Taking the Quantum Leap, page 19
Feynman: How does the particle find the right path?
What happens if we fool light into taking the wrong paths? Can we do this? The answer is yes. When we fool light, we observe the phenomenon called diffraction, the bending and interfering of light with itself. The way we accomplish this is by blocking the natural light paths. Feynman states:
When we put blocks in the way so that the photons could not test all the paths, we found out that they couldn’t figure out which way to go…, 8
It may seem strange to think of light particles losing their way. But what about ordinary particles like baseballs? Feynman continues:
Is it true that the particle doesn’t just “take the right path” but that it looks at all the other possible trajectories? And if by having things in the way, we don’t let it look, that [it will do something like light does?] … The miracle of it all is, of course, that it does just that. That’s what the laws of quantum mechanics say.9
In other words, we can make matter behave like light. We can block some of the natural paths that matter takes in getting from here to there and cause it to interfere with itself, canceling itself out as light waves would. The world follows all possible paths open to it.
Feynman hoped to find how God gave orders to matter. He found that all possible paths, including the least action paths, contribute to the history of an atomic particle. The particle magically follows as many paths from its present to its future as it finds open to it. This discovery would later stimulate Hugh Everett to formulate a bizarre, parallel universe theory of quantum mechanics. By blocking out the natural or least action path, the quantum interference effects could be observed. By using the idea of a “sum over the paths” available to a particle, Feynman could rid us of any picture regarding quantum wave functions.
But somehow this wasn’t enough. Interfering paths or waves still were a mystery.
Bell’s Theorem: Separate Houses with a Common Basement
Physicists are human. They, too, have fears and likes, just like everyone else. Their needs for warmth, security, and the pursuit of happiness are no different than those of anyone else. But quantum mechanics seems to pull the carpet out from under all our traditional beliefs regarding security and predictability. Quantum physics is not “nice.” It is not simple and straightforward. Thus physicists traditionally brought up with the nice formalities of classical Newtonian physics are often outraged or at least disturbed that quantum physics offers no solace to seekers of a deterministic universe.
All possible futures.
All possible pasts.
Classical physics concepts, like all physics concepts, are unfortunately not immune to the slings and arrows of experience. A theory may be beautiful and elegant, but if it doesn’t fit the facts, it’s just plain wrong. A photon emitted many years ago from a distant star makes its way to my eye. Does it exist if my eye is not there to see it? The question is reminiscent of the age-old puzzle, “If a tree falls in the forest and no one is there to hear it, does it make any noise?” The answer appears so obvious: of course it exists. The photon must be there, like the sound waves from the falling tree, whether or not anyone experiences it. At least, that’s the answer if you believe in classical physics.
But alas, quantum mechanics does not seem to agree. Accordingly, the photon comes into existence as a spot on my retina only when I see it. Physicists have been more or less “forced” to accept this mystical position because of the uncertainty principle, which denies existence to objects having both spatial locations and well-defined paths of motion simultaneously. But suppose that the uncertainty principle is simply a sign of our ineptness. Suppose there is a real physical world out there, but we haplessly mess things up as we go about the world discovering it. To our insensitive methods, a whole world remains hidden. Quantum physics does not deny that we play a role in every measurement procedure. Could there be an underlying, unrevealed order to quantum mechanics?
Such may have been the thoughts of David Böhm in the early fifties.10 Böhm led the chorus of those who followed Einstein’s dream of a nongambling God in a revival of the search for hidden variables. By rewriting Schroedinger’s equation in a form more familiar to the workers in the field of statistical mechanics, Böhm was able to point to the key difference between classical and quantum mechanics. This difference appeared as a single term in the equations and was given the name the quantum potential.
This quantum potential acted upon the real classical particle in much the same way that any field of force would act. Thus the potential was capable of accelerating and slowing the motion of the particle. In this, it was like the gravitational potential that acts upon an automobile coasting along a hilly highway. But the quantum potential was also different, for it depended on the distribution of an infinite number of possible locations of the particle. No matter—the particle had only one position and one unique path. However, it was practically impossible for us to determine that uniqueness because we did not quite know which of its infinitely possible positions the single particle had.
Though the Russian physicist Vladimir Fock felt that Bohm’s position was “philosophically incorrect, “11 no one really argued with Böhm and his followers in a convincing manner. Yet the followers of Bohr would soon rise to the occasion. The Bohr-Einstein debate would live again.
The date was April of 1957. It was the Ninth Symposium of the Colston Research Society, held at the University of Bristol, England.12 Böhm presented his Einstein-inspired uncertainty principle position, while Leon Rosenfeld, a contemporary of Bohr, argued for Bohr’s complementarity.
Bohm’s position was that the underlying assumptions of the uncertainty principle (there cannot be a more deterministic theory than quantum theory) are contradicted by the possible existence of a hidden level of reality. Moreover, Böhm stated, it may be totally impossible to detect this level of reality. Rosenfeld, on the other hand, argued that the world is as we experience it. All hidden variables, if they exist, must be connected to our experiences. They must show themselves. It is the peculiar wholeness of the quantum process, the indivisibility of the quantum of action that must be transferred in any observable process, that denies existence to a hidden, more orderly level of reality. We simply cannot help but disturb the universe whenever we observe it.
