Dancing With Myself

by Charles Sheffield

  The converse notion, that quantum theory is only important in the atomic and subatomic world, is false. Quantum indeterminacy is quite capable of revealing itself at the level of everyday living. For example, superconductivity is a macroscopic phenomenon, but it arises directly from the quantum properties of matter.

  However, perhaps the most famous example of the macroscopic implications of quantum indeterminacy, one which has been quoted again and again, is the case of Schrödinger’s cat. This paradox was published in 1935.

  Put a cat in a closed box, said Schrödinger, with a bottle of cyanide, a source of radioactivity, and a detector of radioactivity. Operate the detector for a period just long enough that there is a fifty-fifty chance that one radioactive decay will be recorded. If such a decay occurs, a mechanism crushes the cyanide bottle and the cat dies.

  The question is, without looking in the box, is the cat alive or dead? Quantum indeterminacy insists that until we open the box (i.e., perform the observation) the cat is partly in the two different states of being dead and being alive. Until we look inside, we have a cat that is neither alive nor dead, but half of each.

  There are refinements of the same paradox, such as the one known as Wigner’s friend (Eugene Wigner, born in 1902, was an outstanding Hungarian physicist in the middle of the action in the original development of quantum theory). In this version, the cat is replaced by a human being. That human being, as an observer, looks to see if the glass is broken, and therefore automatically removes the quantum indeterminacy. But suppose that we had a cat smart enough to do the same thing, and press a button? The variations—and the resulting debates—are endless.

  To get out of me problem of quantum indeterminacy, Hugh Everett and John Wheeler in the 1950’s offered an alternative “many-worlds” theory. The cat is both alive and dead, they said—but in different universes. Every time an observation is made, all possible outcomes occur, but the universe splits at that point, one universe for each outcome. We see one result, because we live in only one universe.

  This suggestion is of philosophical but not apparently of practical interest. It will always get just the same experimental results as those of the Copenhagen interpretation.

  We will not try to decide between the Copenhagen interpretation and the Everett-Wheeler many-worlds theory, or other more recent suggestions such as John Cramer’s “transactional interpretation,” published in 1986. Instead, we will accept that quantum indeterminacy is real, and explore the reasons why some people feel that it could be the key to faster-than-light communication.

  4.ACTION AT A DISTANCE

  With waves looking like particles and particles behaving like waves, with energy coming in lumps, with determinacy gone, what was left that the physicists of the late 1920’s could rely on?

  Well, there were still the conservation principles. In any process, momentum had to be conserved, and so did angular momentum. And energy had to be conserved (though since Einstein’s relativity papers in 1905, mass had to be recognized as convertible to energy, and vice versa, according to a precise rule—if “God does not play dice” are Einstein’s most famous words, E = mc2 is certainly his most famous formula). Insisting on these general conservation laws within the new quantum theory not only imposed some order on the confusion, it also led to new physical predictions. Wolfgang Pauli predicted the existence of a new particle, the neutrino, in 1931, based on the conservation principles. That particle was not actually seen until 1954, but most people accepted its existence during that quarter-century wait.

  Angular momentum, or spin, is a variable that quantum theory tells us can take on only a finite set of values. Like the energy levels of atoms, it is quantized. If an object with zero spin breaks into two equal pieces, then conservation of angular momentum tells us that the spins of those pieces must be equal and opposite. (By opposite we mean that the spins are in the opposite sense—imagine two spinning tops, that looked at from above are rotating in clockwise and counterclockwise directions.)

  Now consider one of the two pieces. Quantum indeterminacy tells us that until we look at it, we don’t know the sense of its spin. The two pieces may fly far apart from each other, without our knowing the sense of spin of either one of them, but we can be sure that they must continue to have opposite spins, since their total angular momentum must be zero.

  Suppose that, when the two particles are far apart, we measure the spin of one of them. According to quantum indeterminacy, until that measurement is performed, the particle doesn’t have a defined sense of spin—it has a mixture of two possible spins, and it is only the measurement that forces it into one particular spin.

  But when that happens, the other particle, no matter how far away, must at once take on a spin of the opposite sense to the one that was just measured. Otherwise angular momentum would not be conserved. One particle has affected the other, and the influence has traveled faster than the speed of light.

  A version of this experiment was proposed (as a thought experiment, not a real experiment) by Einstein, Rosen, and Podolsky, in 1935. Their objective was not faster-than-light communication. It was rather to assert that the possibility of measuring a property of one of the particles, without affecting the other, undermined the whole idea of indeterminacy in quantum theory, and therefore that quantum theory was missing some basic element.

  However, another way of looking at the situation can be adopted: suppose that we accept quantum theory. Then the second particle is affected by the measurement we made on the first one. We have achieved “action at a distance,” something that most physicists object to on general philosophical grounds. Any theory that allows action at a distance is called a non-local theory. We are led to one of two alternative conclusions:

  (a) There is something incomplete or wrong in quantum theory; or

  (b) The universe permits non-local effects, where one action here can instantly affect events far away.

