THE DEMISE OF CAUSE AND EFFECT, AND OF DETERMINISM?
Part of what Albert Einstein and Niels Bohr discussed when they walked the streets of Berlin in 1920 was the analysis of the Bohr atom that Einstein performed in the summer of 1916. It was in an atmosphere of respect and friendship that Bohr and Einstein began to take opposite sides regarding the validity and implications of quantum theory.
Einstein found that his calculations could predict neither the timing of the transition from one of Bohr's stationary states to another of lower energy, nor the direction in which the resulting light quantum would be emitted. He determined mathematically that transitions might occur at any time, at random, apparently without cause. This meant that, if he trusted his analysis, Einstein would have to give up his classical notion of cause and effect. This troubled him deeply. (Experiments and studies yet to come would add to his concern.)
In the classical, commonly held, view of the world, everything would have a cause and effect. If at any time we could (hypothetically) know everything about the status of every atom in the world, we could in principle calculate everything that had happened everywhere before and predict everything that would happen everywhere afterward. It would be a deterministic world.
Einstein, like most of the rest of the physics community, believed that this was a correct view. However, with his recent analysis he found that even if he knew the present state of the atom and which orbit the electron was in, he wouldn't know if or when it might transition to another orbit. And if he didn't know the direction in which the light quantum would be launched, he couldn't predict what it might cause to happen. Extending this uncertainty to the rest of the atoms in the world, determinism, even in principle, would be gone. His conception (and that of most others) of the way that the universe works would be radically changed.
Einstein felt that this uncertainty and loss of causality just couldn't be, that the emerging quantum mechanics must just be a step on the way to something else, something better that would preserve causality. In contrast, Bohr accepted Einstein's results. He concluded that no predictions ever were or ever would be possible: there never was a predictable “cause and effect,” at least on a microscopic scale.
UNCERTAINTY—A FORMAL AND FUNDAMENTAL EXPLANATION FOR INDETERMINACY
In late April 1926, Werner Heisenberg delivered a lecture on his matrix mechanics at the University of Berlin. Einstein subsequently invited the young physicist up to his apartment for an informal discussion on the subject. Heisenberg cites this visit as important to his next accomplishment, particularly a comment by Einstein to the effect that it was theory that indicated what could be observed. Another communication was also a factor. In a letter in October, Wolfgang Pauli described that only momentum but not position could be determined in his analysis (using Max Born's ideas on probability) of the collision of two electrons.
By February 1927, Heisenberg had used his matrix mechanics approach to derive a formal relationship between the uncertainties in various pairs of physical properties. It would become known as the “Heisenberg uncertainty principle.” Particular to our discussion, he found that the uncertainty in a particle's position times the uncertainty in its momentum would always be greater than or equal to Planck's constant divided by 4π. (There it is again, Planck's constant.) In symbolic shorthand, we express this as (Δx)(Δp) ≥ h/4π. Recognizing that the change in momentum, Δp, is approximately m times the change in velocity, Δv, for particles having mass and moving at speeds slow compared to the speed of light, we then have (Δx)(m)(Δv) ≥ h/4π, or, dividing both sides of the equation equally by m so that they stay in balance, (Δx)(Δv) ≥ h/4πm. The larger the mass, the larger the number divided into Planck's constant and the smaller the product of the two uncertainties. (This is often used to explain why we never as a practical matter actually see any uncertainty in the velocity or position of massive objects like grains of sand or baseballs, or rockets or planets. Even a tiny, barely visible, grain of sand is a million billion billion times more massive than the electron, so the uncertainty in the combination of its velocity and its position is very, very, very small. Conversely, the small mass of the electron explains the relatively large uncertainties in position inherent in the spread-out clouds of probability for the location of the electron.)
There is another way to look at uncertainty in position. Grains of sand and larger objects are composed of atoms, and the uncertainty in the size of the atoms is given by the extent of the wavefunctions (represented by probability clouds) of the atom's lower-energy occupied electron states. So the extent of these clouds is a measure of the “fuzziness” and uncertainty in the location of the edges of any larger object composed of atoms. This fuzziness is very, very, very, small in comparison with the overall dimensions of objects composed of billions of atoms. So, we don't as a practical matter deal with uncertainties in the position of large objects, like grains of sand, baseballs, and so on.
Heisenberg thought that the uncertainty principle, forged from matrix mechanics, would support this (his) theory as the preferred formulation of quantum mechanics. He would soon be disappointed.
The ideas in Heisenberg's emerging paper on uncertainty sparked initial criticism from Bohr of some of the physical arguments, and there were ensuing protracted discussions regarding interpretation. Heisenberg argued that the act of observation perturbed the state of an object, so that one really couldn't know that state. It was Bohr's view that the uncertainty would instead and always result from the operation of any observing or measuring apparatus. (Actually, the uncertainty is inherent in the physics and exists whether or not measurement is involved.)
Bohr insisted that waves and particles are just complementary aspects of the same entity, and, to Heisenberg's chagrin, Bohr preferred to explain uncertainty using Erwin Schrödinger's wave mechanics. The argument strained relations between the two men. Heisenberg's paper describing uncertainty as a product of matrix mechanics was published at the end of May 1927. In a postscript he cited Bohr's point of view, that uncertainty was a part of wave-particle duality.
THE COPENHAGEN INTERPRETATION
In subsequent months, Bohr refined his ideas on the dual nature of particles into a principle, which he called complementarity: stating that the observation of either wave or particle characteristics (but not both) would be displayed in any situation depending on the choice of information sought by the observer or selected by the nature of the measuring or observational device.1 Combining this with aspects of Heisenberg's uncertainty, matrix mechanics, and Born's probability interpretation of Schrödinger's wave mechanics, he devised what would later be called the “Copenhagen interpretation” of quantum mechanics. A central tenet is that the act of observation or measurement selects just one of a number of possible physical outcomes for any event, based only on probabilities.
