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Physics + MathPhysics & Math

Quantum Gambling and the Nature of Reality

American physicist David Bohm proposed an entirely new way of understanding quantum physics—but that had been proven impossible 20 years before, by John von Neumann, the greatest mathematical genius alive.

ByAdam BeckerNOVA NextNOVA Next
john-bell
John Bell discussing experimental tests of his theorem in 1982

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In 1952, John Bell saw the impossible done. Bell was a young physicist working in the particle accelerator division of the Atomic Energy Research Establishment in England; he spent his days finding new and better ways to smash subatomic particles together at high speeds, turning energy directly into mass, and searching for the fundamental constituents of all matter.

But the impossible thing wasn’t in a particle accelerator. It was in a new paper by the American physicist David Bohm. Bohm’s paper proposed an entirely new way of understanding quantum physics—but that had been proven impossible 20 years before, by John von Neumann, the greatest mathematical genius alive. Searching Bohm’s paper for errors, Bell quickly realized that there were none. Bohm had clearly found another interpretation for the strange mathematics of quantum physics, despite von Neumann’s proof. How? Where had the mighty von Neumann gone wrong, and why hadn’t anyone seen it before Bohm?

Bell had never been happy with quantum physics. “I hesitated to think it was wrong,” he said, “but I knew it was rotten.” To Bell, the theory seemed incredibly vague about the true nature of reality. The godfather of quantum physics, Niels Bohr, talked about a division between the world of big objects, where classical Newtonian physics ruled, and small objects, where quantum physics applied. But Bohr was maddeningly unclear about the location of the boundary between these worlds. Bohr “seems to have been extraordinarily insensitive to the fact that we have this beautiful mathematics, and we don’t know which part of the world it should be applied to,” said Bell. Frustrated with the situation, Bell had even gotten into fights with one of his quantum physics instructors at Queens College in Belfast. “I was getting very heated and accusing him, more or less, of dishonesty,” Bell recalled later. “He was getting heated too and said ‘You’re going too far.’ But I was very engaged and angry that we couldn’t get all that clear.”

Yet Bell eventually made an uneasy peace with quantum physics. Part of the reason was the wild success of the theory: it explained why the sun shines and how our eyes see; it showed the true origin of the periodic table of the elements and explained why objects like chairs and bones are solid. But there was more to Bell’s change of heart. Shortly before graduating from Queens in 1949, he heard about von Neumann’s proof that supposedly showed the vagueness of quantum physics was here to stay—that there was no other way of understanding the theory. Bell hadn’t been able to read the original proof himself since it was in German, a language Bell didn’t know. But upon hearing of the proof’s existence from a reputable source, Bell “got on with more practical things” than his concerns about the vagueness at the heart of quantum physics, as he later put it.

Bell eventually made an uneasy peace with quantum physics.

Three years later, Bohm’s papers shattered the fragile peace that Bell had made with the quantum. Bohm had found another way of thinking about quantum physics—a much more precise way, to Bell’s mind. Rather than being vague about the nature of the quantum world, Bohm suggested that subatomic particles were guided by “pilot waves,” and it was the interaction of these waves and particles that led to all the seemingly-bizarre consequences of quantum physics. And because the mathematics of Bohm’s theory was identical to that of the usual quantum mechanics, it could reproduce all of its wild successes.

This was exactly the kind of thing that had purportedly been ruled out by von Neumann’s proof. How had Bohm, a relatively unknown physicist, shown up von Neumann, arguably the greatest mathematician alive? Bell had to know. But he couldn’t do it without reading von Neumann’s original proof. And by the time that proof was published in English, in 1955, life had intervened for Bell: he had gotten married and gone off to Birmingham to get his PhD in particle physics. Yet Bohm’s work “was never completely out of my mind,” Bell said. “I always knew that it was waiting for me.”

Finally, in 1963, Bell returned to the puzzle of Bohm’s theory. He discovered that von Neumann’s revered proof quickly withered under mild scrutiny. “The von Neumann proof, if you actually come to grips with it, falls apart in your hands!” said Bell. “There is nothing to it. It’s not just flawed, it’s silly!” Bell wrote up his thorough demolition of von Neumann’s proof (and two similar proofs that had cropped up more recently) and sent it off for publication. But something was still bothering him. He had shown that Bohm’s theory wasn’t ruled out by von Neumann’s proof, or any other. But Bohm’s theory did have a puzzling feature: the motion of a particle in one place could have an instantaneous effect on a far-distant pilot wave. “Terrible things happened in the Bohm theory,” said Bell. “For example, the [paths of] particles were instantaneously changed when anyone moved a magnet anywhere in the universe.” This immediate action-at-a-distance, known as “nonlocality,” was disturbing to Bell. Einstein’s special relativity dictated that no object or causal influence could ever go faster than the speed of light. Yet Bohm’s theory seemed to fly in the face of this.