  Starting in 1976 and continuing today, experiments have been performed to test which conclusion is correct. They are done by evaluating an expression known as Bell’s inequality, first published in 1964, which gives different results in the two situations (a) and (b).

  The experiments are difficult, but they come down firmly in favor of (b). The universe is non-local; action at a distance is part of nature; and an event here can, under the right circumstances, affect (immediately!) another one far away.

  Faster-than-light communication?

  Unfortunately, no. To achieve communication, some information must be transferred after we have made our observation on one of the two particles. Say that we created a thousand particle pairs. Half the particles fly away together on a spaceship, and their sister particles stay here. Now we test the ones that are here, and observe their spin. We now know what the spins of the other particles must be—but we can’t tell our colleagues on the ship! And they don’t know if we have done those measurements or not, since when they do measurements, they find no pattern to the spins, even if those spins were determined by what we did here. If we could somehow affect the spins that we measure, then the other spins, far away, would change, and we would have a message. But that’s exactly what quantum indeterminacy tells us we can’t do. We have no control over what we will find when we make the measurements.

  Let’s change the question. Quantum theory seems to give us a non-local universe, one in which two events can affect each other unconstrained by the speed of light. Once we accept the idea of action at a distance, is there anything else in the quantum world to give us hope that faster-than-light travel or communication might be possible?

  There is. We remarked earlier that the quantum jumps between electron states in the Bohr atom do not take place via a succession of intermediate states. They sit in one state, and then they are, with no time of transition, instantaneously in another state. We also pointed out that quantum phenomena are not, as one might think, restricted to
the world of the very small, such as atoms and electrons. Superconductivity is a purely quantum phenomenon. Might there be some sort of “quantum jumping” associated with it, which could allow events in one place to affect events in another, unconstrained by the speed of light?

  Ten years ago, I think that every physicist would have said no, just as every physicist would probably have said we would not have superconductors operating at liquid nitrogen temperatures before 1990. Today, we are at the “could be” stage. If we can, by our experiments, show that some events—even one pair of events—far apart in space are coupled, then the universe permits action at a distance. Once we admit that, since all the universe was once intimately coupled (at the time of the Big Bang—see the article, “Something for Nothing”) then it may be just as coupled today, albeit in unobservable ways.

  In the case of superconductivity, the theory tells us that the whole superconductor constitutes a single quantum state. If it changes that state, all the superconductor changes. However, we can make a superconducting ring or cylinder of any size we choose. If a change of state is induced at one end of it, that state change appears immediately at the other end, and should be measurable.

  With the increased availability of superconducting materials, we seem to be just one step away from a great potential breakthrough—a practical test to make one part of a superconducting device respond to another, unconstrained by the limitation of light-speed.

  And if it does not? Then we are back to the drawing boards. Quantum theory is even more subtle and complex than it appears today. The soul-searching and agonizing of the world’s greatest physicists for the past sixty years will go on, perhaps until a unified understanding of gravity and quantum theory is achieved.

  5.THE COMING TRIUMPH

  We suddenly had a new view of the world, one which was so radically different from all that came before that the older generation of scientists could never fully comprehend it. Many of them would, in fact, spend their remaining years trying to refute it.

  The new theory was full of totally unfamiliar concepts; just as bad, it called for the use of mathematical techniques quite unlike any needed for earlier models of the universe. Worse yet, the mathematics contained at its heart deep paradoxes, with processes of thought that defied all logic.

  Only the new, upstart generation of scientists were able to master that new mathematics, resolve those paradoxes, absorb and be comfortable with the new world-view, and finally transform it to a subject easy enough to be taught in any school….

  I am not referring to quantum theory.

  I am talking about the theories of motion and universal gravitation developed by Isaac Newton, and presented to the world in the “Principia Mathematica” in 1687.

  Newton introduced the concepts of absolute space and absolute time, alien ideas to people who had always thought in terms of the relative positions of objects. He suggested that one set of laws—mathematical laws—governed the whole universe. And he spoke a mathematical language that was too hard for almost all his contemporaries.

  Before Newton, astronomical calculations and proofs were geometrical or algebraic. He invented the calculus, and then made it a central mathematical tool, to be learned and used if the new system of the world was to be explored and understood. That same calculus, in its notions of limiting processes, brought into existence philosophical questions and logical paradoxes that would take a century and a half to dispose of.

  And it was only the later generations who would become totally comfortable with the use of the calculus. Not until half a century after Newton’s death did the theory become, in the hands of Euler and Lagrange and Laplace, the easy tool, powerful and flexible, that it is today.