Fig. 6.1. “Youngsters” Enrico Fermi (left), Werner Heisenberg, and Wolfgang Pauli (right) at the Como Conference in 1927. (Photograph by Franco Rasetti, courtesy of AIP Emilio Segre Visual Archives, Segre Collection, Fermi Film Collection.)
Bohr presented this Copenhagen view at a meeting of the International Physics Congress in Como, Italy, in September 1927. Among the attendees were Planck, Pauli, de Broglie, Heisenberg, Sommerfeld, Born, and Enrico Fermi. Notably absent were the only two scientists likely to strongly present arguments in opposition to Bohr's theory: Einstein, who would not set foot in fascist Italy, and Schrödinger, who was in the process of moving after being offered and accepting Planck's chair in Berlin. (Planck would retire as professor emeritus.)
COPENHAGEN CHALLENGED—CLASH OF TITANS: SOLVAY 1927 AND 1930
The Como conference was just a prelude to the Fifth Solvay Conference, which was to be held in Brussels later that year. Consistent with diplomatic developments underway at the time, permission was granted by the king of the Belgians to lift the ban on German participation. This time, Einstein and Schrödinger would be present, and the battle over the validity, meaning, and interpretation of quantum mechanics would begin. It would lead in the course of the next eighty-some years to concepts that have strained our classically based sense of credibility further and further.
The weeklong conference started on Monday, October 24, 1927. Hendrik Lorentz chaired the sessions.
Lorentz is shown in the center of the first row of the photo of attendees, in Figure 1.1, between Einstein and Marie Curie. He shared the Nobel Prize in Physics in 1902 for his work on the influence of magnetism on radiation, but he is perhaps better known for his Lorentz transformations, which were utilized by Einstein in his theory of special relativity. Included are the phenomena of “time dilation” and “length contraction,” also known as “Lorentz contraction,” which are seen in clocks and objects moving at high speeds relative to an observer. Einstein wrote of Lorentz: “To me personally he meant more than all the others encountered in my life's journey.”2
The topic of the conference was “Electrons and Photons,” but it had been made clear that the conference would be devoted to the new quantum mechanics and related questions.3 The first three days were spent summarizing and discussing experimental and theoretical progress in areas related to the topic. Einstein and Bohr had been asked to present, but they had refused. They had encouraged and facilitated the work of others but felt that they had not contributed sufficiently themselves. Bohr, Heisenberg, Born, and Pauli (we'll call them the “Copenhagen group”) would promote the Copenhagen view, at its core the essential features of quantum mechanics outlined in Chapter 5. Schrödinger, de Broglie, and Einstein would disagree with Copenhagen on more than interpretation. They were seeking a different physics.
De Broglie spoke the next afternoon, describing his seminal suggestion of particle waves, Schrödinger's extension of the idea, and then putting forward the concept of “pilot waves” as an alternative to Born's “probability interpretation” of wave mechanics. Unlike the Copenhagen group, which would have the electron behave as either a particle or a wave, de Broglie envisaged the electron to be a particle “surfing” on a real physical wave that would lead or “pilot” the electron to follow one course or another. (So, in the two-slit experiment, for example, the pilot wave might diffract through the two slits while directing the particle through only one of them.) The concept was attacked from the left and the right: on the one hand by Bohr and company, who wanted to assert their Copenhagen view; on the other, by Schrödinger, who pressed his wave mechanics and the wave nature of the electron. He was still trying to resolve quantum physics with classical ideas. Einstein, who had encouraged de Broglie, remained silent. (De Broglie's pilot wave theory was extended by David Bohm in 1952, but without much acceptance at that time. More on that later.)
On Wednesday morning, Born and Heisenberg shared a presentation of matrix mechanics, Dirac-Jordan transformation theory, Born's probability interpretation of wave mechanics, and the uncertainty principle. In their view, Planck's constant was a result of the basic wave-particle duality of matter. They concluded by stating that quantum mechanics was a “closed theory,” complete in itself and no longer susceptible to modification. Though Einstein had been impressed by all that quantum mechanics had accomplished, he was of the opinion that it was just a step on the way to something else, not a closed theory at all. Still, he said nothing.
Schrödinger spoke in the afternoon. He pointed out that there were two theories under the name of quantum mechanics: (1) his wave mechanics, which portrayed objects in a familiar three-dimensional space, and (2) the matrix mechanics of Heisenberg and Dirac, which involved a highly abstract multidimensional space. While the latter would work for hydrogen in three dimensions; helium (with two electrons) could only be represented in a space of six dimensions; lithium (with three electrons) would require nine dimensions, and so on. In his view, the matrix approach could only be a mathematical tool, and ultimately any physical situation described would have to be presented in a realistic three-dimensional space. He also asked how the matrix theory would provide a mechanism for the sudden transition of the electron from one state to another, the quantum jump.
Schrödinger was optimistic that the two theories would ultimately be resolved into one. But he rejected Born's probability interpretation of his wavefunction (mathematics indicating the probability of finding a pointlike particle at any given location). Instead, he proposed that the wave was the electron, somehow with a spread-out electric charge. None of the other leading physicists would accept this view, though the community in general found wave mechanics to be a much easier formalism than matrix mechanics for examining the workings of the physical world.
Bohr presented the Copenhagen view. Wave-particle duality is intrinsic in nature within the context of complementarity: the basic tenet is that wave and particle aspects of an object are mutually exclusive in any particular observation. He divided the world into two parts: the micro world, which would be described by quantum mechanics; and the macro world, which would be described in the language of classical physics. The instruments of observation and measurement would lie in the macro world. Reality in the micro world did not exist in the absence of observation. The electron didn't exist at any particular place until some measurement located it. (Heisenberg would go further, to say that it didn't exist at all, anywhere, until the measurement was made.) This would be extended further to say that the electron didn't exist until some cognizant being observed the results of the measurement. There would be no objective preexisting reality.
