The Irish physicist John Stewart Bell, who in 1964 proposed a way to observe ‘spooky action’ of particles experimentally, at the Large Electron-Positron Collider at CERN, near Geneva, Switzerland, 1989

Corbin O’Grady Studio/Science Source

The Irish physicist John Stewart Bell, who in 1964 proposed a way to observe ‘spooky action’ of particles experimentally, at the Large Electron-Positron Collider at CERN, near Geneva, Switzerland, 1989

In physics, as in politics, there is a time-honored notion that all action is ultimately local. Aptly enough, physicists call this the “principle of locality.” What the principle of locality says, in essence, is that the world consists of separately existing physical objects, and that these objects can directly affect one another only if they come into contact.

It follows from the principle of locality that remote things can affect each other only indirectly, through causal intermediaries that bridge the distance between them. I can affect you, for instance, by extending my arm and giving you a pat on the cheek, or by calling you on your cell phone (electromagnetic radiation), or even—very, very slightly—by wiggling my little finger (gravitational waves). But I can’t affect you in a way that jumps instantly across the expanse of space that separates us, without anything traveling from me to you—by sticking a pin in a voodoo doll, say. That would be a “nonlocal” influence.

The idea of locality emerged early in the history of science. For the Greek atomists, it was what distinguished naturalistic explanations from magical ones. Whereas the gods were believed to be capable of acting nonlocally, by simply willing remote events to occur, genuine causality for the atomists was always local, a matter of hard little atoms bumping into one another. Aristotle adhered to the principle of locality; so did Descartes. Newton (to his own distress) seemed to depart from it, since gravity in his theory was an attractive force that somehow reached across empty space, perhaps instantaneously. But in the nineteenth century Michael Faraday restored locality by introducing the concept of a “field” as an all-pervading, energy-carrying medium through which forces like gravity and electromagnetism are transmitted from one object to another—not instantaneously, as would be the case with nonlocal action, but at a fixed and finite speed: the speed of light.

The principle of locality promises to render the workings of nature rational and transparent, allowing complex phenomena to be “reduced” to local interactions. Nonlocality, by contrast, has always been the refuge of the occult and the hermetic, of believers in “sympathies” and “synchronicity” and “holism.”

Albert Einstein had a deep philosophical faith in the principle of locality. He couldn’t imagine how science could proceed without it. “Unless one makes this kind of assumption,” Einstein said, “physical thinking in the familiar sense would not be possible.” He dismissed the possibility of voodoo-like, space-defying, nonlocal influences as “spooky action at a distance” (spukhafte Fernwirkung).

But in the 1920s Einstein, alone among his contemporaries, noticed something disturbing: the new science of quantum mechanics looked to be at odds with the principle of locality. It seemed to entail “spooky action at a distance.” He took this to mean that there must be something seriously amiss with the quantum theory, which he himself had helped create. (Einstein’s 1921 Nobel Prize was for his work on the photoelectric effect, a quantum phenomenon, not for his discovery of relativity.) He came up with clever thought-experiments to make the problem he saw vivid. Defenders of the quantum consensus, chief among them Niels Bohr, endeavored to rebut Einstein, yet they failed to appreciate the true force of his logic. Meanwhile, quantum theory’s growing record of success in explaining chemical bonding and predicting new particles made Einstein’s qualms look merely “philosophical”—which can be a term of abuse in physics.

And so the matter stood until 1964, a little under a decade after Einstein’s death. That was when an Irish physicist named John Stewart Bell did what no one had imagined was possible: he showed that Einstein’s philosophical objection could be put to an experimental test. If quantum mechanics was right, Bell proved, “spooky action” could actually be observed in the lab. And when the experiment Bell described was carried out—imperfectly in Berkeley in the 1970s, more decisively in Paris in 1982, and near authoritatively in Delft late last year—the “spooky” predictions of quantum mechanics were vindicated.

Yet the reaction to this news—from physicists with an interest in philosophy, from philosophers with an interest in physics—has been strangely equivocal. Some have declared the revelation that nature flouts the principle of locality to be “mind-boggling” (the physicist Brian Greene) and “the single most astonishing discovery of twentieth-century physics” (the philosopher Tim Maudlin). Others think that nonlocality, though perhaps a little spooky on the face of it, is nothing to get metaphysically exercised over, since it “still follows the ordinary laws of cause and effect” (the physicist Lawrence Krauss). Still others—notwithstanding Bell and the subsequent experiments—deny that the world genuinely contains nonlocal connections. Prominent among them is the Nobel laureate Murray Gell-Mann, who insists that all the talk of “action at a distance” amounts to a “flurry of flapdoodle.”


