “I make no hypotheses” (“Hypotheses non fingo”), which means that he based his laws upon sound experimental evidence, and nothing else. His criteria for the validity of everything that he wrote was that anyone should be able to reproduce his experiments and come up with the same results. If it could be verified experimentally, it was true. If it could not be verified experimentally, it was suspect.
The church took a dim view, to say the least, of this position. Since it had been saying things for fifteen hundred years which hardly were subject to experimental verification, Newtonian physics, in effect, was a direct challenge to the power of the church. The power of the church was considerable.fn2 Shortly before Newton’s birth, Galileo was seized by the Inquisition for declaring that the earth revolves around the sun and for drawing unacceptable theological implications from his beliefs. He was forced to recant on penalty of imprisonment or worse. This made a considerable impression on many people, among them another founder of modern science, the Frenchman, René Descartes.
In the 1630’s Descartes visited the royal gardens at Versailles, which were known for their intricate automata. When water was made to flow, music sounded, sea nymphs began to play, and a giant Neptune, complete with trident, advanced menacingly. Whether the idea was in his mind before this visit or not, Descartes’s philosophy, which he supported with his mathematics, became that the universe and all of the things in it also were automata. From Descartes’s time to the beginning of this century, and perhaps because of him, our ancestors began to see the universe as a Great Machine. Over the next three hundred years they developed science specifically to discover how the Great Machine worked.
Newton’s second great contribution to science was his law of gravity. Gravity is a remarkable phenomenon, even though we take it for granted. For example, if we hold a ball off the ground, and then release it, the ball falls straight down to the ground. But how did that happen? The ground did not reach up and pull the ball down, yet the ball was pulled to the earth. The old physics called this unexplainable phenomenon “action-at-a-distance”. Newton himself was as puzzled as anyone. He wrote in his famous Philosophiae Naturalis Principia Mathematica:
. . . I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses . . . it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies . . .4
Newton clearly felt that a true understanding of the nature of gravity was beyond comprehension. In a letter to Richard Bently, a classical scholar, he wrote:
. . . that one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.5
In short, action-at-a-distance could be described, but it could not be explained.
Newton’s thesis was that the same force which pulls apples downward also keeps the moon in orbit around the earth and the planets in orbit around the sun. To test his idea, he calculated various movements of the moon and the planets, using his own mathematics. Then he compared his findings with the observations of astronomers. His calculations and their observations matched! In one stroke Newton set aside the assumption of an essential difference between earthly and heavenly objects by showing that both of them are governed by the same laws. He established a rational celestial mechanics. What had been the purview of the gods, or God, came now within the comprehension of mortals. Newton’s gravitational law does not explain gravity (that was done by Einstein in his general theory of relativity) but it does subject the effects of gravity to a rigorous mathematical formalism.
Newton was the first person to discover principles in nature which unify large tracts of experience. He abstracted certain unifying concepts from the endless diversity of nature and gave those concepts mathematical expression. Because of this, more than anything else, Newton’s work has influenced us so forcefully. Newton showed us that the phenomena of the universe are structured in rationally comprehensible ways. He gave us the most powerful tool in history. In the West we have used this tool, if not wisely, certainly to the best of our ability. The results, both positive and negative, have been spectacular. The story of our enormous impact on our environment begins with the work of Newton.
It was Galileo Galilei who, following the Middle Ages, first quantified the physical world. He measured the motion, frequency, velocity, and duration of everything from falling stones to swinging pendulums (like the chandelier in his cathedral). It was René Descartes who developed many of the fundamental techniques of modern mathematics and gave us the picture of the universe as a Great Machine. It was Isaac Newton who formulated the laws by which the Great Machine runs.
These men struck boldly against the grip of scholasticism, the medieval thought system of the 12th to the 15th centuries. They attempted to place “man” at the center of the stage, or at least back on the stage; to prove to him that he need not be a bystander in a world governed by unfathomable forces. It is perhaps the greatest irony of history that they accomplished just the opposite.
Joseph Weizenbaum, a scientist at the Massachusetts Institute of Technology, wrote, in reference to computers:
Science promised man power. . . . But, as so often happens when people are seduced by promises of power, the price is servitude and impotence. Power is nothing if it is not the power to choose.6
How did this happen?
