Quantum Strangeness

by George Greenstein

  The next morning, after a gourmet breakfast, we gathered around a large table downstairs. One of the participants [it happened to be John Bell that first morning] stood up to deliver a brief talk. He had not spoken for five minutes before someone interrupted him with a comment. Someone else then chimed in with a comment on the comment— and we were off.

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  For the rest of the week, participants gathered around the table to discuss some of the most fascinating and profound problems of modern physics. … But the conference did not take place only around that table. It also took place out in the garden, and on the streets of Amherst as two or three participants would break away from the group and wander off for a stroll. It took place over meals, which were invariably huge and invariably delicious. The conversations would zip from topic to topic with astonishing rapidity— from the implications of a recent experiment to the standings of the New York Mets, from culinary delights to a possible new theorem four of the participants thought they had just discovered (those four skipped going out to a movie with the rest of us one evening, stayed up to all hours, and eventually decided that their promising new approach was probably no more than a dead end …).

  At one point [during a picnic] Greenstein spotted John Bell and [another participant] off in a corner … that afternoon they had squared off. For years Bell had probed with astonishing brilliance and depth the foundations of quantum theory, and he has argued that the theory is plagued by fundamental inadequacies. [The other participant], in turn, has argued with great subtlety that the mysteries of quantum mechanics have been widely exaggerated, and that in reality the theory poses difficulties no deeper than those raised by many other branches of physics. That afternoon their debate had risen to a passionate intensity.

  Greenstein grew perturbed. [The two] stood with heads together, isolated from the rest of the throng. Were they at it again? Had emotions risen so high that they had grown furious with one another? Greenstein sidled unobtrusively over to eavesdrop— and found them quietly comparing their cameras.7

  Tragically, Bell died, entirely unexpectedly, shortly after the conference.

  As perhaps you can tell, Bell made an extraordinary impression on me.

  His presence was both gigantic and gentle. I felt that I was in the presence of someone who thought more deeply, more intensely, and more honestly

  than most— and who was at the same time among the most considerate

  people I have ever met.

  Never have I encountered a person more committed to getting to the heart

  of a matter, and to a ruthless clarity and honesty. He was passionate in his argumentation. This was so even when he was an undergraduate. During his

  very first course in quantum mechanics its mysteries had disquieted him— as did what he regarded as too cavalier an attitude toward these mysteries on the part of the teacher. He remonstrated with that teacher. According to Bell’s own testimony years later, he got into a heated argument, essentially accusing the professor— a man who had gone out of his way to assist him— of dishonesty.

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  And yet John Bell was one of the gentlest people I have ever met. He was

  considerate, respectful, gracious. He would fight over ideas, but the fights were never personal. You could disagree with him without angering him.

  And in some remarkable way, he could attack your ideas without attacking

  you. John Bell was a gentle battler.

  Bell’s work was pioneering. He showed the way to a new insight. His was

  the first step— and the first step is always the hardest one. You may have noticed that I have made no attempt to show the actual theorem Bell had

  proved. Rather, I have talked about it only in general terms. The reason is that his combination of mathematical quantities is something of a complicated mess, and the proof that they obey his restriction is more complicated still. But in the years following on Bell’s work other people have proved

  theorems analogous to his, going beyond his work in various ways. In particular, a generalization of his work has been found that is so simple and straightforward that it is actually possible to give the proof in a nontechnical book. This “Bell­ like theorem” is described in the appendix.

  Bell’s combination of mathematical quantities is, to me at least, quite

  strange. Nothing about it has any clear and simple interpretation, any

  immediately obvious intuitive significance. It just happens to be true that this particular combination of fractions happens to have the property he

  found. Indeed, my guess is that nobody would have found his result even

  slightly interesting— were it not for the amazing fact that quantum theory makes a different prediction.

  How on earth did Bell do it? What led him to formulate this particular

  mathematical expression, and to ask whether it agreed with the predictions of quantum theory? I know of no writings in which Bell explained the train of thought that lead him to his theorem. I know of no one who asked him.

  But I can hazard a guess as to what Bell might have replied to such a

  question. He might have said the same thing that every creative person

  would say: that it involved work— lots and lots of work, months and years

  of immersing himself in the problem, of wrestling with it day in and day

  out, living with it morning, noon, and night. He might have said that he

  used one approach and then another, trying this and trying that, groping

  about in the darkness— but a darkness that, as the effort wore on, seemed

  to be slowly lifting. He might have said that he sought to identify what was

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  good about an approach that almost worked, and what was bad about one

  that came nowhere near working, and that he modified his various attempts

  accordingly. He might have said that the final result seemed to have come

  to him in a flash (but only after endless slogging). Or he might have said that it came to him gradually, incrementally, with agonizing slowness.