This ongoing debate and its historical background are engagingly described by George Musser in Spooky Action at a Distance. Musser writes that the disagreement over nonlocality is “intellectually pure.” There is nothing financial or personal about it. And if it seems stubbornly unresolvable, that may be because it goes to a deeper issue: Just what should we expect from physics—a recipe for making predictions, or a unified picture of reality?

That was the issue that divided Einstein and Bohr in the early days of quantum mechanics. Einstein was, metaphysically speaking, a “realist”: he believed in an objective physical world, one that existed independently of our observations. And he thought the job of physics was to give a complete and intelligible account of that world. “Reality is the real business of physics” was how he put it.

Bohr, by contrast, was notoriously slippery in his metaphysical commitments. At times he sounded like an “idealist” (in the philosophical sense), arguing that physical properties become definite only when they are measured, and hence that reality is, to some extent, created by the very act of observation. At other times he sounded like an “instrumentalist,” arguing that quantum mechanics was meant to be an instrument for predicting our observations, not a true representation of a world lurking behind those observations. “There is no quantum world,” Bohr provocatively declared.

Bohr was happy with the quantum theory; Einstein was not. Popular accounts often claim that Einstein objected to quantum mechanics because it made randomness a fundamental ingredient of reality. “God does not play dice,” he famously said. But it was not randomness per se that bothered Einstein. Rather, it was his suspicion that the appearance of randomness in quantum mechanics was a sign that the new theory didn’t tell the whole story of what was going on in the physical world. And the principle of locality had an important part in this suspicion.

Here is the simplest of the thought-experiments designed to illustrate this, which has become known as “Einstein’s Boxes.” Start with a box that contains a single particle—say, an electron. According to quantum mechanics, an electron confined to a box does not have a definite location until we look inside to see just where it is. Prior to that act of observation, the electron is in a mixture of potential locations spread throughout the box. This mixture is mathematically represented by a “wave function,” which expresses the different probabilities of detecting the electron at the various locations inside the box if you do an experiment. (In French, the wave function is evocatively called densité de présence.) Only when the observation is made does potentiality turn into actuality. Then the wave function “collapses” (as physicists say) to a single point, and the electron’s location becomes definite.

Now suppose that, before any such observational experiment is carried out, we put a partition through the middle of the box containing the electron. If this is done in the appropriate way, the wave function of the electron inside will be split in two: loosely speaking, half of the wave function will be to the left of the partition, half to the right. This is a complete quantum description of the physical situation: there is no deeper fact about which side of the partition the electron is “really” on. The wave function does not represent our ignorance of where the particle is; it represents genuine indeterminacy in the world.

Next, we separate the two partitioned halves of the box. We put the left half-box on a plane for Paris, and the right half-box on a plane for Tokyo. Once the boxes have arrived at their respective destinations, a physicist in Tokyo does an experiment to see whether there is an electron in the right half-box. Quantum mechanics says the result of this experiment will be purely random, like flipping a coin. Since the wave function is equally split between the two half-boxes, there is a 50–50 chance that the Tokyo physicist will detect the presence of an electron.

Well, suppose she does. With that, the wave function collapses. The act of detecting an electron in the Tokyo box causes the part of the wave function associated with the Paris box to vanish instantaneously. It’s as though the Paris box telepathically knows the (supposedly random) outcome of the Tokyo experiment and reacts accordingly. Now if a physicist in Paris looks in the left half-box, he is certain not to find an electron. (Of course, the “collapse” could have gone the other way, and the Paris physicist could have found the electron.)


That is the orthodox quantum story, as developed by Bohr, Werner Heisenberg, and other founders of the theory. It is called the “Copenhagen interpretation” of quantum mechanics, since Bohr was the head of the physics institute at the University of Copenhagen. According to the Copenhagen interpretation, the very act of observation causes the spread-out probability wave to collapse into a sharply located particle. Hence what has been called the best explanation of quantum mechanics in five words or less: Don’t look: waves. Look: particles.