Newton’s laws of motion describe what happens to a moving object. Once we know the laws of motion we can predict the future of a moving object provided that we know certain things about it initially. The more initial information that we have, the more accurate our predictions will be. We also can retrodict (predict backward in time) the past history of a given object. For example, if we know the present position and velocity of the earth, the moon, and the sun, we can predict where the earth will be in relation to the moon and the sun at any particular time in the future, giving us a foreknowledge of eclipses, seasons, and so on. In like manner, we can calculate where the earth has been in relation to the moon and the sun, and when similar phenomena occurred in the past.
Without Newtonian physics the space program would not be possible. Moon probes are launched at the precise moment when the launch site on the earth (which simultaneously is rotating around its axis and moving forward through space) is in a position, relative to the landing zone on the moon (which also is rotating and moving) such that the path traversed by the spacecraft is the shortest possible. The calculations of the earth, moon, and spacecraft movements are done by computer, but the mechanics used are the same ones that are described in Newton’s Philosophiae Naturalis Principia Mathematica.
In practice, it is very difficult to know all the initial circumstances pertaining to an event. Even a simple action such as bouncing a ball off a wall is surprisingly complex. The shape, size, elasticity and momentum of the ball, the angle at which it was thrown, the density, pressure, humidity and temperature of the air, the shape, hardness and position of the wall, to name a few of the essential elements, are all required to know where and when the ball will land. It is increasingly difficult to obtain all of the data necessary for accurate predictions when more complex actions are involved. According to the old physics, however, it is possible, in principle, to predict exactly how a given event is going to unfold if we have enough information about it. In practice, it is only the enormity of the task that prevents us from accomplishing it.
The ability to predict the future based on a knowledge of the present and the laws of motion gave our ancestors a power they had never known. However, these concepts carry within them a very dispiriting logic. If the laws of nature determine the future of an event, then, given enough information, we could have predicted our present at some time in the past. That time in the past also could have been predicted at a time still earlier. In short, if we are to accept the mechanistic determination of Newtonian physics—if the universe really is a great machine—then from the moment that the universe was created and set into motion, everything that was to happen in it already was determined.
According to this philosophy, we may seem to have a will of our own and the ability to alter the course of events in our lives, but we do not. Everything, from the beginning of time, has been predetermined, including our illusion of having a free will. The universe is a prerecorded tape playing itself out in the only way that it can. The status of men is immeasurably more dismal than it was before the advent of science. The Great Machine runs blindly on, and all things in it are but cogs.
According to quantum mechanics, however, it is not possible, even in principle, to know enough about the present to make a complete prediction about the future. Even if we have the time and the determination, it is not possible. Even if we have the best possible measuring devices, it is not possible. It is not a matter of the size of the task or the inefficiency of detectors. The very nature of things is such that we must choose which aspect of them we wish to know best, for we can know only one of them with precision.
As Niels Bohr, another founder of quantum mechanics, put it:
. . . In quantum mechanics, we are not dealing with an arbitrary renunciation of a more detailed analysis of atomic phenomena, but with a recognition that such an analysis is in principle excluded.7 (Italics in the original)
For example, imagine an object moving through space. It has both a position and a momentum which we can measure. This is an example of the old (Newtonian) physics. (Momentum is a combination of how big an object is, how fast it is going, and the direction that it is moving). Since we can determine both the position and the momentum of the object at a particular time, it is not a very difficult affair to calculate where it will be at some point in the future. If we see an airplane flying north at two hundred miles per hour, we know that in one hour it will be two hundred miles farther north if it does not change its course or speed.
The mind-expanding discovery of quantum mechanics is that Newtonian physics does not apply to subatomic phenomena. In the subatomic realm, we cannot know both the position and the momentum of a particle with absolute precision. We can know both, approximately, but the more we know about one, the less we know about the other. We can know either of them precisely, but in that case, we can know nothing about the other. This is Werner Heisenberg’s uncertainty principle. As incredible as it seems, it has been verified repeatedly by experiment.
Of course, if we picture a moving particle, it is very difficult to imagine not being able to measure both its position and momentum. Not to be able to do so defies our “common sense”. This is not the only quantum mechanical phenomenon which contradicts common sense. Commonsense contradictions, in fact, are at the heart of the new physics. They tell us again and again that the world may not be what we think it is. It may be much, much more.