Objective reality was essential to Einstein's view of the world. He would point to the moon and contend that it existed whether he was looking at it or not. For him, science was the discovery and understanding of the objectively existing world. And at that time he would not accept uncertainty or that the state or properties of an object would be governed by probabilities. “God does not play dice” (with the universe). He would not accept complementarity, which condemned the wave and particle nature of objects to always be observed separately. For Einstein, there had to be a deeper underlying theory that explained the results of quantum mechanics without sacrificing his fundamental view of a real universe and science's role to discover it.
If Einstein could demonstrate that quantum mechanics was in any way flawed, it wouldn't be considered a closed theory, and the door would be open to seek a better, deeper understanding. His approach to analysis and demonstration in physics often involved hypothetical gedanken (thought) experiments. Without actually doing anything in the laboratory, he would test theories by tracing out on paper or in his mind what would happen in various posed experimental tests. He signaled to Lorentz that he would like to speak. The following indented paragraphs describe his use of this approach to attack the claims of the Copenhagen group.
Single-Slit Thought Experiment
Einstein went to the blackboard and sketched out light particles passing through a single slit in a screen and then impinging on a photographic plate. After emerging from the slit, the photons would spread out [like the water waves emerging from each of the openings in the breakwater in Figure 2.2] according to a wavefunction that would indicate the likelihood that a photon would hit the plate at any point. According to the Copenhagen interpretation of quantum mechanics, at the moment that a single photon hits the screen (at the moment of measurement), the wavefunction for that particle “collapses” to a single spiked peak showing 100 percent probability of the electron being at the point of impact. Einstein asked how the information of the impact could be transmitted instantaneously, faster than the speed of light, to the farther regions of the plate so that the wavefunction in those locations would be triggered to collapse to zero except at the single point of impact. He reasoned that this collapse would either violate “locality” or show the assumption of the collapse of a probability wavefunction (and therefore the Copenhagen interpretation) to be flawed.
Locality had seemed to have been thoroughly tested experimentally classically and was a key element in classical physics, including Einstein's special theory of relativity. It means that objects could only be affected by direct impetus, either by being struck by another object (for example by a photon), or by being moved by the force of an electric, magnetic, or gravitational field. None of these influences, nothing, could be transmitted at a speed faster than the speed of light.
Another Explanation
Einstein went on to explain that the observed pattern of interference could result from a classical statistical distribution of the passage of many, many photons. Not only was quantum mechanics wrong, he would say, but the interference results could actually be explained with classical theory. Quantum mechanics wasn't even necessary. A double whammy!!
Bohr had no immediate reply, but later that evening he would respond for the Copenhagen group: The wavefunction was an abstract mathematical entity, had no physical reality, and therefore would not be bound by locality. And he was able to show that Einstein's statistical argument was wrong.
Shifting to a double-slit thought experiment, Einstein next made the case that the position and momentum of a particle could be measured to greater precision than the uncertainty principle would allow.
Bohr sketched out the apparatus and analyzed the experiment in detail, again finding that Einstein's arguments were flawed, and further refining the test to demonstrate complementarity.
In the end, Bohr and his colleagues were able to refute all of the challenges offered by Schrödinger and Einstein. There were still questions, but no flaws in the theory had been revealed. Einstein was still unconvinced. But Paul Ehrenfest, who was unbiased, somewhat of a facilitator, and a good friend of both Einstein and Bohr, would comment that Bohr had pretty much prevailed.
In the next several years, Einstein suffered some health problems, took time off to recover, and began his work to unify the theories of gravity and electromagnetism to produce a “unified field theory.” He hoped it would also provide answers to what he still believed to be serious problems with quantum mechanics, and complete the theory. Uncertainty was still on his mind.
Kumar relates, quoting Heisenberg, that most of the action between Einstein and the Copenhagen group actually took place outside of the meeting rooms.4 In the morning, over breakfast in the hotel where all of the attendees stayed, Einstein would present the group with a new challenge to the uncertainty principle. Details of the challenge would be clarified during the walk to the Institute for Physiology, where the meetings were held. The group would begin to analyze the challenge over lunch. In the early evening, the Copenhagen group would meet to formulate a response, and Bohr would deliver their findings to Einstein over dinner. The entire interaction between Einstein and the group would take place in a spirit of good humor. (Figure 6.2 shows Einstein and Bohr walking together in Brussels seven years later, as they might have walked in 1927.)
Fig. 6.2. Einstein (left) and Bohr in Brussels in 1934. (Photograph by Paul Ehrenfest, courtesy of AIP Emilio Segre Visual Archives, Ehrenfest Collection.)
When it came time for the Sixth Solvay Conference in 1930, Einstein delivered what at first appeared to be a fatal blow to the Copenhagen interpretation. The topic of the conference was the magnetic properties of matter. The format and venue of the meeting were the same as it had been three years earlier. There were thirty-four attendees, twelve of them already or later to be Nobel laureates. Again, the dialogue between Einstein and the Copenhagen group would occur between the formal sessions. This time Einstein attacked another aspect of the uncertainty principle. (Remember, if any one aspect of quantum mechanics, including uncertainty, was found to be invalid, then the Copenhagen group would have to admit that quantum mechanics was not a closed theory. It would then be open to the modification and improvement that Einstein felt would be necessary.)
Heisenberg's uncertainty applies to various “conjugate pairs” of physical properties and variables. One such pair, described earlier, is the position and momentum of an object. As we discussed, Heisenberg found that the uncertainty in an object's position times the uncertainty in its momentum would be greater than or equal to Planck's constant, h, divided by 4π, written in physics shorthand as (Δx)(Δp) ≥ h/4π. Another conjugate pair is energy and time. In this case, the uncertainty in an object's energy times the uncertainty in the time interval for measuring the energy is related to Planck's constant, h, by the formula (ΔE)(Δt) ≥ h/4π.
Einstein confronted Bohr with the following thought experiment.