  But most of all, I imagine, he might have leaned back in his chair and

  smiled, and said that in the last analysis he really did not know how he had done it.

  11 Stigma

  One day in his office at CERN Bell was visited by a young physicist who told Bell that he was gearing up to do an experiment based on Bell’s Theorem.

  “Do you have a permanent position?” was Bell’s response.

  It was a joke— but only something of a joke. Bell knew all too well,

  indeed from personal experience, that there was a stigma attached to doing such work. Bell’s stature in the field was secure, but that of his visitor was not: the proposed experiment was to count toward his PhD dissertation

  work. Bell knew that the young man was taking a risk, for his experiment

  would take place amid a general atmosphere of indifference.

  Not for eight years after his groundbreaking discovery was the first

  experiment conducted to test Bell’s result. And not for seventeen years was the second set of experiments performed. That does not exactly add up to a burst of excited attention. The same pattern is found in the attention paid by other scientists to the article in which Bell announced his discovery.

  Most important discoveries in science are greeted by an immediate and

  intense burst of interest. In contrast, Bell’s was greeted with a near­ complete disinterest. Hardly anyone paid any notice. It was only slowly, over a period of more than a decade, that attention to his theorem slowly built up.

  This indifference was part of a wider pattern. Perhaps my own testimony

  will be illuminating here. I was certainly aware, in a vague way, of Bell’s result in those days. But I paid it little attention. Why? Had you been there to ask me, I would have said that it wa
s simply because I was busy with

  other things.

  And to be honest, this is a perfectly valid response. At every stage of

  one’s life, there are a few things that one is doing, and there is a well­ nigh infinite number of things that one is not doing. By now I find myself fascinated with Bell’s work and its implications— but, by the same token, I am

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  not working on the composition of the rings of Saturn, or the origin of the moon, or the nature of quasars. There are only so many hours in the day.

  Looking back on my career, it seems to me that many times my choice

  of what to work on has been influenced by what everybody else was working on. If everybody in my field was fascinated by such­ and­ such an issue, then I was likely to be too. And usually that issue was indeed fascinating, and worthy of attention— and indeed, much fine work was being done on it,

  and many wonderful results obtained. Why turn one’s back on all this good

  stuff? Why spend time way off in the boondocks, working on an issue that

  nobody else cared about?

  But in the end I cannot say that I find any of this fully persuasive. None of it really accounts for the great silence that greeted Bell’s work. There was a near­ total lack of interest, a well­ nigh universal shrug. Was it all just a matter of fashion, of the style of work people prefer to do? (The reader may be surprised to read of fashion playing a role in science. And of course it has no place if we are speaking of its dictating the results of scientific research: the physical universe is not a matter of opinion or taste. But it is another matter entirely if we are speaking of the choice of what research to conduct.)

  Why did the great mystery, which so engrossed the founders of quantum

  mechanics, simply seem to pass out of fashion for so many years?

  Part of the reason was John von Neumann.

  Von Neumann was a mathematician, one of the most prestigious of his

  age. Born in Hungary to wealthy parents— his father, a banker, was elevated to the nobility— he was raised in an 18­ room apartment on the top floor

  above the multigenerational family business. There, his parents realized

  that they had a child prodigy on their hands. By the age of six he was doing the sort of arithmetic that the rest of us would find hard on paper: he was doing it in his head. Within two years he had learned calculus. At 15 he

  began private studies with a prominent mathematician who found himself blinking back tears on encountering so prodigious a talent. By his late twenties he had published 32 major scientific papers, at the rate of nearly one a month.

  This extraordinary genius was no recluse. He loved the good life. He

  appreciated food (his wife joked that he could count everything except calories) and drink and conversation. And he loved clothes. Invariably dressed formally, he was so elegant that one of his teachers inquired at his doctoral

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  exam “Pray, who is the candidate’s tailor?” He did his best work surrounded by cacophony, and at his office would regularly blast loud German march

  music out on his phonograph. He was a ghastly driver.

  Von Neumann’s fellow mathematicians were frankly astounded at his

  talent. One, whose lectures von Neumann attended as a student, said that

  he “was the only student I was ever afraid of.” He made seminal contributions over an extraordinarily wide swath, ranging from the foundations of mathematics all the way up to game theory and economics. He worked on

  weapon design— he took part in the Manhattan Project, which developed

  the atomic bomb, and he contributed to the design of the hydrogen bomb.

  And he worked on quantum theory.