Since we cannot determine both the position and momentum of subatomic particles, we cannot predict much about them. Accordingly, quantum mechanics does not and cannot predict specific events. It does, however, predict probabilities. Probabilities are the odds that something is going to happen, or that it is not going to happen. Quantum theory can predict the probability of a microscopic event with the same precision that Newtonian physics can predict the actual occurrence of a macroscopic event.
Newtonian physics says, “If such and such is the case now, then such and such is going to happen next.” Quantum mechanics says, “If such and such is the case now, then the probability that such and such is going to happen next is . . . (whatever it is calculated to be).” We never can know with certainty what will happen to the particle that we are “observing”. All that we can know for sure are the probabilities for it to behave in certain ways. This is the most that we can know because the two data which must be included in a Newtonian calculation, position and momentum, cannot both be known with precision. We must choose, by the selection of our experiment, which one we want to measure most accurately.
The lesson of Newtonian physics is that the universe is governed by laws that are susceptible to rational understanding. By applying these laws we extend our knowledge of, and therefore our influence over, our environment. Newton was a religious person. He saw his laws as manifestations of God’s perfection. Nonetheless, Newton’s laws served man’s cause well. They enhanced his dignity and vindicated his importance in the universe. Following the Middle Ages, the new field of science (“Natural Philosophy”) came like a fresh breeze to revitalize the spirit. It is ironic that, in the end, Natural Philosophy reduced the status of men to that of helpless cogs in a machine whose functioning had been preordained from the day of its creation.
Contrary to Newtonian physics, quantum mechanics tells us that our knowledge of what governs events on the subatomic level is not nearly what we assumed it would be. It tells us that we cannot predict subatomic phenomena with any certainty. We only can predict their probabilities.
Philosophically, however, the implications of quantum mechanics are psychedelic. Not only do we influence our reality, but, in some degree, we actually create it. Because it is the nature of things that we can know either the momentum of a particle or its position, but not both, we must choose which of these two properties we want to determine. Metaphysically, this is very close to saying that we create certain properties because we choose to measure those properties. Said another way, it is possible that we create something that has position, for example, like a particle, because we are intent on determining position and it is impossible to determine position without having some thing occupying the position that we want to determine.
Quantum physicists ponder questions like, “Did a particle with momentum exist before we conducted an experiment to measure its momentum?”; “Did a particle with position exist before we conducted an experiment to measure its position?”; and “Did any particles exist at all before we thought about them and measured them?” “Did we create the particles that we are experimenting with?” Incredible as it sounds, this is a possibility that many physicists recognize.
John Wheeler, a well-known physicist at Princeton, wrote:
May the universe in some strange sense be “brought into being” by the participation of those who participate? . . . The vital act is the act of participation. “Participator” is the incontrovertible new concept given by quantum mechanics. It strikes down the term “observer” of classical theory, the man who stands safely behind the thick glass wall and watches what goes on without taking part. It can’t be done, quantum mechanics says.8
The languages of eastern mystics and western physicists are becoming very similar.
Newtonian physics and quantum mechanics are partners in a double irony. Newtonian physics is based upon the idea of laws which govern phenomena and the power inherent in understanding them, but it leads to impotence in the face of a Great Machine which is the universe. Quantum mechanics is based upon the idea of minimal knowledge of future phenomena (we are limited to knowing probabilities) but it leads to the possibility that our reality is what we choose to make it.
There is another fundamental difference between the old physics and the new physics. The old physics assumes that there is an external world which exists apart from us. It further assumes that we can observe, measure, and speculate about the external world without changing it. According to the old physics, the external world is indifferent to us and to our needs.
Galileo’s historical stature stems from his tireless (and successful) efforts to quantify (measure) the phenomena of the external world. There is great power inherent in the process of quantification. For example, once a relationship is discovered, like the rate of acceleration of a falling object, it matters not who drops the object, what object is dropped, or where the dropping takes place. The results are always the same. An experimenter in Italy gets the same results as a Russian experimenter who repeats the experiment a century later. The results are the same whether the experiment is done by a skeptic, a believer, or a curious bystander.
Facts like these convinced philosophers that the physical universe goes unheedingly on its way, doing what it must, without regard for its inhabitants. For example, if we simultaneously drop two people from the same height, it is a verifiable (repeatable) fact that they both will hit the ground at the same time, regardless of their weights. We can measure their fall, acceleration, and impact the same way that we measure the fall, acceleration, and impact of stones. In fact, the results will be the same as if they were stones.