To Einstein, this was absurd. How could merely looking inside a box cause spread-out potentiality to snap into sharp actuality? And how could looking inside a box in Tokyo instantly change the physical state of a box on the other side of the world in Paris? That would be “spooky action at a distance”—a clear contravention of the principle of locality.

Einstein’s intuition was just what common sense would suggest: the particle must have been in one box or the other all along. Therefore, Einstein concluded, quantum mechanics must be incomplete. It offers a blurry picture of a sharp reality rather than (as its defenders insisted) a sharp picture of a blurry reality.

Bohr never confronted the simple logic of Einstein’s Boxes. Instead, he focused his polemical attention on a later and more elaborate thought-experiment, one that Einstein came up with in the 1930s after he had left Germany and relocated to the Institute for Advanced Study in Princeton. It is referred to by the initials “EPR,” after Einstein and his two junior collaborators, Boris Podolsky (from Russia) and Nathan Rosen (from Brooklyn).

The EPR thought-experiment involves a pair of particles that get created together and then go their separate ways. Einstein saw that, according to quantum mechanics, such particles would be “entangled”: they would stay correlated regardless of how far apart they moved. As an example, consider what happens when an “excited” atom—an atom whose energy level has been artificially boosted—sheds its excess energy by emitting a pair of photons (particles that are components of light). These two photons will fly off in contrary directions; eventually they will travel to opposite sides of the galaxy and beyond. Yet quantum mechanics says that, no matter how vast the separation between them, the two photons will remain entangled as a single quantum system. When subjected to the same experiment, each will respond exactly as its partner does. If, for example, you see the near photon successfully make its way through a polarizing filter (like the kind in sunglasses), you automatically know that its distant partner would do so as well, provided the near and distant filters are set at the same angle.

You might think that such entangled particles are no more mysterious than a pair of identical twins who have moved to different cities; if you see that twin A in New York has red hair, you automatically know that twin B in Sydney is a redhead too. But unlike hair color, quantum properties do not become definite until they are subjected to a measurement. When particle A is measured, it snaps out of a mixture of possibilities into a definite state, and this supposedly forces its entangled partner B to snap out of its own mixture of possibilities into an exactly correlated state.

If quantum mechanics is right, the entangled particles are not like a pair of identical twins; rather, they are like the magical coins that are sometimes imagined in thought experiments: although they are not altered or weighted in any manner, they know to always land the same way when flipped. It is as though there were a telepathic link between the entangled particles, one that enables them to coordinate their behavior instantaneously across vast distances—even though all known methods of communication are, in accord with relativity, limited by the speed of light.

Einstein’s conclusion in the EPR thought-experiment was the same as in Einstein’s Boxes: such a link would be “spooky action at a distance.” Quantum entanglement can’t be real. The tightly choreographed behavior of the widely separated particles must be pre-programmed from the start (as with identical twins), not a matter of correlated randomness (as with magic coins). And since quantum theory doesn’t account for such pre-programming—referred to by physicists as “hidden variables”—it gives an incomplete description of the world.

The EPR reasoning is clear enough up to this point. But the paper that Einstein, Podolsky, and Rosen published in 1935 went further, attempting to discredit the Heisenberg uncertainty principle, which states that certain pairs of physical properties of a particle—such as the particle’s position and its momentum—cannot both be definite at the same time. (Einstein later blamed this overreach on the younger Podolsky, who wrote the last section of the EPR paper.) That muddied matters sufficiently to give Bohr the opening he needed for his rebuttal—which proved to be a masterpiece of obscurity. A decade after he produced it, Bohr confessed that he himself had difficulty making sense of what he had written. Yet as Musser observes, “most physicists just wanted the Bohr-Einstein debate to be over, so they could get on with applying quantum mechanics to practical problems. Because Bohr promised closure, they rallied around him and wrote off Einstein as a has-been.”

One later physicist who stood apart from this consensus was John Stewart Bell (1928–1990). The son of a Belfast horse-trader, Bell made his career in applied physics, helping to design the first particle accelerator at CERN (the European physics center near Geneva). But he also looked on the conceptual foundations of physics with a philosopher’s eye. In the clarity and rigor of his thought, Bell rivaled Einstein. And like Einstein, he had misgivings about quantum mechanics. “I hesitated to think it might be wrong, but I knew that it was rotten,” he said.1

Reflecting on the EPR thought-experiment, Bell ingeniously saw a way to tweak it so that it could be made into a real experiment, one that would force the issue between quantum mechanics and locality. His proof that this was possible, now famous as “Bell’s theorem,” was published in 1964. Amazingly, it required just a couple of pages of high school algebra.

