The Dancing Wu Li Masters

by Gary Zukav

  Once the photon is set in motion the wave function associated with it would continue to develop (change) according to a causal law (the Schrödinger wave equation) until the photon interacts with the observing system. At that instant, one of the possibilities contained in the wave function would actualize and the other possibilities contained in the wave function would cease to exist. They simply would disappear. The wave function, that strange animal that von Neumann was attempting to describe, would “collapse.” The collapse of this particular wave function would mean that the probability of one of the possible results of the photon-measuring-device interaction became one (it happened) and the probability of the other possibilities became zero (they were no longer possible). After all, a photon can be detected only in one place at a time.

  The wave function, according to this view, is not quite a thing yet it is more than an idea. It occupies that strange middle ground between idea and reality, where all things are possible but none are actual. Heisenberg likened it to Aristotle’s potential.

  This approach has unconsciously shaped the language, and therefore the thinking, of most physicists, even those who consider the wave function to be a mathematical fiction, an abstract creation whose manipulation somehow yields the probabilities of real events which happen in real (versus mathematical) space and time.

  Needless to say, this approach also has caused a great deal of confusion, which is as unclear today as it was in von Neumann’s time. For example, exactly when does the wave function collapse? (The Problem of Measurement.) Is it when the photon strikes the photographic plate? Is it when the photographic plate is developed? Is it when we look at the developed plate? Exactly what is it that collapses? Where does the wave function live before it collapses? and so on. This view of the wave function, that it can be described as a real thing, is generally the view of the wave function attributed to von Neumann. However, the real-wave-function description is only one of two approaches to understanding quantum phenomena which he discussed in The Mathematical Foundations of Quantum Mechanics.

  The second approach, to which von Neumann devoted much less time, is a re-examination of the language by which it is necessary to express quantum phenomena. In the section “Projections as Propositions,” he wrote:

  …the relation between the properties of a physical system on the one hand, and the projections [wave function] on the other, makes possible a sort of logical calculus with these. However, in contrast to the concepts of ordinary logic, this system is extended by the concepts of “simultaneous decidability” [the uncertainty principle] which is characteristic for quantum mechanics.2

  This suggestion, that the novel properties of quantum theory can be used to construct a “logical calculus” which is “in contrast to the concepts of ordinary logic,” is what von Neumann considered the alternative to describing wave functions as real things.

  Most physicists, however, have adopted a third explanation of wave functions. They dismiss them as purely mathematical constructions, abstract fictions which represent nothing in the world of reality. Unfortunately, this explanation leaves forever unanswered the question, “How, then, can wave functions predict so accurately probabilities which can be verified through actual experience?” In fact, how can wave functions predict anything when they are defined as completely unrelated to physical reality. This is a scientific version of the philosophical question, “How can mind influence matter?”

  Von Neumann’s second approach to understanding the paradoxical puzzles of quantum phenomena took him far beyond the boundaries of physics. This brief work pointed to a fusion of ontology, epistemology, and psychology which only now is beginning to emerge. In short, the problem, said von Neumann, is in the language. Herein lies the germ of what was to become quantum logic.

  In pointing to the problem of language, von Neumann put his finger on why it is so difficult to answer the question, “What is quantum mechanics?” Mechanics is the study of motion. Therefore, quantum mechanics is the study of the motion of quanta—but what are quanta? According to the dictionary, a quantum is a quantity of something. The question is, a quantity of what?

  A quantum is a piece of action (a piece of the action?). The problem is that a quantum can be like a wave, and then again it can be like a particle, which is everything that a wave isn’t. Furthermore, when a quantum is like a particle, it is not like a particle in the ordinary sense of the word. A subatomic “particle” is not a “thing.” (We cannot determine simultaneously its position and momentum.) A subatomic “particle” (quantum) is a set of relationships, or an intermediate state. It can be broken up, but out of the breaking come more particles as elementary as the original. “…Those who are not shocked when they first come across quantum theory,” said Niels Bohr, “cannot possibly have understood it.”3

  Quantum theory is not difficult to explain because it is complicated. Quantum theory is difficult to explain because the words which we must use to communicate it are not adequate for explaining quantum phenomena. This was well known and much discussed by the founders of quantum theory. Max Born, for example, wrote:

  The ultimate origin of the difficulty lies in the fact (or philosophical principle) that we are compelled to use words of common language when we wish to describe a phenomenon, not by logical or mathematical analysis, but by a picture appealing to the imagination. Common language has grown by everyday experience and can never surpass these limits. Classical physics has restricted itself to the use of concepts of this kind; by analyzing visible motions it has developed two ways of representing them by elementary processes: moving particles and waves. There is no other way of giving a pictorial description of motions—we have to apply it even in the region of atomic process, where classical physics break down.4

  This is the view currently held by most physicists: We encounter problems explaining subatomic phenomena when we try to visualize them. Therefore, it is necessary to forgo explanations in terms of “common language” and restrict ourselves to “mathematical analysis.” To learn the physics of subatomic phenomena we first must learn mathematics.