“But there is a difference between people and stones!” you might say. “Stones have no opinions or emotions. People have both. One of these dropped people, for example, might be frightened by his experience and the other might be angry. Don’t their feelings have any importance in this scheme?”
No. The feelings of our subjects matter not in the least. When we take them up the tower again (struggling this time) and drop them off again, they fall with the same acceleration and duration that they did the first time, even though now, of course, they are both fighting mad. The Great Machine is impersonal. In fact, it was precisely this impersonality that inspired scientists to strive for “absolute objectivity.”
The concept of scientific objectivity rests upon the assumption of an external world which is “out there” as opposed to an “I” which is “in here”. (This way of perceiving, which puts other people “out there”, makes it very lonely “in here”). According to this view, Nature, in all her diversity, is “out there”. The task of the scientist is to observe the “out there” as objectively as possible. To observe something objectively means to see it as it would appear to an observer who has no prejudices about what he observes.
The problem that went unnoticed for three centuries is that a person who carries such an attitude certainly is prejudiced. His prejudice is to be “objective”, that is, to be without a preformed opinion. In fact, it is impossible to be without an opinion. An opinion is a point of view. The point of view that we can be without a point of view is a point of view. The decision itself to study one segment of reality instead of another is a subjective expression of the researcher who makes it. It affects his perceptions of reality, if nothing else. Since reality is what we are studying, the matter gets very sticky here.
The new physics, quantum mechanics, tells us clearly that it is not possible to observe reality without changing it. If we observe a certain particle collision experiment, not only do we have no way of proving that the result would have been the same if we had not been watching it, all that we know indicates that it would not have been the same, because the result that we got was affected by the fact that we were looking for it.
Some experiments show that light is wave-like. Other experiments show equally well that light is particle-like. If we want to demonstrate that light is a particle-like phenomenon or that light is a wave-like phenomenon, we only need to select the appropriate experiment.
According to quantum mechanics there is no such thing as objectivity. We cannot eliminate ourselves from the picture. We are a part of nature, and when we study nature there is no way around the fact that nature is studying itself. Physics has become a branch of psychology, or perhaps the other way round.
Carl Jung, the Swiss psychologist, wrote:
The psychological rule says that when an inner situation is not made conscious, it happens outside, as fate. That is to say, when the individual remains undivided and does not become conscious of his inner contradictions, the world must perforce act out the conflict and be torn into opposite halves.9
Jung’s friend, the Nobel Prize-winning physicist, Wolfgang Pauli, put it this way:
From an inner center the psyche seems to move outward, in the sense of an extraversion, into the physical world . . .10
If these men are correct, then physics is the study of the structure of consciousness.
The descent downward from the macroscopic level to the microscopic level, which we have been calling the realm of the very small, is a two-step process. The first step downward is to the atomic level. The second step downward is to the subatomic level.
The smallest object that we can see, even under a microscope, contains millions of atoms. To see the atoms in a baseball, we would have to make the baseball the size of the earth. If a baseball were the size of the earth, its atoms would be about the size of grapes. If you can picture the earth as a huge glass ball filled with grapes, that is approximately how a baseball full of atoms would look.
The step downward from the atomic level takes us to the subatomic level. Here we find the particles that make up atoms. The difference between the atomic level and the subatomic level is as great as the difference between the atomic level and the world of sticks and rocks. It would be impossible to see the nucleus of an atom the size of a grape. In fact, it would be impossible to see the nucleus of an atom the size of a room. To see the nucleus of an atom, the atom would have to be as high as a fourteen-story building! The nucleus of an atom as high as a fourteen-story building would be about the size of a grain of salt. Since a nuclear particle has about 2,000 times more mass than an electron, the electrons revolving around this nucleus would be about the size of dust particles!
The dome of Saint Peter’s basilica in the Vatican has a diameter of about fourteen stories. Imagine a grain of salt in the middle of the dome of Saint Peter’s with a few dust particles revolving around it at the outer edges of the dome. This gives us the scale of subatomic particles. It is in this realm, the subatomic realm, that Newtonian physics has proven inadequate, and that quantum mechanics is required to explain particle behavior.