Was this nonlocality in the pilot-wave interpretation an essential feature of quantum physics? Bell asked this question at the conclusion of his paper demolishing von Neumann’s proof, leaving it unanswered as a possible avenue for future work. But Bell wanted to know now. He immediately started looking for an answer. “I explicitly set out to see if…I could devise a little model that would complete the quantum-mechanical picture and leave everything local,” Bell said. “Everything I tried didn’t work. I began to feel that it very likely couldn’t be done. Then I constructed an impossibility proof.”

Bell’s proof showed that, if the predictions of quantum physics held true in a certain kind of experimental setup, then nature had to be nonlocal. In other words, Bell showed that if quantum physics was right, then sometimes, far-distant things could influence each other faster than the speed of light.

This proof, known as Bell’s theorem, is an astonishing result that has been called the “most profound discovery of science.” It’s also been the subject of intense debate ever since Bell published his result over fifty years ago. To understand that debate, we need to understand Bell’s proof—and to understand Bell’s proof, let’s play some quantum roulette.

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A Tale of Two Roulette Balls

A new casino has opened up in the small town of Bellville, California, in the sparsely-populated northeastern corner of the state—and it’s owned by Ronnie the Bear, who is suspected of having mob connections. Fatima and Gillian, two inspectors from the California Gaming Bureau, head up to Bellville to check out the casino before it opens, because they know Ronnie is probably up to something.

Ronnie’s casino floor has an overcomplicated roulette setup, possibly to impress the inspectors. In the center of the room is a large machine, with a chute extending out from each side to the roulette tables at either end of the floor. At each of the two roulette tables, there are three roulette wheels, with a smaller spinning dial in the center. In accordance with state law, the roulette wheels only have alternating squares of red and black on them, not numbers—roulette wheels with numbers on them are illegal in the state of California (Figure 1). Once Fatima and Gillian are each seated at one of the tables, Ronnie presses a button on the machine, and a roulette ball appears in each of the chutes, rolling toward the tables. The inspectors spin the center dial while the balls are en route, and each roulette ball lands automatically in whichever wheel is selected, eventually settling on a red or black square. (Figure 2).

Figure 1
Figure 1: (a) A California roulette wheel. (b) The “triple wheel" at Ronnie’s casino, with the selector dial in the center.

Gillian and Fatima do this many times over, to inspect the properties of these wheels thoroughly, and they take detailed notes on the outcomes: which wheel was used and what color came up on each run. Black and red show up in roughly equal proportions, and after several dozen runs, the inspectors go back to their office to compare their notes.

Figure 2
Figure 2: The roulette tables at Ronnie the Bear’s casino in Bellville

The inspectors find that each table’s roulette wheels really do seem completely random—red and black each came up almost exactly half the time. But there are strange correlations between Fatima’s notes and Gillian’s notes. Each time the small dials at the two tables selected the same wheel number, the two roulette balls landed on the same color. For example, on run 87, both dials both pointed to wheel 2—and both roulette balls landed on red (Figure 3). The inspectors conclude that the balls are pre-programmed in the giant roulette-ball machine, in order to ensure they always land on the same color when they go to matching wheels.

Figure 3
Figure 3: A sample of Gillian’s notes and Fatima’s notes, compared

But then Fatima notices a second pattern in the results. When Fatima and Gillian didn’t use corresponding wheels, they only got the same outcome 25% of the time. Fatima doesn’t think that this can be right. She writes out the eight different possible instruction sets that the roulette balls can be carrying (Figure 4).

Figure 4
Figure 4: The only possible instruction sets for the roulette balls

A ball with the first of these instruction sets, ‘Red Red Red,’ would always land in a red slot no matter what wheel it was placed in. A ball with the second set, ‘Red Red Black,’ would always land in a red slot if it were placed into wheels 1 or 2, but would always come up black in wheel 3, and so on. Fatima points out that no matter which of these instruction sets the roulette balls are sharing, her results and Gillian’s results should match more than 25% of the time when they don’t use corresponding roulette wheels:

  • If the two balls are sharing instruction sets Red Red Red or Black Black Black, then they’ll match 100% of the time, even when they end up in differently-numbered wheels.
  • If the two balls are sharing one of the other instruction sets, then when Fatima and Gillian are using differently-numbered wheels, the balls should land on the same color one-third (33%) of the time. For example: say the instruction set is Black Red Red. Then Fatima and Gillian will get different colors if they’re using wheel combinations 1&2, 2&1, 1&3, or 3&1. But they’ll get the same color if they’re using wheel combinations 2&3 or 3&2—two out of the six total possibilities, or one-third. The other instruction sets (other than Black Black Black and Red Red Red) work the same way.