Suppose, Einstein said, there are many quanta of light, many photons bouncing around inside of a box. (The box is shown in Fig. 6.3, suspended by a spring from a cantilevered beam.)
A shutter over a window in the box is opened and then quickly closed, allowing just one photon to escape out sideways. The shutter can be operated according to a clock, which thus notes the time of the photon's departure with a high level of certainty. The clock is synchronized to another clock located outside, away from the box, so that the observation of time (done on the outside clock) in no way influences the box and its contents. (To this point Bohr is unperturbed. He knows that experimental uncertainty in the measurement of the wavelength, w, of the photon will [by Planck's formula E = hc/w, described in Chapter 1] translate into an uncertainty in the energy.) But then Einstein stated that the box would be weighed before the photon is emitted and then weighed again afterward. (The weighing could be accomplished by noting the height of the box against a pointer attached to the stand supporting the beam. The heavier the box, the lower it would drop against the tension of the spring.)
Fig. 6.3. Photo of Niels Bohr's blackboard just after he died in 1962. Apparently he was still thinking of Einstein's photon-from-a-box thought experiment, sketched at the bottom center. (Image from AIP Emilio Segre Visual Archives.)
Bohr immediately realized that uncertainty was in trouble. Here's why:
Einstein's formula E = Mc2 (from his theory of special relativity) would predict that the box would change its mass because of the energy carried away from it by the photon. By weighing the box before and after the photon's escape, Einstein would be able to measure the change in mass of the box and then (using this formula) calculate the energy of the photon. In this way he would get a precise, exact, measure of the photon's energy without the uncertainty that would be imposed by trying to make direct measurements on the photon itself. There would be zero uncertainty in the calculation of energy, and therefore zero uncertainty in the product of this uncertainty times whatever uncertainty existed in the measurement of time. (Zero times anything is zero.) The uncertainty principle would be violated since it predicts that the product of these uncertainties must always be greater than h/4π. Quantum mechanics as the Copenhagen group envisioned it, including uncertainty, would be shown to have this flaw and would therefore be considered to be incomplete.
Bohr conferred with his colleagues, but none could find anything wrong with Einstein's argument. They were relatively unconcerned, confident that a way out would be found. Bohr was still greatly concerned. In Bohr-like fashion he sought to examine the details of measurement, sketching out a simple concept of the box with its clock and shutter, the box hanging by a spring like a grocers scale with a pointer to measure its displacement as a way of indicating weight.
Bohr struggled. Eventually, in the early hours of the morning, he found what he was looking for. Einstein had invoked relativity. He would out-Einstein Einstein. It was very subtle.
Bohr noted that light, photons, would need to shine on the box and the pointer in order for its location to be read. The photons, each having momentum, would jostle the box in a small way. Its position, and therefore the mass and energy of the box would be uncertain.
And the measurement of time would also be uncertain: The more accurate the reading made of the pointer's position, that is, the more accurate the reading of the mass change of the box of light and the associated energy of the single emitted photon, the greater would be the required number of these externally generated photons and the greater the random jostling that they would produce. Einstein's theory of general relativity, the same theory that successfully predicted the bending of the path of light as it passes the sun, also requires that time slows and clocks tick more slowly if they are moving in a gravitational field. So, if a change in mass is measured by weighing it under the force of gravity as Einstein suggested, then Einstein's clock in the box would (because of random movement in the gravitational field) run in a random way more slowly than the initially synchronized clock viewed by the observer.
Time would be uncertain, and the more accurate the measurement of mass and energy, the more uncertain time would become. This was exactly what Heisenberg's uncertainty principle said of the conjugate quantities of time and energy!
Einstein had no rebuttal. He still maintained that quantum theory was incomplete, but from this time on he would try to demonstrate this head-on rather than indirectly by attacking uncertainty.
Most of the leading physicists taking positions in the various universities throughout Europe were directly or indirectly a product of Bohr's Institute. His constant invitation to visit, share, and collaborate had produced a cadre of believers whose students would now carry on with the Copenhagen interpretation. Einstein in his Institute in Berlin had preferred to work alone. He stood out (with Schrödinger) as a reactionary, nearly lone holdout still seeking to demonstrate an objective reality.
EINSTEIN GAINS THE UPPER HAND? ENTANGLEMENT AND THE (EPR) PARADOX
In 1935, Einstein launched another attack. By this time he was working at Princeton in the United States. Together with colleagues Boris Podolsky and Nathan Rosen, he devised yet another thought experiment and delivered the findings in a paper published in May in the American journal Physical Review, titled “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?” Their answer was “No!” The experiment involved an aspect of quantum mechanics later to be labeled by Schrödinger as “entanglement.” The EPR (Einstein, Podolsky, Rosen) paper was concerned with entangled properties of momentum and position, but we illustrate entanglement here because of their relevance to experiments to be described later on, by considering photons with the entangled property of polarization.
As we will discuss later on, entanglement allows the possibility of superpowerful quantum computers, quantum encryption, and even one type of teleportation. Objects are entangled if they are both part of the same wavefunction. A good example of entangled particles is the pair of photons that can be induced to be emitted within nanoseconds of each other from a calcium atom.
All photons are electromagnetic in nature and, thinking classically of waves to understand definitions, are polarized as described in Appendix A. Their tiny electric fields alternate in time and space like a rope whipped up and down, left and right, or at some odd angle in between. Whatever the angle, the oscillations of electric field lie in only one plane, vertical, for example, as depicted in Figure A.1(c) of the Appendix.
The two photons from the calcium atom are constrained by the physics of the emission process of our example to have identical polarizations and to travel in opposite directions. Their polarizations can be at any angle. If a measurement of polarization is made on either photon, let's say by passing it through a polarized filter, it will either make it through or not. If the filter were set to pass vertically polarized photons, and our photon were polarized in the vertical plane, it would pass through. If it were polarized in the horizontal plane, it wouldn't make it through. If it were polarized at some odd angle, it will either entirely make it through the vertical filter or not at all, with some probability of each result depending on the angle of its initial polarization relative to the vertical. The photon doesn't partly make it through. It either assumes the polarization that passes the filter or the orientation 90 degrees from that and doesn't pass. This goes back to quantum mechanics and the particle and quantum nature of photons: they don't get split.