  “Not so!” says David Finkelstein, Director of the School of Physics at the Georgia Institute of Technology. Mathematics, like English, also is a language. It is constructed of symbols. “The best you can get with symbols is a maximal but incomplete description.”5 A mathematical analysis of subatomic phenomena is no better qualitatively than any other symbolic analysis, because symbols do not follow the same rules as experience. They follow rules of their own. In short, the problem is not in the language, the problem is the language.

  The difference between experience and symbol is the difference between mythos and logos. Logos imitates, but can never replace, experience. It is a substitute for experience. Logos is the artificial construction of dead symbols which mimics experience on a one-to-one basis. Classical physical theory is an example of a one-to-one correspondence between theory and reality.

  Einstein argued that no physical theory is complete unless every element in the real world has a definite counterpart in the theory. Einstein’s theory of relativity is the last great classical theory (even though it is a part of the new physics) because it is structured in a one-to-one way with phenomena. Unless a physical theory has one-to-one correspondence with phenomena, argued Einstein, it is not complete.

  Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory.6 [Italics in the original.]

  Quantum theory does not have this one-to-one correspondence between theory and reality (it cannot predict individual events—only probabilities). According to quantum theory, individual events are chance happenings. There are no theoretical elements in quantum theory to correspond with each individual event that actually happens. Therefore quantum theory, according to Einstein, is incomplete. This was a basic issue of the famous Bohr-Einstein debates.

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nbsp; Mythos points toward experience, but it does not replace experience. Mythos is the opposite of intellectualism. Ceremonial chants at primitive rituals (like football games) are good examples of mythos. They endow experience with value, originality, and vitality, but they do not seek to replace it.

  Theologically speaking, logos is the original sin, the eating of the fruit of knowledge, the expulsion from the Garden of Eden. Historically speaking, logos is the growth of the literary revolution, the birth of the written tradition out of the oral tradition. From any point of view, logos (literally) is a dead letter. “Knowledge,” wrote e. e. cummings, “is a polite word for / dead but not buried imagination.” He was talking about logos.

  Our problem, according to Finkelstein, is that we cannot understand subatomic phenomena, or any other kind of experience, through the use of symbols alone. As Heisenberg observed:

  The concepts initially formed by abstraction from particular situations or experiential complexes acquire a life of their own.7 [Italics added].

  Getting lost in the interaction of symbols is analogous to mistaking the shadows on the wall of the cave for the real world outside the cave (which is direct experience). The answer to this predicament is to approach subatomic phenomena, as well as experience in general, with a language of mythos rather than a language of logos.

  Finkelstein put it this way:

  If you want to envision a quantum as a dot then you are trapped. You are modeling it with classical logic. The whole point is that there is no classical representation for it. We have to learn to live with the experience.

  Question: How do you communicate the experience?

  Answer: You don’t. But by telling how you make quanta and how you measure them, you enable others to have it.8

  According to Finkelstein, a language of mythos, a language which alludes to experience but does not attempt to replace it or to mold our perception of it is the true language of physics. This is because not only the language that we use to communicate our daily experience, but also mathematics, follows a certain set of rules (classical logic). Experience itself is not bound by these rules. Experience follows a much more permissive set of rules (quantum logic). Quantum logic is not only more exciting than classical logic, it is more real. It is based not upon the way that we think of things, but upon the way that we experience them.

  When we try to describe experience with classical logic (which is what we have been doing since we learned to write), we put on a set of blinders, so to speak, which not only restricts our field of vision, but also distorts it. These blinders are the set of rules known as classical logic. The rules of classical logic are well defined. They are simple. The only problem is that they do not correspond to experience.

  The most important difference between the rules of classical logic and the rules of quantum logic involves the law of distributivity. The law of distributivity, or the distributive law, says that “A, and B or C” is the same as “A and B, or A and C.” In other words, “I flip a coin and it comes up heads or tails” has the same meaning as “I flip a coin and it comes up heads, or I flip a coin and it comes up tails.” The distributive law, which is a foundation of classical logic, does not apply to quantum logic. This is one of the most important but least understood aspects of von Neumann’s work. In 1936, von Neumann and his colleague, Garrett Birkhoff, published a paper which laid the foundations of quantum logic.9

  In it they used an example of a familiar (to physicists) phenomenon to disprove the distributive law. By so doing they demonstrated mathematically that it is impossible to describe experience (including subatomic phenomena) with classical logic, because the real world follows different rules. The rules that experience follows they called quantum logic. The rules which symbols follow they called classical logic.

