*The 2022 Physics Nobel Prize is misunderstood even by the Nobel prize committee itself. What the work of John Clauser, Alain Aspect and Anton Zeilinger has shown, building on John Bell’s ideas, isn’t that quantum mechanics cannot be replaced by a deterministic, hidden variables theory. What it has shown is that quantum mechanics, as well as all of physics, is non-local. “Spooky action at a distance”, what Einstein had found disturbing about quantum mechanics, is real and emerging technologies depend on it, argues Tim Maudlin. *

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The presentation of the 2022 Nobel Prize in Physics to John Clauser, Alain Aspect and Anton Zeilinger is a bittersweet moment for those of us who work in the foundations of physics. It is mostly bittersweet because John Bell, whose brilliant theoretical work provided in impetus and basis for the experimental work done by the laureates, did not live long enough to receive this same recognition for his achievement.

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Bell died unexpectedly of a cerebral hemorrhage in 1990 at the age of 62. His seminal work was done in 1963, so this has been a long time coming. Bell’s work has rightly been characterized as the spark that fueled the “second quantum revolution”, arising from the appreciation of the potential technological usefulness of *entanglement* in quantum systems. But the primary focus of Bell’s work in 1963 was the related question of *locality*. Unfortunately, many news accounts of the implications of Bell’s work and the experiments based on it—including the press release from the Nobel committee itself—have not correctly recounted the situation. So the announcement is also bittersweet because it mischaracterizes what Bell did.

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Einstein’s main complaint about quantum theory was not the indeterminism. It was rather what he called “spooky action-at-a-distance”.

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# Is the Problem Indeterminacy or Spooky Action at a Distance?

Albert Einstein did not like the orthodox, so-called “Copenhagen” understanding of quantum theory. His most oft-repeated and quotable complaint is that according to Copenhagen “God plays dice with the universe”, i.e. the fundamental physical laws are indeterministic and probabilistic rather than deterministic (as Newton’s and Maxwell’s were). But Einstein’s main complaint about quantum theory was not the indeterminism. It was rather what he called “spooky action-at-a-distance”. These two issues are related: in the Copenhagen approach (which postulates both that the mathematical wavefunction used to describe a system provides a *complete* physical description and that it suddenly “collapses” when a measurement is done) it is not just that the collapse is random and unpredictable, but that it has physical effects instantaneously far away from where the collapse occurred. For example, when a dot forms on a screen, indicating that a particle was “found” there, the wavefunction of the particle everywhere else in the universe is instantly reduced to zero. Einstein objected to this sudden universal physical change, not least because it would have to be produced faster than light. His objections began in the 1920’s, when the “new quantum theory” was formulated.

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Einstein’s spooky action-at-a-distance amounted to the claim that what Alice does to her particle in her lab can have an instantaneous physical effect on the state of Bob’s particle in his lab, arbitrarily far away.

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In 1935, together with Boris Podolsky and Nathan Rosen, Einstein made the issue even more obvious and acute by discussing an experimental set-up using a pair of particles (rather than just one) prepared in a special sort of quantum state called an *entangled* state. According to the theory, these particles could be separated to an arbitrary distance from one another (one sent to Alice and the other to Bob) and separately experimented on. Einstein’s spooky action-at-a-distance amounted to the claim that what Alice does to her particle in her lab can *have an instantaneous physical effect* on the state of Bob’s particle in his lab, arbitrarily far away. What they argued was that the Copenhagen understanding of quantum theory—in which the wavefunction provides a complete physical description of the system—requires such spooky action-at-a-distance. Why?

*Two entagled particles: For Einstein, Podolsky and Rosen, "spooky action at a distance" was not acceptable. *

Einstein, Podolsky and Rosen (EPR) constructed a wavefunction such that, although the outcome of a position measurement made by Alice cannot be predicted and so would be regarded as the outcome of an indeterministic and random process, it *can* be predicted with certainly by Bob on the basis of the outcome of *his own* observation of the position of *his* particle. According to Copenhagen, Bob can be in this position to make better predictions than Alice (from the original wavefunction) because his experiment has the effect of *collapsing* the wavefunction of the pair of particles and therefore, because they are entangled, *changing* the physical state of Alice’s. And since Bob (but not Alice) knows how the collapse occurred, he can make better predictions than she can.