Tim Noble and Sue Webster: Self-Imposed Misery, 2010, a sculpture in which a two-­dimensional ­human silhouette emerges from the projection of a more complicated three-dimensional ­array. Analogously, according to Jim Holt and others, the mystery of quantum nonlocality suggests that the three-dimensional space we experience might be a ­projection of a ­higher-dimensional reality in which the concept of distance is radically different.

© Tim Noble and Sue Webster. All Rights Reserved, DACS, London/ARS, NY 2016. Photo: Andy Keate

Tim Noble and Sue Webster: Self-Imposed Misery, 2010, a sculpture in which a two-­dimensional ­human silhouette emerges from the projection of a more complicated three-dimensional ­array. Analogously, according to Jim Holt and others, the mystery of quantum nonlocality suggests that the three-dimensional space we experience might be a ­projection of a ­higher-dimensional reality in which the concept of distance is radically different.

The gist of Bell’s idea was to get entangled particles to reveal their nonlocal connection—if indeed there was one—by interrogating them more subtly. This could be done, he saw, by measuring the spin of the particles along different angles. Because of the peculiarities of quantum spin, each measurement would be like asking the particle a “yes”/“no” question. If two separated but entangled particles are asked the same question—that is, if their spins are measured along the same angle—they are guaranteed to give the same answer: either both “yes” or both “no.” There’s nothing necessarily magical about such agreement: it could have been programmed into the pair of entangled particles when they were created together.

But if entangled particles are asked different questions—that is, if their respective spins are measured along different angles—quantum mechanics then predicts a precise statistical pattern of matches and mismatches in their “yes”/“no” answers. And with the right combination of questions, Bell proved, this pattern would be unambiguously nonlocal. No amount of pre-programming, no “hidden variables” of the kind envisaged by Einstein, could explain it. Such a tight correlation, Bell proved, could only mean that the separated particles were coordinating their behavior in some way not yet understood—that each “knew” not only which question its distant twin was being asked, but also how the twin answered.

All that remained to settle Einstein’s quarrel with quantum mechanics was to do the experiment Bell outlined and see whether or not this statistical pattern emerged. It took technology a little while to catch up, but by the early 1970s physicists had begun to test Bell’s idea in the lab. In experiments measuring properties of pairs of entangled photons, the pattern of statistical correlation Bell identified has invariably been observed. The verdict: spooky action is real.

So was Einstein wrong? It would be fairer (if a bit melodramatic) to say that he was betrayed by nature—which, by violating the principle of locality, turned out to be less reasonable than he imagined. Yet Einstein had seen more deeply into quantum mechanics than Bohr and the other defenders of quantum orthodoxy. (Einstein once remarked that he had given a hundred times as much thought to quantum mechanics as he had to his own theory of relativity.) He realized that nonlocality was a genuine and disturbing feature of the new theory and not, as Bohr and his circle seemed to regard it, a mere mathematical fiction.

Let’s pause here to note just how strange the quantum connection between entangled particles really is. First, it is undiluted by distance—unlike gravity, which falls off in strength. Second, it is discriminating: an experiment done on one photon in an entangled pair affects only its partner, wherever that partner may be, leaving all other photons, near and far, untouched. The discriminating nature of entanglement again stands in contrast to gravity, where a disturbance created by the jostling of one atom will ripple out to affect every atom in the universe. And third, the quantum connection is instantaneous: a change in the state of one entangled particle makes itself felt on its partner without delay, no matter how vast the gulf that separates them—yet again in contrast to gravity, whose influence travels at the speed of light.

It is the third of these features of quantum nonlocality, its instantaneousness, that is the most worrisome. As Einstein realized early on, it would mean that the entangled particles were communicating faster than the speed of light, which is generally forbidden by the theory of relativity. If, for example, particle A is near the earth and its entangled twin B is near Alpha Centauri (the nearest star system to the sun), a measurement performed on A will alter the state of B instantly, even though it would take 4.3 years for light to get from A to B.