Therefore, when Fatima and Gillian aren’t using corresponding roulette wheels, they should be getting the same color at least 33% of the time, since there are no instruction sets that would make such matches less common than that. And yet, they only match 25% of the time under those circumstances. The inspectors are forced to conclude that the roulette balls are not sharing instruction sets. Yet the roulette balls always land on matching colors when Gillian and Fatima are using corresponding roulette wheels, so they clearly do have some kind of coordination going on—that’s what led the inspectors to suspect the balls were sharing instruction sets to begin with. Therefore, to account for these results, the roulette balls must be sending signals to each other after they know which wheel they’re arriving at.

Stranger Photons

Ronnie’s casino actually exists. But the roulette balls there are not really roulette balls—they’re pairs of photons, tiny packets of light. The roulette wheels are polarizers, machines that measure polarization (a property of light) along three different directions, selected randomly while the photons are in flight toward the machines. The two photons in each pair are “entangled” with each other, which is a term from quantum physics that just means the photons behave in the bizarre way described in the story about Ronnie’s casino. And Bell’s theorem is the proof embedded in the story, the one that Fatima figured out.

Just as in the story about the casino, there’s something strange going on with these photons, and it can’t be accounted for by assuming the photons have hidden instructions that they carry with them from the moment they separate. And entangled photons really do behave this way, so something very strange must be going on in quantum physics. But what, exactly, did Bell prove? To understand this, let’s take a closer look at what happened at Ronnie’s casino.

We started out with the assumption that roulette balls can’t magically communicate with each other instantaneously across long distances (though we never explicitly stated this until the end). Physicists call this no-instantaneous-signaling assumption “locality.” This idea of locality led us to the conclusion that there must be hidden instruction sets in the roulette balls themselves, because that was the only way to account for the perfectly matched outcomes when Gillian and Fatima used the same roulette wheels. But the fact that their outcomes didn’t match more than 25% of the time when they didn’t use the same wheel as Fatima ruled out the possibility of hidden instructions. Therefore, something must be wrong with our assumption: locality must be violated.

In the case of Ronnie’s casino, the roulette balls could still be communicating by radio. But in real experiments, the roulette balls are photons traveling at the speed of light. Those photons are heading to two polarizers that can be very far apart—in some experiments, as far as hundreds of kilometers. Once one photon arrives at a polarizer, no light-speed signal could possibly reach the other photon before it too reaches a polarizer and makes its decision about what to do. In short, the results of real experiments with entangled photons mean that something, some influence, is going faster than light. Entanglement is not just an artifact of the mathematics of quantum physics: it’s a real phenomenon, an actual instantaneous connection between far-distant objects. (It provably cannot be used for faster-than-light signaling, though—to do that, you’d need to be able to control which color each roulette ball landed on at the casino.)

Entanglement is not just an artifact of the mathematics of quantum physics: it’s a real phenomenon.

This is an astonishing result. How can it be right? Relativity dictates that faster-than-light signals are impossible, on pain of paradox. And relativity is one of the best-tested and most solid foundations of modern physics; nonlocality would put it at risk. Is there any other way out of Bell’s theorem? For a long time, some physicists claimed that there was another assumption in Bell’s proof, that of hidden instruction sets. Don’t assume that there are any hidden instructions in the roulette balls at all, the argument went, and Bell’s theorem has no force. But this isn’t correct. We didn’t assume that there were any instructions in the roulette balls, at least not at the start of the proof. Instead, we merely assumed locality, and this inevitably led us to the conclusion that there must be instructions in the roulette balls, in order to account for the perfect match between Gillian and Fatima’s results when they were both using the same roulette wheels. If pairs of roulette balls always land on the same color, then either they’re sharing instruction sets from the start, or they’re somehow communicating once they reach the roulette wheels. There’s no assumption of hidden instructions—there’s merely an assumption of locality, and the behavior of the roulette balls forced us to consider hidden instructions. So this isn’t a good way to save locality. As John Bell put it, “I don’t know any conception of locality which works with quantum mechanics. So I think we’re stuck with nonlocality.”

There might be other ways out of Bell’s theorem: branching multiple universes, signals sent backward in time, or even vast cosmic conspiracies that go back to the Big Bang itself. But these options are even more strange and controversial than nonlocality. And some physicists have suggested denying the very idea of an external reality in order to avoid the conclusion that nature is nonlocal. But denying realism to break Bell’s proof invariably breaks the concept of locality as well—a Pyrrhic victory for those determined to keep physics local at all costs.

In short, Bell’s theorem tells us that either there are subtle signals in nature that can travel faster than light, or something even weirder than that is going on. Either way, Bell’s theorem gives us a glimpse at the true face of the universe, revealing a world that is utterly different from our everyday perspective on reality.

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Excerpted from What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics by Adam Becker. Published by Basic Books, an imprint of Perseus Books, LCC, a subsidiary of Hachette Book Group, Inc. Copyright © 2018 by Adam Becker. All rights reserved.

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