  Finkelstein uses a version of Birkhoff and von Neumann’s example to disprove the law of distributivity. Finkelstein’s demonstration requires only three pieces of plastic. These three pieces of plastic are contained in the envelope attached to the back cover of this book. Remove them from their envelope now and examine them.* Notice that they are transparent and tinted about the color of sunglasses. In fact, pieces of plastic just like these but thicker are used for sunglasses. They are very effective in reducing glare because of their particular characteristics. These pieces of plastic are called polarizers and, of course, the sunglasses which use them are called polaroid sunglasses.

  Polarizers are a special kind of light filter. Most frequently they are made of stretched sheets of plastic material in which all the molecules are elongated and aligned in the same direction. Under magnification the molecules look something like this.

  These long, slender molecules are responsible for the polarization of the light which passes through them.

  The polarization of light can be understood most easily as a wave phenomenon. Light waves from an ordinary light source, like the sun, emanate in every fashion, vertically, horizontally, and every way in between. This does not mean only that light radiates from a source in all directions. It means that in any given beam of light some of the light waves are vertical, some of the light waves are horizontal, some are diagonal, and so forth. To a light wave, a polarizer looks something like a picket fence. Whether it can get through the fence or not depends upon whether it is aligned with the fence or not. If the polarizer is aligned vertically, only the vertical light waves make it through. All of the other light waves are obstructed. All of the light waves that pass through a vertical polarizer are aligned vertically. This light is called vertically polarized light.

  If the polarizer is aligned horizontally, only the horizontal light waves make it through. All of the other light waves are obstructed (first illustration, next page). All of the light waves that pass through a horizontal polarizer are aligned horizontally. This light is called horizontally polarized light.

  No matter how the polarizer is aligned, all of the light waves passing through it are aligned in the same plane. The arrows on the polarizers indicate the direction in which the light passing through them is polarized (which way the molecules in the plastic are elongated).

  Take one of the polarizers and hold it with the arrow pointing up (or down). The light coming through this polarizer now is polarized vertically. Now take another polarizer and hold it behind the first polarizer with its arrow also pointing up (or down). Notice that, except for a slight attenuation due to the tint, all of the light that gets through the first polarizer also gets through the second polarizer.

  Now rotate one of the polarizers from vertical to horizontal. As it is rotated, notice that less and less light gets through the pair. When one of the polarizers is vertical and the other polarizer is horizontal, no light gets through them at all. The first polarizer eliminates all but the horizontally polarized light waves. They are eliminated by the second polarizer, which passes only vertically polarized light. The result is that no light passes both the vertical and the horizontal polarizer. It does not matter whether the first polarizer is vertical and the second polarizer is horizontal or the other way round. The order of the filters is not important. In either case, no light passes through them.

  Whenever two polarizers are oriented at right angles to each other they block all light. No matter how the pair is twisted or turned as a unit, as long as they remain at right angles to each other, no light passes through them.

  With this in mind, we come now to the third filter. Align the third filter so that it polarizes light diagonally and place it in front of the horizontal polarizer and the vertical polarizer. Nothing happens. If the first two filters (the horizontal and the vertical polarizer) block all the light, the addition of a third filter, of course, scarcely can affect the situation.

  In a similar manner, if we place the diagonal polarizer on the other side of the horizontal-vertical combination, nothing happens. No light gets through the filters.

  Now we come to the interesting part. Put the diagonal polarizer between the horizontal polarizer a
nd the vertical polarizer. Light gets through the three filters when cut off!

  In other words, a combination of horizontal and vertical polarizers is as much a barrier to light waves as a wooden door. A diagonal polarizer in front of or behind such a combination does not affect this phenomenon. However, if a diagonal polarizer is sandwiched in between the horizontal polarizer and the vertical polarizer, light gets through all three of them. Remove the diagonal polarizer and the light disappears again. It is blocked by the combination of horizontal and vertical polarizers.

  Diagrammatically, the situation looks like this:

  How can this happen? According to quantum mechanics, diagonally polarized light is not a mixture of horizontally polarized light and vertically polarized light. We cannot simply say that the horizontal components of the diagonally polarized light passed through the horizontal polarizer and the vertical components of the diagonally polarized light passed through the vertical polarizer. According to quantum mechanics, diagonally polarized light is a separate thing-in-itself. How can a separate thing-in-itself get through all three filters but not through two of them?