Many physicists tend to brush off this apparent conflict between relativity theory and quantum mechanics. They point out that even though quantum entanglement does seem to entail “superluminal” (faster than light) influences, those influences can’t be used for communication—to send messages, say, or music. There is no possibility of a “Bell telephone” (as in “John,” not “Alexander Graham”). And the reason is quantum randomness: although entangled particles do exchange information between themselves, a would-be human signaler can’t control their random behavior and encode a message in it. Since it can’t be used for communication, quantum entanglement doesn’t give rise to the sort of causal anomalies Einstein warned about—like being able to send a message backward in time. So quantum theory and relativity, though conceptually at odds with each other, can “peacefully coexist.”

For John Bell, that wasn’t good enough. “We have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory,” he observed in a 1984 lecture. If our picture of physical reality is to be coherent, Bell believed, the tension between relativity theory and quantum mechanics must be confronted.

In 2006, an impressive breakthrough along these lines was made by Roderich Tumulka, a German-born mathematician at Rutgers. Building on the insights of Bell and other philosophically-minded physicists, Tumulka succeeded in creating a model of nonlocal entanglement that fully abides by Einsteinian relativity. Contrary to what is widely believed, relativity does not completely rule out influences that are faster than light. (Indeed, physicists sometimes talk about hypothetical particles called “tachyons” that move faster than the speed of light.) What relativity does rule out is absolute time: a universal “now” that is valid for all observers. Entangled particles would seem to require such a universal clock if they are to synchronize their behavior across vast distances. But Tumulka found a way around this. He showed how a certain speculative extension of quantum mechanics—known, for complicated reasons, as “flashy GRW”—could allow entangled particles to act in synchrony without violating relativity’s ban on absolute simultaneity. Although the mechanism behind this nonlocal “spooky action” remains obscure, Tumulka at least proved that it is logically consistent with relativity after all—a result that might well have surprised Einstein.2

Strangely, Tumulka’s feat of reconciling nonlocality with relativity goes unmentioned by Musser. This is a grave omission in an otherwise enlightening (and highly entertaining) book, one that takes us beyond earlier popular treatments into the speculative thickets of contemporary physics: cosmic “wormholes,” “branes,” “twistors,” and so forth. Far from being a quietist about nonlocality, Musser ends up embracing its most extreme implications: “Nonlocality does mean we live in a holistic universe, one that isn’t reducible to its spatial parts.”

In a holistic universe, things that seem to be far apart may, at a deeper level of reality, not be truly separate at all. The space of our everyday experience might be an illusion, a mere projection of some more basic causal system. A nice metaphor for this (proposed by the philosopher Jenann Ismail) is the kaleidoscope. Don’t think of entangled particles as “magical coins” somehow exchanging messages across space. Rather, think of them as being like the multiple images of a glass bead tumbling about in a kaleidoscope—different mirror reflections of the same underlying particle.

Despite such radical implications, the physics profession has (for the most part) taken the demonstration of nonlocality in stride. Younger physicists who have grown up with nonlocality don’t find it all that spooky. “The kids here say, that’s just the way it is,” one senior physicist tells Musser. Among the elder generation, there seems to be a widespread impression that the weirdness of nonlocality can be evaded by taking a “non-realist” view of quantum mechanics—by looking upon it the way Niels Bohr did, as a mathematical device for making predictions, not a picture of reality. One contemporary representative of this way of thinking is Stephen Hawking, who has said, “I don’t demand that a theory correspond to reality because I don’t know what it is…. All I’m concerned with is that the theory should predict the results of measurements.”

Yet a deeper understanding of entanglement and nonlocality is also crucial to resolving the perennial argument over how to “interpret” quantum mechanics—how to give a realistic account of what happens when a measurement is made and the wave function mysteriously and randomly “collapses.” This is the very problem that vexed Einstein, and it is one that still vexes a small and contentious community of physicists (like Sir Roger Penrose, Sheldon Goldstein, and Sean Carroll) and philosophers of physics (like David Z. Albert, Tim Maudlin, and David Wallace) who continue to demand from physics the same thing that Einstein did: a unified and intelligible account of how the world really is. For them, the conceptual foundations of quantum mechanics, and the role of “spooky action” in those foundations, remain very much a work in progress.