  Scientists have been struggling with quantum theory, what it means, and what lies at its roots, for over half a century. If the earlier revolution in thought that took place in Newton’s time is any guide, a century from now our descendants will look back at our difficulties, and wonder what all the fuss was about. They will see in the 1980’s and 1990’s the clear trail of the most significant papers, the ones that removed the paradoxes and made quantum theory so simple. They will have absorbed the quantum world-view so thoroughly and so early that they will be unable to comprehend the source of our confusions.

  Hindsight is a wonderful thing.

  But there’s no need to envy our great-great-grandchildren. A hundred years from now, they will surely be struggling with their own surprises, their own paradoxes, their total inability to fathom some new mystery that grew, oak-like, from a small acorn of inconsistency between observation and theory that we are not even aware of today.

  Or do I have it completely wrong? Will they be sitting back, with all of nature fully understood and nothing left to baffle them?

  I don’t know. As Pogo remarked in another context, either way it’s a mighty sobering thought.

  6.SOME READING

  The articles in this book are intended to be self-contained. However, occasionally I will recommend a few works that I consider well worth finding and reading. Usually these are books, and books moreover written for the non-specialist, rather than journal articles.

  This has three advantages. It shortens the list of references. It directs the reader to works available in bookstores rather than only in university libraries; and it points to works with a higher level of readability than the original source material.

  It also has three less desirable consequences. First, the reader is always at least one step away from primary data sources. Second, popular texts sometimes gain readability at the expense of accuracy and detail. And third, books normally lag journals by at least a year or two, thus the information that they contain is less current.

  Gribbin, J. In Search Of Schrödinger’s Cat. Bantam, 1984. Clear, readable, and complete (as much as any book can be complete, when the subject is quantum theory).

  Gamow, G. Thirty Years That Shook Physics. Dover reprint of Doubleday text, 1966. With the author’s own strange sketches of the people described. Here is one quotation that gives you the feel for the whole thing: “It often happens that ‘absent-minded professor’ stories grow up around famous scientists. In most cases these stories are not true, merely the invention of wags, but in the case of Dirac all the stories are really true, at least in the opinion of this writer. For the benefit of future historians we give some of them here.”

  The Born-Einstein Letters. Max Born, Editor. Walker & Company, New York, 1971. Great men, in every sense, and great Letters. You see quantum theory as it was being developed.

  Feynman, R.P. The Character of Physical Law. MIT Press, 1967. Thoughts on the nature of physics, by another of the century’s greatest physicists.

  Penrose, R. The Emperor’s New Mind. Oxford University Press, 1989. This book is fascinating but controversial, since its main thesis is that the human brain is not an algorithmic device (i.e., we are not “computers made of meat”). However, it is not that thought, but an important sub-text, that concerns us here. Penrose argues that the collapse of the quantum wave function upon observation is caused not by anything as subjective as the observation itself, but by the fact that the observation creates a critical space-time curvature, at which point the assumption of linear superposition of quantum theory breaks down.

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  story: nightmares of the classical mind

  “…the quantum mechanics paradoxes, which can truly be said to be the nightmares of the classical mind…”

  —Ilya Prigogine, Nobel Prizewinner, 1977

  We had come to re-animate a corpse.

  GOG filled the sky ahead of us, eight kilometers long, a dark, silent figure nailed to a giant cross of metal girders.

  We were silent, too. Vilfredo Germani was taking us to a rendezvous at the center of the crucifix, but unt
il we arrived at the Glory Of God there was nothing to do but gather around the forward screen and stare at the looming figure.

  “Not a glimmer there,” said Celia Germani at last. “Nothing.”

  “What did you expect? A pilot light?” Her father did not turn to look at her. We were less than ten kilometers from GOG.

  She gave me a nudge in the ribs with her elbow, and a second later her hand crept like a little mouse into mine. She scratched her nails gently against my palm.

  “That’s not so daft as you might think,” said Malcolm McCollum. He was the fourth member of the experimental crew, and our expert on anything to do with power systems. “If GOG was set up to run off solar power, there might still be systems ticking over. In fact, I’m hoping there will be. It’ll make start-up a lot easier.”

  Vilfredo Germani said nothing more, but he shook his head. He must have checked the status of the Glory Of God before he made his proposal, and if he thought there was no power on GOG he was probably right. But after Thomas Madison’s death, the return to Earth had been so random and disorganized that anything was possible. No one had a clear idea which sections were still airtight, which power systems had been left on to drain the reserves, or even if everyone on GOG had got away safely. Was there still the possibility of a desiccated corpse or two in one of the station’s convoluted corridors?

  I said nothing at all about that thought. As a late addition and supernumerary to the party, I was supposed to work hard and keep my mouth shut. The original exploration group was to have been just the Germanis, father and daughter, plus McCollum and the shuttle pilots. It was only Celia’s wheedling that had persuaded her father to add me to the group at the last moment.