A subatomic particle is not a “particle” like a dust particle. There is more than a difference in size between a dust particle and a subatomic particle. A dust particle is a thing, an object. A subatomic particle cannot be pictured as a thing. Therefore, we must abandon the idea of a subatomic particle as an object.
Quantum mechanics views subatomic particles as “tendencies to exist” or “tendencies to happen”. How strong these tendencies are is expressed in terms of probabilities. A subatomic particle is a “quantum”, which means a quantity of something. What that something is, however, is a matter of speculation. Many physicists feel that it is not meaningful even to pose the question. It may be that the search for the ultimate “stuff” of the universe is a crusade for an illusion. At the subatomic level, mass and energy change unceasingly into each other. Particle physicists are so familiar with the phenomena of mass becoming energy and energy becoming mass that they routinely measure the mass of particles in energy units.fn3 Since the tendencies of subatomic phenomena to become manifest under certain conditions are probabilities, this brings us to the matter of statistics.
Because there are millions of millions of subatomic particles in the smallest space that we can see, it is convenient to deal with them statistically. Statistical descriptions are pictures of crowd behavior. Statistics cannot tell us how one individual in a crowd will behave, but they can give us a fairly accurate description, based on repeated observations, of how a group as a whole behaves.
For example, a statistical study of population growth may tell us how many children were born in each of several years and how many are predicted to be born in years to come. However, the statistics cannot tell us which families will have the new children and which ones will not. If we want to know the behavior of traffic at an intersection, we can install devices there to gather data. The statistics that these devices provide may tell us how many cars, for instance, turn left during certain hours, but not which cars.
Statistics is used in Newtonian physics. It is used, for example, to explain the relationship between gas volume and pressure. This relation is named Boyle’s Law after its discoverer, Robert Boyle, who lived in Newton’s time. It could as easily be known as the Bicycle Pump Law, as we shall see. Boyle’s Law says that if the volume of a container holding a given amount of gas at a constant temperature is reduced by one half, the pressure exerted by the gas in the container doubles.
Imagine a person with a bicycle pump. He has pulled the plunger fully upward, and is about ready to push it down. The hose of the pump is connected to a pressure gauge instead of to a bicycle tire, so that we can see how much pressure is in the pump. Since there is no pressure on the plunger, there is no pressure in the pump cylinder and the gauge reads zero. However, the pressure inside the pump is not actually zero. We live at the bottom of an ocean of air (our atmosphere). The weight of the several miles of air above us exerts a pressure at sea level of 14.7 pounds on every square inch of our bodies. Our bodies do not collapse because they are exerting 14.7 pounds per square inch outward. This is the state that we usually read as zero on a bicycle pressure gauge. To be accurate, suppose that we set our gauge to read 14.7 pounds per square inch before we push down on the pump handle.
Now we push the piston down halfway. The interior volume of the pump cylinder is now one half of its original size, and no air has been allowed to escape, because the hose is connected to a pressure gauge. The gauge now reads 29.4 pounds per square inch, or twice the original pressure. Next we push the plunger two thirds of the way down. The interior volume of the pump cylinder is now one third of its original size, and the pressure gauge reads three times the original pressure (44.1 pounds per square inch). This is Boyle’s Law: At a constant temperature the pressure of a quantity of gas is inversely proportional to its volume. If the volume is reduced to one half, the pressure doubles; if the volume is reduced to one third, the pressure triples, etc. To explain why this is so, we come to classical statistics.
The air (a gas) in our pump is composed of millions of molecules (molecules are made of atoms). These molecules are in constant motion, and at any given time, millions of them are banging into the pump walls. Although we do not detect each single collision, the macroscopic effect of these millions of impacts on a square inch of the pump wall produces the phenomenon of “pressure” on it. If we reduce the volume of the pump cylinder by one half, we crowd the gas molecules into a space twice as small as the original one, thereby causing twice as many impacts on the same square inch of pump wall. The macroscopic effect of this is a doubling of the “pressure”. By crowding the molecules into one third of the original space, we cause three times as many molecules to bang into the same square inch of pump wall, and the “pressure” on it triples. This is the kinetic theory of gases.
In other words, “pressure” results from the group behavior of a large number of molecules in motion. It is a collection of individual events. Each individual event can be analyzed because, according to Newtonian physics, each individual event is theoretically subject to deterministic laws. In principle, we can calculate the path of each molecule in the pump chamber. This is how statistics is used in the old physics.