EPR observed that this postulation of collapse, and its attendant spooky action, was completely unnecessary. It was only forced on the Copenhagen view because they insisted on the completeness of the wavefunction. Much more reasonable, they argued, is to assume that the outcomes of both Alice’s and Bob’s experiments are *determined by the local situation in their own labs*, and all Bob is doing by his experiment is *finding out about Alice’s particle*, not *changing the physical state* of Alice’s particle. But to pursue this sort of account, one has to concede that the wavefunction does not provide a complete description of the system, which the Copenhagenists were unwilling to do.

This is how things stood for over two decades: EPR argued that to save locality and avoid spooky action-at-a-distance one had to postulate that a quantum system has physical characteristics (such as, for example, the exact position of a particle) that are not recorded or reflected in its wavefunction. These additional postulated physical characteristics came to be known as “hidden variables” (although, as Bell pointed out, it is a very misleading name since the additional variables better not be “hidden” if they are to help solve the problem).

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Bell proved that even a deterministic "hidden variables" theory cannot save locality and replicate all the quantum predictions. Therefore no local theory, of any sort, can return the quantum predictions.

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# Deterministic Quantum Mechanics and Non-Locality

A critical event in our story occurs in 1952 when David Bohm, deeply influenced by discussions with Einstein, publishes a paper laying out an interpretation of quantum theory “in terms of hidden variables”, i.e. a theory that explicitly postulates the incompleteness of the wavefunction. The idea had already been discovered by Louis De Broglie in 1927, but he abandoned the theory for some time. The theory (sometimes called “De Broglie/Bohm theory” or “pilot wave theory” or “Bohmian Mechanics”) is deterministic, and so denies that God plays dice. And it is a “hidden variables” theory that makes the same predictions as the standard Copenhagen quantum theory. The article caught the attention of John Bell, who immediately appreciated what Bohm had accomplished. But the theory was also manifestly and undeniably non-local: it directly postulated spooky action-at-a-distance in its dynamics. In Bohm’s theory, Bob’s experiment can indeed *physically effect* (and not just *provide information about*) the goings-on in Alice’s distant lab. So the theory was of no interest to Einstein, as it did not eliminate the non-locality.

It occurred to Bell to ask whether the achievement of Bohm’s theory—the determinism and general physical clarity of the theory—could somehow be retained but the non-locality eliminated. In 1963, on sabbatical, he had the time to look into the question and he discovered an astonishing fact. Bell considered experiments similar to—but also crucially different from—the ones EPR had discussed. He could do this also due to Bohm’s help: Bohm, in his textbook on quantum theory, had reconfigured the EPR set-up to deal with a particle’s *spin* rather than its position or momentum, as EPR had. Since the spins of particles can be measured in any direction, that immediately suggests a whole universe of experimental possibilities. When Alice and Bob set their spin-measuring apparatuses in the same direction, they always get opposite results: one particle will be deflected up and the other down (although quantum theory does not predict which will go up and which down). So once again, when Bob sees the outcome in his lab, he can make better predictions about what Alice will see than Alice can. But if the two directions of the measuring devices are offset from each other, these perfect correlations slowly degrade.

Bell took a close look at exactly how they degrade and discovered an amazing thing: *the full set of quantum mechanical predictions for these sorts of experiments cannot be reproduced by any local theory*. The EPR correlations, of course, could be recovered by a local theory: it just had to be a deterministic and hence a “hidden variables” theory. But Bell proved that even a deterministic hidden variables theory cannot save locality and replicate all the quantum predictions. Therefore *no local theory, of any sort*, *can return the quantum predictions*. In other words, if quantum theory is predictively accurate in these cases, then locality is a lost cause. One must accept what Einstein called "spooky action-at-a-distance": what is done in one place makes a difference to how things happen in a location and time so far away that even light could not reach there in time.

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The theoretical work by Bell and his successors yields only a conditional conclusion: if Bell’s inequality is violated in the lab, then nature itself must be non-local.