The key thing about entangled photons is this: whatever the polarization measured on the first photon, that same polarization will be measured on the second photon, even though the result on the first photon is based entirely on probabilities as quantum mechanics would expect, and even though the two photons may be far, far away from each other. Both the photon and its entangled partner choose through this one polarization measurement (on the first of the two photons) the same one of two possible results: “pass” or “don't pass” through similarly oriented filters, regardless of the polarization angle of these filters. Once the pass/don't-pass measurement is made on the first photon (once it is shown to have either the polarization of the first filter or the opposite polarization), there is no probability involved in regard to the polarization of the second photon: it will be the same as the polarization measured on the first photon.
EPR examined in thought what would happen with measurements on entangled particles that had been allowed to travel far, far away from each other. We illustrate the EPR argument with our two photons.
Quantum mechanics as envisioned by Bohr would say that the photons’ entangled polarization would not be determined until a measurement was made on one of the photons by trying to pass it through a polarized filter: either it would pass or not and be in a “pass” state, or not, as a result of the measurement. A similar measurement made immediately afterward on the other, far-away, photon would always show it to be in exactly the same polarization state as the first photon: that is, it would pass through a similarly oriented polarized filter, or not, in exact correspondence with what happened with the first photon. Its polarization would also be determined by the measurement on the first photon.
EPR would ask how this is possible. How did the second photon know the randomly determined polarization of the first photon, so that it could assume its same polarization state?
Either (1) the experiment would violate locality (the requirement that events are caused by contact or the transmission of forces no faster than the speed of light) by transferring information to the second photon instantaneously, what Einstein would call “spooky action at a distance.” (The transfer of forces or information faster than the speed of light was not allowed according to any prior classical experiments or the much-trusted theory of special relativity, a part of classical theory). Or (2) the photons had the same polarizations all along, in which case quantum mechanics was lacking and incomplete as a theory because it should have been able to describe the definite preexisting polarization of the pair of photons—no probabilities involved.
Bohr had thought that he and the others of the Copenhagen group had disproved Einstein's classical sense of objective preexisting reality through their Copenhagen view of quantum mechanics that said that a subjective measurement would force an outcome based on probabilities, that the properties measured in particles would not only be found but actually determined at the instant of measurement. EPR turned the argument around. They asked, why assume that quantum mechanics is right? Since nothing could tell the second particle (faster than the speed of light) what state it should be in, and its state is clearly linked to that of the first particle, then both particles had to be in the measured state all along. Something had to be wrong or incomplete about quantum mechanics since it was not able to predict this prior state. Perhaps there were as yet unknown “local hidden variables” involved in the theory that would describe this preexisting state of the particles. The Copenhagen interpretation of quantum mechanics or quantum mechanics as a complete theory was threatened.
This was not an idle debate or an argument of philosophy, though it seems philosophical. Here were the best of scientific minds trying to determine the nature of our physical world based on experiments that had been or could be performed.
Bohr dropped everything else that he was doing and spent the next six weeks working night and day to analyze and draft a reply to the EPR paper. When he was done, he wrote a paper that bore the same title as that used by EPR: “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?” But his answer was “Yes.”
The paper was not well written. Bohr had been unable to find any error in the EPR thought experiment and could only argue that EPR's was not a strong-enough case. Paul Dirac initially thought that Einstein had disproved quantum mechanics. In the years that followed, the dispute became essentially a standoff. Which view one took became a matter more of belief than science. But quantum mechanics worked to describe the submicroscopic world, and because of that most physicists, including Dirac, still tended to favor Bohr.
Much later, in 1949, Bohr would suggest that entanglement meant that the particles could not be considered as individual objects. He would reason that they were essentially one object, linked by a single wavefunction: a measurement on one particle essentially constituted a measurement on both particles, simultaneously bringing about the entangled properties in both. No need for faster-than-light transmission of cause and effect.
Fifteen years later still, a theorem was derived that suggested an experiment that would resolve concretely the dispute as to whether quantum mechanics would prevail as a complete theory. The experiment would be a resolution between a world based on probabilities and a world based on objective reality. The theorem came to be called “Bell's theorem” or “Bell's inequality.” We'll learn more of that later.
SCHRÖDINGER'S CAT AND “MANY WORLDS”
The EPR paper prompted a series of letters between Einstein and Schrödinger. In one of these, Schrödinger (perhaps anticipating Bohr's later observation) would comment that the act of measurement should immediately break entanglement and leave the properties of the second particle to be independent of those of the first. In another, addressing Copenhagen's ad hoc separation of micro and macro phenomena, Einstein sought to demonstrate the absurdity of the Copenhagen interpretation as it might apply to larger objects. This triggered a subsequent paper, published by Schrödinger, in which he went a step further, describing in a paragraph what is referred to as the “Schrödinger's cat paradox” (which is more known to the general public than is Schrödinger himself or his key theoretical work on wave mechanics).
Schrödinger agreed with the Copenhagen interpretation that all of the information on the probabilities of future events is included in his time-dependent set of mathematical wavefunctions for the state of an object or system. But he disagreed with the part of their interpretation that required that the state of an object can only be determined by observation or test by a cognizant observer. In his own words (but translated from the original German and presented by Kumar), Schrödinger wrote as follows:
A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The wave function of the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.5
Kumar continues:
According to Schrödinger and common sense, the cat is either dead or alive, depending on whether or not there has been a radioactive decay. But according to Bohr and his followers, the realm of the subatomic is an Alice in Wonderland sort of place: because only an act of observation can decide if there has been a decay or not, it is only this observation that determines whether the cat is dead or alive. Until then the cat is consigned to quantum purgatory, a superposition of states in which it is neither dead nor alive.6
Twenty years later, a solution would be proposed to the problem exemplified by the Schrodinger's cat paradox. As you will come to see, it would involve the concept of the simultaneous existence of “many worlds.”