Quantum mechanics also uses statistics, but there is a very big difference between quantum mechanics and Newtonian physics. In quantum mechanics, there is no way to predict individual events. This is the startling lesson that experiments in the subatomic realm have taught us.
Therefore, quantum mechanics concerns itself only with group behavior. It intentionally leaves vague the relation between group behavior and individual events because individual subatomic events cannot be determined accurately (the uncertainty principle) and, as we shall see in high-energy particles, they constantly are changing. Quantum physics abandons the laws which govern individual events and states directly the statistical laws which govern collections of events. Quantum mechanics can tell us how a group of particles will behave, but the only thing that it can say about an individual particle is how it probably will behave. Probability is the major characteristic of quantum mechanics.
This makes quantum mechanics an ideal tool for dealing with subatomic phenomena. For example, take the phenomenon of common radioactive decay (luminous watch dials). Radioactive decay is a phenomenon of predictable overall behavior consisting of unpredictable individual events.
Suppose that we put one gram of radium in a time vault and leave it there for sixteen hundred years. When we return, do we find one gram of radium? No! We find only half a gram. This is because radium atoms naturally disintegrate at a rate such that every sixteen hundred years half of them are gone. Therefore, physicists say that radium has a “half life” of sixteen hundred years. If we put the radium back in the vault for another sixteen hundred years, only one fourth of the original gram would remain when we opened the vault again. Every sixteen hundred years one half of all the radium atoms in the world disappear. How do we know which radium atoms are going to disintegrate and which radium atoms are not going to disintegrate?
We don’t. We can predict how many atoms in a piece of radium are going to disintegrate in the next hour, but we have no way of determining which ones are going to disintegrate. There is no physical law that we know of which governs this selection. Which atoms decay is purely a matter of chance. Nonetheless, radium continues to decay, on schedule, as it were, with a precise and unvarying half life of sixteen hundred years. Quantum theory dispenses with the laws governing the disintegration of individual radium atoms and proceeds directly to the statistical laws governing the disintegration of radium atoms as a group. This is how statistics is used in the new physics.
Another good example of predictable overall (statistical) behavior consisting of unpredictable individual events is the constant variation of intensity among spectral lines. Remember that, according to Bohr’s theory, the electrons of an atom are located only in shells which are specific distances from the nucleus (see here). Normally, the single electron of a hydrogen atom remains in the shell closest to the nucleus (the ground state). If we excite it (add energy to it) we cause it to jump to a shell farther out. The more energy we give it, the farther out it jumps. If we stop exciting it, the electron jumps inward to a shell closer to the nucleus, eventually returning all the way to the innermost shell. With each jump from an outer shell to an inner shell, the electron emits an energy amount equal to the energy amount that it absorbed when we caused it to jump outward. These emitted energy packets (photons) constitute the light which, when dispersed through a prism, forms the spectrum of one hundred or so colored lines that is peculiar to hydrogen. Each colored line in the hydrogen spectrum is made from the light emitted from hydrogen electrons as they jump from a particular outer shell to a particular inner shell.
What we did not mention earlier is that some of the lines in the hydrogen spectrum are more pronounced than others. The lines that are more pronounced are always more pronounced and the lines that are faint are always faint. The intensity of the lines in the hydrogen spectrum varies because hydrogen electrons returning to the ground state do not always take the same route.
Shell five, for example, may be a more popular stopover than shell three. In that case, the spectrum produced by millions of excited hydrogen atoms will show a more pronounced spectral line corresponding to electron jumps from shell five to shell one and a less pronounced spectral line corresponding to electron jumps from, say, shell three to shell one. That is because, in this example, more electrons stop over at shell five before jumping to shell one than stop over at shell three before jumping to shell one.
In other words, the probability is very high, in this example, that the electrons of excited hydrogen atoms will stop at shell five on their way back to shell one, and the probability is lower that they will stop at shell three. Said another way, we know that a certain number of electrons probably will stop at shell five and that a certain lesser number of electrons probably will stop at shell three. Still, we have no way of knowing which electrons will stop where. As before, we can describe precisely an overall behavior without being able to predict a single one of the individual events which comprise it.