It might seem that if we cannot observe anything without changing what we observe, we should perhaps drop the idea that anything exists without our observing it. But then along came John S. Bell and his strange theorem. Bell offered a proof that the hidden variable interpretation sought after by those physicists desiring a deeper, more mechanical, cause-effect basis of reality could reveal an even worse kind of order. Real particles may exist according to Bell, but they follow very strange orders. These orders border on what we now call psychic phenomena.
How did we get to such a strange world view? The heart of the problem for John Stewart Bell was the arbitrary division of the world into things and observers of things. Quantum mechanics did not really tell us where this dividing line was to be drawn and who was observing what? Bell felt that a study of the problem of hidden variables would shed some light. He had become fascinated with the chapter on indeterministic physics in Max Born’s book, Natural Philosophy of Cause and Chance, 13 and he had read Bohm’s 1952 papers on hidden variables. He decided then to present his thoughts in the Reviews of Modern Physics, 14 but due to an editorial error, Bell’s paper, written in 1964, was not published until 1966.
In this review paper, Bell expressed his view that earlier mathematical proofs by the eminent mathematician John von Neumann (who decided that hidden variables were not possible because they were inconsistent with quantum mechanics) were too stringent. He successfully constructed a hidden variable theory describing particles that were spinning like tops.
Paradoxically, while he was writing his review, he was also working on a second paper that contradicted the conclusions of the first paper. He had become obsessed with the Einstein-Podolsky-Rosen argument, and it was the content of this second paper that became known as “Bell’s Theorem.”15 There, Bell proved that any “local” hidden variable theory cannot reproduce all of the statistical predictions of quantum mechanics.
The key word in his paper is local, and it means “on the spot,” happening at a precise location. A local hidden variable is something that only affects things at a particular location. For example, a bottle of champagne awaits me. I open it and it explodes, popping the cork to the ceiling. That explosion depended on the state of the bubbly in the bottle, locally there in front of me. While it is true that the bottler prepared the shipment of wine bottles, all containing champagne from the same barrel, the condition of the champagne upon arrival depended strictly on the environment within each bottle. Those clods who left their bottles in the sun before they opened them have no excuse for the spoilage that resulted. Certainly, their carelessness cannot affect my bottle, which has been carefully preserved in my cool cellar. Thus local variables are quite reasonable.
Nonlocal variables are not at all reasonable. Change any one of them here and something happens elsewhere instantly. In other words, nonlocal variables are our old friend, the Einstein Connection. Bell’s proof showed that hidden variables only affecting the immediate environment would produce observable results that contradict the predictions of quantum mechanics. In other words, if there were hidden variables that behaved reasonably, there would be observable consequences that were entirely unreasonable. How could they be unreasonable? They would alter the “crap” tables of reality.
And now we come to the second part of Bell’s theorem: that local hidden variables cannot reproduce all of the statistical predictions of quantum mechanics. The key word here is statistical. All of us are conditioned by statistics. We literally live in a statistical world. Statistics tell us that people only live seventy years, dogs less than twenty. They also tell us how fast we can drive safely, how much we can eat, and what we should pay for life and medical insurance. They even govern what we will be able to watch on television or in cinemas.
Statistics enable us to discern the underlying laws that govern behavior. Whether the subject is baseballs, rocket ships, atoms, or people, statistics describe normal behavior, what we should expect to observe. Consequently, whenever we observe and label something an abnormality or a deviation we mean that what we observed is not statistically predicted to occur.
Take the famous Nielsen rating system for determining what Americans are watching on television, for example. From just over one thousand television sets, the raters can determine what the whole nation is watching. Why? Because the people watching those Nielsen sets are typical Americans in homes around the United States. They are a sample. If seven hundred sets are tuned to “Happy Days” on a given night, the raters expect that 70 percent of all television sets in the country are tuned to that program. But suppose that the people in the sample system decided to have a conspiracy? In other words, suppose they all decided to watch “I, Claudius” on PBS instead of “Happy Days.” Since it is highly unlikely that 70 percent of the nation as a whole would be watching the PBS program, we would have quite a deviation from the statistic norm.
And indeed, Bell’s theorem showed that local hidden variables, like the hypothetical hidden conspiracy of the Nielsen sample system, would create results that would deviate from those predicted by quantum physics. So far, no one has ever observed any phenomenon that deviated from that predicted by quantum mechanics. Thus, if there are hidden variables, the rules they follow are not local.