In the interim, our one of these many worlds would sink once again into war.
NAZI GERMANY, NUCLEAR PHYSICS, AND THE BOMB
Between 1928 and 1930, Hitler's National Socialist party moved from just 12 seats in the Reichstag to 107 seats, making it the second largest party in Germany. What precipitated the change was the crash of the financial markets on Wall Street.
American banks, in trouble, demanded repayment of short-term loans which had stimulated the German economy. German unemployment, which was at 1.3 million workers in 1929, rose to three million in 1930. A year later, Germany was in deep depression and political upheaval. Hitler exploited a simmering anti-Semitism by blaming Germany's problems on the Jews. He was appointed chancellor in January 1933. State-sponsored Nazi violence began when the Reichstag was set on fire just one month later. More than a quarter of Germany's roughly sixty-five million people would vote for the Nazi Party in the Reichstag election in March.
Five days after the Reichstag fire, Einstein, who was lecturing at Caltech in the United States (and had arranged to spend a few months per year at the newly formed Institute for Advanced Studies [IAS] at Princeton), decided not to return to Germany. He stated publicly that he wouldn't live in a country where basic freedoms were restricted. He was vilified in the German press. In May “un-German” and “Jewish-Bolshevik” books and documents were looted from libraries and bookstores and burned in every university town in Germany. Included were the works of Brecht, Freud, Kafka, Marx, Proust, Zola, and Einstein.
The Law for the Restoration of the Career Civil Service had passed in April. Civil servants not of Aryan origin were to retire. Universities were state institutions, and by 1936 over 1,600 scholars had left their posts. A third were scientists. (Twenty of these either had been or would be awarded Nobel prizes.) Included were a quarter of all members of the physics community and half of the theorists.
Schrödinger didn't have to leave Berlin, but he did so out of protest. Protest by the rest of the German physics community was feeble at best, but scientists in other countries set their organizations to helping out. Ernest Rutherford chaired the Academic Assistance Council in England, which served as a clearinghouse in finding positions. Bohr's institute became a staging post, and he and his brother helped to set up the Danish Committee for Support of Intellectual Workers in Exile. The better-known physicists would be able to find places outside of Germany. It was much more difficult for the rest.
Born didn't have to leave because of a “grandfather” clause in the law, but he felt uncomfortable among unsupportive colleagues. He left Germany to lecture for three years at Cambridge and then to take the chair of natural philosophy at the University of Edinburgh in Scotland. His institute, the “cradle of quantum mechanics”7 in Göttingen, essentially ceased to exist.
In the late 1920s, physics was mainly concerned with the quantum mechanics of the electrons surrounding the nuclei of atoms. During the 1930s, experimental work would provide information toward an understanding of the nucleus itself. Bohr had visited Einstein at Princeton on several occasions. When he returned in January 1939, he brought news that European laboratories had discovered fission—that heavy elements might break apart into smaller elements, releasing large amounts of energy and neutrons in the process. These might trigger the fission of additional atoms in a chain reaction that could be used to build an atomic bomb. Bohr also reported that Germany had stopped the sale of uranium ore from the mines that it now controlled in Czechoslovakia. (Approximately 0.7 percent of uranium ore is the fissile isotope uranium-235.)
Under the circumstances, Einstein suspended his pacifist views and in August 1939 wrote a letter to President Roosevelt suggesting that he look into the possibility of building an atomic bomb. In September, Germany attacked Poland. In March 1940, Einstein wrote a second letter to Roosevelt, stating that German interest in uranium had intensified and that much work was being carried out in Germany in secrecy. (He didn't know that Werner Heisenberg was in charge of the German project to develop an atomic bomb.)
In April 1940, Germany occupied Denmark. Bohr stayed in Copenhagen, hoping that his reputation would provide some protection to others who were there. In September 1943, Hitler ordered the deportation of Denmark's eight thousand Jews. Thanks to the Danish people, who hid them in their homes, in hospitals and churches, only three hundred were rounded up. Bohr, whose mother had been Jewish, escaped with his family to Sweden and then was flown to Scotland as a passenger on a British bomber. From there he traveled to the United States. After a brief stop in Princeton, where he met with Einstein and Pauli (who was at the Institute for Advanced Studies at the time), Bohr traveled on to Los Alamos, New Mexico, to take his place among those working on the atomic bomb. He worked under the alias “Nicholas Baker.” The United States hadn't started a serious effort toward the bomb until 1941. When it did, it was codenamed “the Manhattan Project.”
BELL'S INEQUALITY, EXPERIMENT, AND THE NATURE OF REALITY RESOLVED
After the war, Bohr was made a permanent nonresident member of the Institute for Advanced Studies at Princeton. He and Einstein met there in 1946, again in 1954, and several times in between. On all occasions they again discussed quantum mechanics and its implications. Heisenberg also met with Einstein in 1954, stopping by as part of a lecture tour. Neither man could sway Einstein from the latter's belief that quantum mechanics was incomplete, just a stepping-stone toward a broader theory that would describe a “real” and “local” world.
Einstein died of a ruptured aneurism the next year, apparently still thinking about the development of a unified field theory that might include a resolution of the problems he saw in the implications of quantum mechanics. Bohr died of a heart attack in 1962, having sketched Einstein's light-box thought experiment on his blackboard the night before (see Figure 6.3), apparently still carrying on in his mind the debate with his old friend and adversary. In 1964, a young Irishman would construct a theoretical proof that showed a way to resolve their dispute.