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# Bell’s theorem and the 2022 Nobel Prize

Bell’s mathematical result was extended and refined in various ways. Clauser, Michael Horne, Abner Shimony and Richard Holt relaxed Bell’s assumption of perfect correlations and derived the CHSH inequalities, a generalization of the original Bell inequality. No local physics can robustly produce violations of the CHSH inequality for experiments done far apart. Later, Daniel Greenburger, Michael Horne and Zeilinger derived the GHZ example, which involves three entangled particles rather than two. Again, no local theory can reproduce the quantum predictions for experiments done on the triple, and the relevant predictions are not statistical in nature: they are absolute.

The theoretical work by Bell and his successors yields only a conditional conclusion: if Bell’s inequality or the CHSH inequality is violated in the lab, then nature itself must be non-local. Quantum mechanics predicts such violations, but for many physicists that was just a good reason to expect the quantum-mechanical predictions to fail. Non-locality seemed too strange to accept, as it was for Einstein. But the final arbitration of the question had to be left to the experimentalists, some of whom have just received the Nobel prize for their work.

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Unfortunately, much of this history has been garbled in the public discussion of Bell’s work and its experimental tests. The Noble prize committee itself gets it wrong in its press release.

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The first tests were carried out by Clauser and Stuart Freedman in 1972. They appeared to support the quantum-mechanical predictions, but those loath to give up locality seized upon various experimental “loopholes”. One required improving detector efficiencies and another demanded that Alice and Bob have the settings of their apparatuses change so rapidly that information about how they are set could not be sent from one to the other even using signals that travel at the speed of light. Via the subsequent experimental efforts of Aspect and Zeilinger and others, these loopholes have been successively closed, and there is no serious doubt that the quantum-mechanical predictions are accurate.

Further, it has been shown that the quantum-mechanical states that allow for violations of Bell’s inequality are exactly the entangled states, so proving the physical reality of non-locality suggests that entanglement is an exploitable *physical* resource in a quantum system. This realization inspired people working in quantum computation and quantum communication and quantum cryptography to investigate how entangled states might be used for practical purposes. And that set off the second quantum revolution.

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What Bell’s theoretical work and the subsequent experimental work of Clauser, Aspect and Zeilinger proved was non-locality. Ultimately, they proved Einstein wrong in his suspicions against spooky action-at-a-distance.

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Unfortunately, much of this history has been garbled in the public discussion of Bell’s work and its experimental tests. The Nobel prize committee itself gets it wrong in its press release,

"John Clauser developed John Bell’s ideas, leading to a practical experiment. When he took the measurements, they supported quantum mechanics by clearly violating a Bell inequality. This means that quantum mechanics cannot be replaced by a theory that uses hidden variables."

But that statement is flatly false. Indeed, it was a theory that uses hidden variables—Bohmian mechanics—that inspired Bell to find his inequalities, and that theory makes the correct prediction that the inequalities will be violated. The most well-known and highly developed “hidden variables” theory is that of Bohm, and Bell not only did not refute it, he was one of its most vocal proponents. In “On the Impossible Pilot Wave”—Bell’s wonderful paper expositing the theory—he writes

Why is the pilot wave picture ignored in textbooks? Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show that vagueness, subjectivity, and indeterminism are not forced on us by experimental facts, but by deliberate theoretical choice?

If one rightly wonders how such an encomium for a “hidden variables” theory could be written by the man who “disproved hidden variables”, the simple answer is that it wasn’t. What Bell’s theoretical work and the subsequent experimental work of Clauser, Aspect and Zeilinger proved was non-locality, not no-hidden-variables. Ultimately, they proved Einstein wrong in his suspicions against spooky action-at-a-distance. And that, surely, deserves the highest honors one can bestow.

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The long gap between Bell’s proof—and its experimental tests—and the recognition of the accomplishment is regrettable. We should all be very pleased that that recognition has finally arrived. But the delay was in large part due to persistent misunderstandings and even dismissal of Bell’s work by people who had not put in the effort needed to understand it. May the presentation of the Nobel prize mark the end of these mischaracterizations, so the sweet may triumph over the bitter.

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