This brings us to the central philosophical issue of quantum mechanics, namely, “What is it that quantum mechanics describes?” Put another way, quantum mechanics statistically describes the overall behavior and/or predicts the probabilities of the individual behavior of what?
In the autumn of 1927, physicists working with the new physics met in Brussels, Belgium, to ask themselves this question, among others. What they decided there became known as the Copenhagen Interpretation of Quantum Mechanics.fn4 Other interpretations developed later, but the Copenhagen Interpretation marks the emergence of the new physics as a consistent way of viewing the world. It is still the most prevalent interpretation of the mathematical formalism of quantum mechanics. The upheaval in physics following the discovery of the inadequacies of Newtonian physics was all but complete. The question among the physicists at Brussels was not whether Newtonian mechanics could be adapted to subatomic phenomena (it was clear that it could not be), but rather, what was to replace it.
The Copenhagen Interpretation was the first consistent formulation of quantum mechanics. Einstein opposed it in 1927 and he argued against it until his death, although he, like all physicists, was forced to acknowledge its advantages in explaining subatomic phenomena.
The Copenhagen Interpretation says, in effect, that it does not matter what quantum mechanics is about!fn5 The important thing is that it works in all possible experimental situations. This is one of the most important statements in the history of science. The Copenhagen Interpretation of Quantum Mechanics began a monumental reunion which was all but unnoticed at the time. The rational part of our psyche, typified by science, began to merge again with that other part of us which we had ignored since the 1700’s, our irrational side.
The scientific idea of truth traditionally had been anchored in an absolute truth somewhere “out there”—that is, an absolute truth with an independent existence. The closer that we came in our approximations to the absolute truth, the truer our theories were said to be. Although we might never be able to perceive the absolute truth directly—or to open the watch, as Einstein put it—still we tried to construct theories such that for every facet of absolute truth, there was a corresponding element in our theories.
The Copenhagen Interpretation does away with this idea of a one-to-one correspondence between reality and theory. This is another way of saying what we have said before. Quantum mechanics discards the laws governing individual events and states directly the laws governing aggregations. It is very pragmatic.
The philosophy of pragmatism goes something like this. The mind is such that it deals only with ideas. It is not possible for the mind to relate to anything other than ideas. Therefore, it is not correct to think that the mind actually can ponder reality. All that the mind can ponder is its ideas about reality. (Whether or not that is the way reality actually is, is a metaphysical issue). Therefore, whether or not something is true is not a matter of how closely it corresponds to the absolute truth, but of how consistent it is with our experience.fn6
The extraordinary importance of the Copenhagen Interpretation lies in the fact that for the first time, scientists attempting to formulate a consistent physics were forced by their own findings to acknowledge that a complete understanding of reality lies beyond the capabilities of rational thought. It was this that Einstein could not accept. “The most incomprehensible thing about the world,” he wrote, “is that it is comprehensible.”11 But the deed was done. The new physics was based not upon “absolute truth”, but upon us.
Henry Pierce Stapp, a physicist at the Lawrence Berkeley Laboratory, expressed this eloquently:
[The Copenhagen Interpretation of Quantum Mechanics] was essentially a rejection of the presumption that nature could be understood in terms of elementary space-time realities. According to the new view, the complete description of nature at the atomic level was given by probability functions that referred, not to underlying microscopic space-time realities, but rather to the macroscopic objects of sense experience. The theoretical structure did not extend down and anchor itself on fundamental microscopic space-time realities. Instead it turned back and anchored itself in the concrete sense realities that form the basis of social life. . . . This pragmatic description is to be contrasted with descriptions that attempt to peer “behind the scenes” and tell us what is “really happening”.12
Another way of understanding the Copenhagen Interpretation (in retrospect) is in terms of split-brain analysis. The human brain is divided into two halves which are connected at the center of the cerebral cavity by a tissue. To treat certain conditions, such as epilepsy, the two halves of the brain sometimes are separated surgically. From the experiences reported by and the observations made of persons who have undergone this surgery, we have discovered a remarkable fact. Generally speaking, the left side of our brain functions in a different manner than the right side. Each of our two brains sees the world in a different way.