John Stewart Bell was born in 1928 in Belfast, into a poor family “descended from carpenters, blacksmiths, farm workers, laborers and horse dealers.”8 His family managed to send him to a technical high school; he was the only one of the four children afforded a secondary education. Luckily, he found work as a technician at Queens University, was recognized for his drive and talent, was given a small scholarship, and with diligence graduated in 1948 and 1949 with degrees in experimental and mathematical physics, respectively. He went to work in England for the United Kingdom Atomic Energy Research Establishment, married fellow physicist Mary Ross, and then went on to earn a doctorate at the university in Birmingham. In 1960, he and Mary moved to Geneva, where he would work at the European nuclear physics research facility, CERN, there to help in the design of particle accelerators.
Fig. 6.4. John Stewart Bell at CERN in 1982. (Image courtesy of CERN, the European Organization for Nuclear Research.)
Though his job was to design and build scientific apparatus, Bell had from as early as 1945 been following theoretical works regarding the implications of quantum mechanics. We know today that quantum mechanics, with all of its uncertainties and probabilities and nonlocal character, has succeeded without fail in describing our observable universe. But this is not to say that the Copenhagen interpretation at the time would prevail or that quantum mechanics would be viewed as a complete theory. In the following indented paragraphs we examine how Bell began to explore those interpretations that existed at the time.
In 1932, the brilliant young mathematician John von Neumann wrote a book on the mathematical foundations of quantum mechanics that became the definitive reference on the theory. In this book, von Neumann appeared to prove that quantum mechanics could not be reformulated to include “hidden variables” that would allow the objective reality that Einstein sought. Nevertheless, some twenty years later, David Bohm, who had been a student of Robert Oppenheimer at Berkeley, constructed a credible hidden-variables theory related to de Broglie's earlier work describing the electron as a particle “surfing” a pilot wave. Because of von Neumann and other factors, and because quantum mechanics based on the Copenhagen interpretation had become so firmly entrenched, Bohm's work had been pretty much ignored. But not by Bell. Eventually, Bell examined von Neumann's work and found his argument about hidden variables to be flawed.
Stimulated by Bohm's work, Bell in 1964, in a sabbatical year away from CERN, decided to resolve the dispute between the accepted Copenhagen view of quantum mechanics and Einstein's argument that it either violated locality or was incomplete. Einstein concluded the latter. Bell tended to sympathize with Einstein's position and set out to demonstrate the possibility of a “local hidden variables” (LHV) theory alternative to quantum mechanics.9 Based on a theorem that he derived, Bell suggested an experiment to test between LHV and quantum mechanics by measuring the correlations between the passage of particles with entangled spins through differently oriented filters (i.e., pass/pass; or don't pass/don't pass). Each set of particles tries to pass through filters set at different angles. That is, one particle passes through (or not) a filter set at a particular angle, while its entangled partner passes through (or not) a filter set at a different angle. If the correlations fell into a certain range, then Bohr would be right and Einstein would be wrong. It was a difficult test, not accomplished properly until nearly fifteen years later, and then with polarized entangled photons rather than spins. I describe the test as follows.
As with our earlier consideration of entanglement, because we can relate it to the definitive experiments that were eventually performed, we describe Bell's experiment using a pair of polarized photons instead of a pair of particles with oriented spins. (I refer you to Figure A.1(c) and related discussion in Appendix A for a definition of polarization.) The pair of entangled photons is emitted through the two-stage transition of an electron from an excited state in a calcium atom. The two photons travel in opposite directions. Upon measurement, both photons will have the same polarization, but what that polarization might be is unknown. The two photons are each passed through a polarizing filter, and each filter may be oriented at a different angle to the vertical than is its counterpart for the other photon.
Correlated results are achieved if either both photons pass through their filters or both do not pass through their filters. A lack of correlation results if one photon passes the filter and the other doesn't. For LHV, where the two photons are assumed to already have a particular matching polarization when they are emitted, the probability of correlation in the measurements on the two filters is calculated never to be less than one in three (1/3), regardless of how differently the detecting filters may be oriented. (This is “Bell's inequality”: for LHV to be possible, the probability of correlation must be equal to or greater than one in three, about 33 percent.) For quantum entangled particles, where the polarization of both particles is not determined until the first measurement on either of the two particles is made, the probability of correlation in the measurements is calculated to be as low as one in four (= 1/4 or 25 percent).
Bell suggested that many measurements be made at each of many different relative orientations of the two filters, generating a curve of probabilities to see what the minimum probability would actually be. If it were found to be in some range not allowed by LHV, then deriving any LHV theory, including one obtained as a modification of quantum mechanics, would be impossible. For our case of the polarized photons, this meant that some combination of filter orientations would need to be found such that measurements would show a probability of correlation significantly below 33 percent.
Ever more careful and precise sets of measurements were performed to test Bell's inequality, starting with John Clauser and his group at Berkeley in 1969, using photons as described in the indented paragraphs above. Clauser's work found in favor of Bohr's nonlocal quantum mechanics, but it wasn't definitive. In three sets of experiments, similarly with photons, Alain Aspect (pronounced “AHS-pay”) and his group at the Université Paris–Sud in Orsay in 1981 and 1982 found with a high degree of accuracy that the polarizations of the photons could be correlated close to the 25 percent minimum expected from quantum theory and clearly less than the 33 percent minimum required for LHV.10 The conclusion is, with a very, very, very high degree of confidence: Einstein was wrong! In Orzel's words: “the vast majority of physicists agree that the Bell Theorem experiments done by Aspect and company have conclusively shown that quantum mechanics is nonlocal. Our universe cannot be described by any theory in which particles have definite properties at all times, and in which measurements made in one place are not affected by measurements in other places.”11 Said in another way by Kumar: “Aspect's team and others who tested Bell's inequality ruled out either locality or objective reality, but allowed a non-local reality.”12 Einstein would either have to give up objective reality or accept “spooky action at a distance” (and would probably have chosen the latter).