  In 1932 von Neumann published a book entitled Mathematical Founda-

  tions of Quantum Mechanics. It was a hugely influential work— a work of which he himself was quite proud. And in that work he proved— proved

  mathematically, proved rigorously, and without a shadow of a doubt— that

  hidden variables had no place in quantum mechanics.

  My guess is that many physicists found themselves positively relieved at

  this result. If there is one thing that the ongoing argument between Bohr

  and Einstein proved, it is that the question of the interpretation of quantum mechanics is hard— very hard. And now one of the most famous mathematicians in the world had relieved them of the burden of carrying on the task. There were no hidden variables. Quantum mechanics was not half a

  theory. It was a full theory.

  There was only one problem. Von Neumann’s proof was only a “proof.”

  It contained an error.

  But the error was subtle and it eluded people for decades. During the

  intervening period, everyone thought that the problem had been solved. It

  was only years later that the error was discovered.a

  So it is a complicated story. For decades physicists found themselves free to ignore the historical argument that had once raged over the nature of quantum reality. Since they felt they did not have to deal with it, they did not deal with it. So there was plenty of reason for these matters to be relegated to the sidelines.

  a. The error was discovered in 1935 by Grete Hermann— and then again independently by Bell himself many years later.

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  But I believe there is more to the story than this. Because I believe it was not just a matter of indifference. It was a matter of scorn. I think that discussion of the subject was greeted in those days with an active antipathy.

  Look, for instance, at where Bell had chosen to publish his result. Avoiding all the mainstream journals, he had placed it in a new and obscure journal, one that promptly went out of business. Why did Bell hide his great discovery away like this? Why was he worried? I’d say he was worried because of the stigma. At the time, Bell was on sabbatical leave, and he apparently felt uncomfortable asking his host institution to pay the cost of publishing anything on so outlandish a topic. Most scientific journals support themselves financially by assessing authors a fee to cover the cost of publication: these fees can be quite steep. So he chose to publish in one of the few journals that did not levy these charges.

  What had changed from the days of the Bohr– ­ Einstein debates to this?

  The historian of science David Kaiser attributes this shift in attitude to the cataclysm of World War II and the exigencies of the Cold War. Federal

  funding for physics shot up enormously during the war— by a factor of over 50 within a mere seven years. Such a flood of money was bound to have a

  transformative effect on the field.

  The annihilation of Hiroshima and Nagasaki forever altered the status

  of physics in the eyes of the world— and in the eyes of physicists too. Once gentle souls, lost in their ivory towers, physicists suddenly found themselves acting more like hard­ nosed captains of industry. Once they were philosophers, now they were warriors:

  Before the war, Einstein, Bohr, Heisenberg, and Schrödinger had held one model in mind for the aspiring physicist. A physicist should aim, above all, to be a Kulturträger— a bearer of culture— as comfortable reciting passages of Goethe’s Faust from memory or admiring a Mozart sonata as jousting over the strange world of the quantum. The physicists who came of age during and after World War II crafted a rather different identity for themselves. Watching their mentors stride through the corridors of power, advising generals, lecturing politicians, and consulting for major industries, few sought to mimic the otherworldly, detached demeanor of the prewar days.1

  It was not just a matter of self­ image. Physicists were being enlisted as soldiers in the Cold War. People were urgently needed to combat Soviet

  domination in the arms race and the space race— highly trained people

  skilled in the arcana of the new physics.
Enrollments in physics courses

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  exploded. At the start of the World War the United States was turning out

  fewer than 200 physics PhDs per year— but by 1960 that number had more

  than tripled, and by 1970 it had passed 1,500. In such an atmosphere there was no need— and no time, and maybe even no stomach— to go into such

  charming stuff as the ultimate nature of reality. Tough people were wanted: can­ do types who would roll up their sleeves, brush aside the niceties, and get down to cases. People with deadlines to meet and jobs to do.

  And the world got what it wanted.

  Experimental Metaphysics

  12 Experimental …

  Does Bell’s discovery show the hidden­ variables idea to be worthless? Not at all! What it shows is that any local hidden­ variables theory is going to be different from quantum mechanics. Maybe it is quantum mechanics that is

  worthless. For after all, suddenly we realize that we have not one theory but two: on the one hand quantum mechanics; and on the other hand something else, a hidden­ variables picture of the world that does everything that quantum mechanics cannot do and explains the workings of the microworld. It is not a failure to realize that there can be no hidden­ variables picture of the world underlying quantum theory. Perhaps it is a wonderful

  opportunity.

  Because if you have two theories, you might want to ask— which one is

  right? An experiment can decide. An experiment in metaphysics.