# Bell’s math showed that quantum weirdness rang true

## 50 years ago, theorem found a way to dash Einstein’s hopes for physics sanity

*First of two parts*

There’s just enough time left in 2014 to sneak in one more scientific anniversary, and it just might be the most noteworthy of them all. Fifty years ago last month, John Stewart Bell transformed forever the human race’s grasp on the mystery of quantum physics. He proved a theorem establishing the depth of quantum weirdness, deflating the hopes of Einstein and others that the sanity of traditional physics could be restored.

“Bell’s theorem has deeply influenced our perception and understanding of physics, and arguably ranks among the most profound scientific discoveries ever made,” Nicolas Brunner and colleagues write in a recent issue of *Reviews of Modern Physics*.

Before Bell, physicists’ grip on the quantum was severely limited. Weirdness was well established, but not very well explained. Heisenberg’s uncertainty principle had ruined Newton’s deterministic universe — the future could not be completely predicted from perfect knowledge of the present. Waves could be particles and particles could be waves. Cats could be alive and dead at the same time.

Einstein didn’t buy it, insisting that underlying the quantum fuzziness there must exist a solid reality, even if it was inaccessible to human eyes and equations.

But try as he might — and he tried several times — Einstein could devise no experiment showing quantum physics to be in error. The best he could do was demonstrate how unbelievable quantum physics really was. In 1935 he pointed out (as had Erwin Schrödinger at about the same time) that quantum rules apparently defied “locality,” the notion that what happens far away cannot immediately affect what happens here.

As Einstein described it, in a paper with collaborators Boris Podolsky and Nathan Rosen, quantum mechanics — the mathematical apparatus governing the subatomic realm — seemed incomplete. If two particles of light interact and then fly far apart, quantum math describes them as still a single system. Measuring a property of one of the particles therefore instantly tells you what the result would be when someone measured the same property for the other particle. In the language now used to describe this situation, the particles are “entangled.”Typically, the property to be measured would be something like spin (the direction that a particle’s rotational axis points) or polarization (the orientation of the vibrations if you view the light as a wave). Depending on how you create the entangled particles, the spins or polarizations might turn out always to be opposite. That is, if one particle’s spin is measured to be pointing up, the other will surely point down.

At first glance, there seems to be a simple explanation for this mystery. It could be just like sending one of a pair of gloves far away. If the recipient sees a left-handed glove, the one you kept must be right-handed.

But quantum physics is not like that. It’s more like sending away one of a pair of mittens, and the mitten becomes a glove, assuming a handedness when the recipient puts it on. The stay-at-home mitten would then suddenly become a glove with the opposite handedness.

Or at least that is the standard view. Einstein sympathizers contended that maybe some unseen factors, “hidden variables,” controlled the outcome, forcing the mittens to have had a handedness all along. For nearly three decades, there seemed to be no way to resolve that dispute. Both views of quantum physics would, everyone believed, predict exactly the same outcomes for any possible experiments.

But Bell perceived the situation with more sophistication. In a paper published in November 1964, he worked out an ingenious mathematical theorem to show that a hidden-variables reality would produce different experimental results.

Bell’s insight incorporated the fact that quantum math predicts probabilities for outcomes, not definite outcomes. In real entanglement experiments (which at the time could just be imagined), many measurements would be made. If every day you send one of a pair of entangled particles to Alice in D.C. and the other to Bob in L.A., they both can choose to make any of several possible measurements. When they meet once a year in Dallas to compare results, they’ll find that the outcomes match more often than chance. In principle, that correlation could arise either from quantum weirdness or from hidden variables.

But Bell showed that the two explanations predicted different degrees of correlation. In one case, for instance, math using hidden variables predicted that the measurements would match 33 percent of the time. Quantum math, with no hidden variables, predicted a match no more than 25 percent of the time.

(If you want to see the more general logic worked out explicitly, you can find it in Brunner et al’s paper in *Reviews of Modern Physics*, preprint available at arXiv.org.)

These differences, the “Bell inequalities,” gave experiments something definite to test. By the 1970s such experiments had begun, and in the 1980s Alain Aspect and colleagues in France showed definitively that Bell’s inequalities were violated in real experiments. That meant that local hidden variables could not be causing the mysterious connections in quantum entanglement. Einstein’s hope for a deeper reality did not pan out.

“It is a fact that this way of thinking does not work,” Bell said at a physics meeting I attended in 1989. “Einstein’s view, we now know, is not tenable.”

It’s not that the speed of light limit set by Einstein’s special relativity is violated. Entanglement does not, as is sometimes implied, involve instantaneous faster-than-light signaling. Measurement of one particle does not actually immediately determine the property of the other. It simply tells you what that property will be when measured. (I hope I have always been careful to phrase this by saying one measurement *seems* to affect the other.) It’s just that if you know the result of one measurement, you also know the result of the other, no matter which one is measured first. (And in some cases, which one comes first can depend on how fast you’re moving with respect to them, as considerations of special relativity come into play, as I mentioned at the end of an essay in *Science News* in 2008.)

In any case, the deep impact of Bell’s theorem was not really about proving quantum weirdness. Its greater importance was to make the underlying foundations of quantum physics a topic worth pursuing.

“What Bell’s Theorem really shows us is that the foundations of quantum theory is a bona fide field of physics, in which questions are to be resolved by rigorous argument and experiment, rather than remaining the subject of open-ended debate,” Matthew Leifer of the Perimeter Institute for Theoretical Physics in Canada writes in a recent paper.

That debate has made enormous progress in identifying and clarifying quantum phenomena, opening the way to new fields of study such as quantum information theory and new technologies for quantum communication and computation.

Still, experts argue. Bell’s theorems admit some loopholes that may not all have been closed. Perhaps, for instance, hidden variables can still guide quantum particles if reality is not local. And an ongoing debate rages (at the quantum level) about whether the “quantum state” of a particle simply represents knowledge used to make predictions, or is in fact a real thing in itself. This epistemic vs. ontic argument warrants the advertised Part 2 of this post, coming soon.

But don’t hope for a definitive resolution of that issue. That’s not the quantum way.

After Bell’s 1989 talk, I chatted with him briefly, telling him I had enjoyed his book of collected papers on quantum topics. He remarked that I therefore knew more about it all than he did, as he had forgotten most of what he had written.

In the quarter century since then, I’ve read hundreds more papers on quantum physics, at least a couple of dozen books, attended numerous quantum talks at conferences and interviewed many of the world’s leading quantum experts multiple times. So I can confidently say now that John Bell was wrong. I don’t know more than he did about quantum physics, because the more I find out about it the less I know. In fact, I’m pretty sure that I know nothing at all. And I’m beginning to suspect that nobody else knows anything, either. It may just be inherent in the very nature of the universe that we just can’t know. All anybody can do is suspect.

*Follow me on Twitter: **@tom_siegfried*