INTERPRETATIONS OF QUANTUM MECHANICS
The confirmation of Bell's theorem ruled out local hidden-variable interpretations and posthumously settled the dispute between Einstein and Bohr. However, as of 2016, thirteen distinct interpretations have been put forward of how quantum mechanics works).13 I note the three mainstream types of interpretations here.14 One type is the de Broglie/Bohm hidden-variables interpretation (mentioned earlier), which involves additional math to describe a particle surfing a pilot wave. It includes hidden variables that are not local, and so is not ruled out by the Bell experiment. In this interpretation there is a deterministic flow of events, but the determinism in the flow is not observable.
Another type is labeled as “collapse theories,” which, including and like the Copenhagen interpretation, requires that an object be in a superposition of possible states until observation or measurement causes the collapse of the overall wavefunction into just one state and set of properties. As noted earlier, the absurdity of this for large objects was illustrated by Schrödinger's cat paradox, where the cat was deemed to be both dead and alive until observed.
In 1957, a simple solution to the problem of collapse was proposed. Hugh Everett III, a graduate student at Princeton, suggested that our world splits at every event that allows alternative outcomes. All possible outcomes are realized, each in a separate ongoing world. Each of these worlds is split again at the next event, so that there is an ever-branching tree of separate realities. This latter became known as “many worlds,” variations of which make up our third “mainstream” type of interpretation (though, to many, it still seems far-fetched).
Everett was able to show that his approach would yield all of the practical quantum calculations and results provided by the Copenhagen interpretation. As practical physics, it was the same. But at the time that his idea was proposed, the Copenhagen interpretation was well entrenched, and Everett's suggestion went essentially unnoticed for almost ten years. Then cosmologists begin to have trouble with the Copenhagen idea that an objective observer would be required to cause the collapse of the wavefunction into one of its possible outcomes. Where was the outside observer to cause the collapse of the set of wavefunctions describing the universe, so that we have the universe that we occupy? Better to believe in the existence of multiple branching universes requiring no observation and no collapse.
Polls
Kumar cites a poll taken at a physics conference in Cambridge in 1999.15 Ninety physicists were asked about interpretation. Four favored the Copenhagen view. Thirty preferred the “many worlds” concept. Fifty stated “none of the above” or “undecided.” Another poll carried out by Max Tegmark at the Fundamental Problems in Quantum Theory conference in August 1997 cited a 17 percent vote for many worlds, about the same as the 18 percent polled in a Quantum Physics and the Nature of Reality conference in July 2011, which also reported 42 percent for the Copenhagen interpretation.16 So, even to this day, the jury is out regarding which of the various interpretations are likely to be correct and which of the corresponding views of our physical world may be correct. (Hopefully, someday the correct interpretation will be determined by the experimental check of some distinguishing theory, rather than through the expression of a preference by a vote.) Fortunately, quantum mechanics works regardless.
DECOHERENCE—WHY OUR MACROSCOPIC WORLD SEEMS TO BE CLASSICAL
The physical process of “decoherence” is particularly relevant to the many worlds interpretation, but it relates to all of the other interpretations as well. It answers some questions about what happens upon observation or measurement, and it has particular relevance to quantum computing, encryption, and teleportation (as described in Chapter 8). To understand decoherence, we first need to understand what is meant by “cohere.”
Recall from Chapter 5 and the essential features of quantum mechanics that all states of an isolated physical system are described by the wavefunction solutions to Schrödinger's equation for the system, and that these wavefunctions may be incorporated into an overall wavefunction. Well, these wavefunctions are linked together and describe the linkage of all of the constituents of the system. The maintenance of these linkages as the wavefunctions of the system evolve is called coherence.
Sustained coherence occurs when particles stay entangled as they move apart over long distances. It is responsible for the interference of a particle with itself as it is shot to pass through two slits in a barrier, as described for electrons in relation to Figure 3.4. In short, it is what distinguishes quantum phenomena from the classical; coherence is a central feature of our quantum world.
Decoherence is the modification of the wavefunction so that the linkage is weakened between otherwise-separate entities in the system and possible resulting states of observation. The phase relationships within and between wavefunctions are shifted. Decoherence occurs through the interaction of the otherwise-isolated system with the broader environment, for example when molecules in the air destroy the linkage between entangled photons as they travel miles through the atmosphere (in a demonstration of quantum encryption, as described in Chapter 8). And it occurs when the billions of atoms in measuring devices perturb the wavefunction of the particles or system that they are observing or measuring. Orzel points out that “it's a real physical process compatible with any of the interpretations (of quantum mechanics)—but it's particularly important to the modern view of many-worlds (which is sometimes called ‘decoherent histories’ as a result).”17
The many worlds interpretation requires that I in my universe cannot see and am unaware of the me observing the different outcome of an event in another universe. But because both of these universes have evolved from the same set of wavefunctions, they should be linked and interfere with each other, in much the same way that the electron interferes with itself as its wavefunction somehow senses the other slit in the double-slit experiment described in and around Figure 3.4. The argument is that this linkage doesn't happen, the many particles within each of these universes are continually perturbing their wavefunctions, shifting their phase relationships, so that they no longer cohere or interfere. The two universes then behave as if they are separate, isolated systems.
Decoherence even places the Copenhagen interpretation in a more favorable light, explaining the difference between the interactions of microscopic and macroscopic systems, why macroscopic objects don't display quantum behavior. The perturbations of billions of atoms in macroscopic objects causes decoherence, so that only the most likely of possible separate results is visible, in the same way that attempting to observe which slit the electron went through destroys interference and yields only the results expected if the electron had gone through one slit. To explore this subject further, I recommend that you read from Chad Orzel18 or Brian Greene.19
Soon, in Chapter 8, because we have already laid some of the groundwork for it in our discussion of the hydrogen atom and polarized photons, we'll take a peek at a few present and future related applications of quantum mechanics. (Much more of future applications will follow in Part Five of this book, beginning with Chapter 18.) But now, let's first examine the meaning of science in the context of all of the new ideas that we have been describing.