The left side of our brain perceives the world in a linear manner. It tends to organize sensory input into the form of points on a line, with some points coming before others. For example, language, which is linear (the words which you are reading flow along a line from left to right), is a function of the left hemisphere. The left hemisphere functions logically and rationally. It is the left side of the brain which creates the concept of causality, the image that one thing causes another because it always precedes it. The right hemisphere, by comparison, perceives whole patterns.
Persons who have had split-brain operations actually have two separate brains. When each hemisphere is tested separately, it is found that the left brain remembers how to speak and use words, while the right brain generally cannot. However, the right brain remembers the lyrics of songs! The left side of our brain tends to ask certain questions of its sensory input. The right side of our brain tends to accept what it is given more freely. Roughly speaking, the left hemisphere is “rational” and the right hemisphere is “irrational”.13
Physiologically, the left hemisphere controls the right side of the body and the right hemisphere controls the left side of the body. In view of this, it is no coincidence that both literature and mythology associate the right hand (left hemisphere) with rational, male, and assertive characteristics and the left hand (right hemisphere) with mystical, female, and receptive characteristics. The Chinese wrote about the same phenomena thousands of years ago (yin and yang)although they were not known for their split-brain surgery.
Our entire society reflects a left hemispheric bias (it is rational, masculine, and assertive). It gives very little reinforcement to those characteristics representative of the right hemisphere (intuitive, feminine, and receptive). The advent of “science” marks the beginning of the ascent of left hemispheric thinking into the dominant mode of western cognition and the descent of right hemispheric thinking into the underground (underpsyche) status from which it did not emerge (with scientific recognition) until Freud’s discovery of the “unconscious” which, of course, he labeled dark, mysterious, and irrational (because that is how the left hemisphere views the right hemisphere).
The Copenhagen Interpretation was, in effect, a recognition of the limitations of left hemispheric thought, although the physicists at Brussels in 1927 could not have thought in those terms. It was also a re-cognition of those psychic aspects which long had been ignored in a rationalistic society. After all, physicists are essentially people who wonder at the universe. To stand in awe and wonder is to understand in a very specific way, even if that understanding cannot be described. The subjective experience of wonder is a message to the rational mind that the object of wonder is being perceived and understood in ways other than the rational.
The next time you are awed by something, let the feeling flow freely through you and do not try to “understand” it. You will find that you do understand, but in a way that you will not be able to put into words. You are perceiving intuitively through your right hemisphere. It has not atrophied from lack of use, but our skill in listening to it has been dulled by three centuries of neglect.
Wu Li Masters perceive in both ways, the rational and the irrational, the assertive and the receptive, the masculine and the feminine. They reject neither one nor the other. They only dance.
This is quantum mechanics. The next question is, “How does it work?”
fn1 The dark-adapted eye can detect a single photon. Otherwise, only the effects of subatomic phenomena are available to our senses (a track on a photographic plate, a pointer movement on a meter, etc.).
fn2 At the time of Newton’s discoveries, the power of the church already had been challenged by Martin Luther. Newton himself was a pious person. The specific argument of the church was not with empirical method, but with the theological conclusions that were being developed from Newton’s ideas, conclusions which involved the concept of God as creator and the central position of man in creation.
fn3 Strictly speaking, mass, according to Einstein’s special theory of relativity, is energy and energy is mass. Where there is one, there is the other.
fn4 This was the 5th Solvay Congress at which Bohr and Einstein conducted their now-famous debates. The term “Copenhagen Interpretation” reflects the dominant influence of Niels Bohr (from Copenhagen) and his school of thought.
fn5 The Copenhagen Interpretation says that quantum theory is about correlations in our experiences. It is about what will be observed under specified conditions.
fn6 The philosophy of pragmatism was created by the American psychologist, William James. Recently, the pragmatic aspects of the Copenhagen Interpretation of Quantum Mechanics have been emphasized by Henry Pierce Stapp, a theoretical physicist at the Lawrence Berkeley Laboratory in Berkeley, California. The Copenhagen Interpretation, in addition to the pragmatic part, has the claim that quantum theory is in some sense complete; that no theory can explain subatomic phenomena in any more detail.
An essential feature of the Copenhagen Interpretation is Bohr’s principle of complementarity (to be discussed later). Some historians practically equate the Copenhagen Interpretation and complementarity. Complementarity is subsumed in a general way in Stapp’s pragmatic interpretation of quantum mechanics, but the special emphasis on complementarity is characteristic of the Copenhagen Interpretation.