Nonlocal hidden variables or parameters are, therefore, the only kinds admitted to provide the substructure for a deterministic world. To have an orderly house, you need a collective network basement, one that is common to all of the houses on the block. For nonlocal means just the opposite of local. Whenever a nonlocal parameter varies, it instantly affects objects that are not in its immediate environment. If there were, for example, nonlocal hidden variables governing the opening of my champagne bottle, they would affect the conditions of all champagne bottles processed at the same time as mine. Thus when I pop my cork, the other bottles would also lose some carbonation. And that disagreeable flattening of all those other bottles would occur instantly, at the moment I opened my bottle. While such a deterministic world would give us a kind of cause effect basis for reality, we would all be victimized by the instantaneous whims of those we happened to have interacted with in the past. Bell concluded:
In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not … [satisfy Einstein’s objections in the EPR Paradox].16
Clearly, the price of determinism is too high. We sought hidden variables in the first place to rid us of those tachyonic (faster than light) ghosts. But if we insist on a well-ordered world of observation, the underworld is indeed magical.
The rules followed by hidden variables are far more unruly than the laws of observed variables. The deeper we go in our search for law and order, the more we find ghosts and goblins, monsters and boogeymen. “Is there any hope?” cry the classical realists. Yes, provided that someone can prove that quantum mechanics yields the wrong predictions about the world. So far, however, quantum physics has given excellent results.17
Probing the depths of reality is much like probing our own depths in a psychological study. I am reminded of Carl Jung’s archetypes, forms of what now is called the “collective unconscious mind.” These forms are, in some sense, buried in a deep pool called “the unconscious.” They are said to exist in all of us. But do they? I think not. Furthermore, I don’t believe there is any collective unconsciousness at all. We create it when we seek it, in much the same way that physicists create “hidden variables” when they seek an underlying order to reality.
Thus, there are no “hidden variables.” Why not? Because, simply, we don’t need them to explain anything. The world is already paradoxical and fundamentally uncertain. Further digs lead not to anthropological discoveries, but to human’s creative ability to form from that which is not, that which is. Since there is nothing out there until we find it, we are discovering nothing more than ourselves. No wonder we find paradox wherever we look.
We are that nothing we seek. Just as zero is both plus 10 and minus 10 at the same time, we are composed of complementary properties. If we seek ultimate order or ultimate chaos, we create a monster. What we seek already preexists as imagination or can exist because of imagination. Our imaginations are constantly changing. Nothing is forbidden to them. If quantum physics continues to give a correct picture of reality, then perhaps little is impossible. As one physicist put it: that which is not forbidden is compulsory.
We Has Found the Hidden Variables: They Is Us!
A few years ago I visited physicist John Clauser in his laboratory at the University of California, Berkeley. We had been attending a series of discussions concerning Bell’s theorem. Clauser was one of the first physicists to attempt an experiment measuring the limits set by Bell’s mathematical theorem. His results confirmed quantum mechanics; the hidden variables, if they existed, were nonlocal. As I entered Clauser’s lab, I was amused to see, attached to his door, the words that introduce this part of the chapter. They are adapted from these immortal words of Pogo, Walt Kelley’s comic character: “We has found the enemy, and they is us!”
Clauser’s experiment tested what we meant by physical reality—specifically, objectivity and locality, which he abbreviated as O + L or simply OL. Objectivity is what we have been talking about up to now in this book. It means the existence of a physical universe independent of the actions of my thoughts. The opposite of objectivity is subjectivity—the world as it appears through my eyes. Colors for a color-blind individual are subjectively influenced. So are likes and dislikes of people’s personalities.
A world without objectivity and locality would be a very subjective world. It would consist of one element: me. This is the world of the quantum solipsist.
The world of the quantum solipsist bears some resemblance to Descartes’ “I think, therefore I am.” A quantum solipsist says: I am the only reality. Everything out there is in my mind. To change reality—that is, to change objects into different objects—I need to change my mind. To the extent that I am able to do this, so appears the world as I see it. My failures to achieve dramatic results, such as floating off the ground or traveling backwards and forwards in time as easily as I do so in space, are perhaps due to my lack of imagination.
Similar to solipsism, we have a way of thinking called positivism. Positivism denies everything except sense perceptions as the only admissible basis for human knowledge. What we know is simply what we sense. In contrast, let us add the two ingredients, objectivity and locality. Objectivity means material reality, and locality means that whatever happens here and now can only be caused or affected by past events that were materially connected to the here and now.
And now let us look at a letter written by philosopher Karl Popper to physicist John Clauser, whose experiments confirmed that both objectivity and locality were impossible. Clauser’s experiments showed that a world that is both objective and local—attributes we normally take for granted as the basis for our own world—is not our world. Our world conforms to the rules of quantum mechanics, and quantum mechanics (QM) denies material reality and locality. Clauser and Home describe their results in the conclusion of their 1974 paper in the Physical Review D:
Physicists have consistently attempted to model microscopic phenomena in terms of objective entities, preferably with some definable structure. The present paper has addressed the question of whether or not the existing formalism of quantum mechanics can be recast or perhaps reinterpreted in a manner which restores the objectivity of nature, and thus allows such models (deterministic or not) to be made. We have found that it is not possible to do so in a natural way, consistent with locality, without an observable change of the experimental predictions.18
