The Socks

1978 and 1981

In 1978, when John Bell first met Reinhold Bertlmann, at the weekly tea party at the Organisation Européenne pour la Recherche Nucléaire, near Geneva, he could not know that the thin young Austrian, smiling at him through a short black beard, was wearing mismatched socks. And Bertlmann did not notice the characteristically logical extension of Bell’s vegetarianism—plastic shoes.

Deep under the ground beneath these two pairs of maverick feet, ever-increasing magnetic fields were accelerating protons (pieces of the tiny center of the atom) around and around a doughnut-shaped track a quarter of a kilometer in diameter. Studying these particles was part of the daily work of CERN, as the organization was called (a tangled history left the acronym no longer correlated with the name). In the early 1950s, at the age of twenty-five, Bell had acted as consultant to the team that designed this subterranean accelerator, christened in scientific pseudo-Greek “the Proton Synchrotron.” In 1960, the Irish physicist returned to Switzerland to live, with his Scottish wife, Mary, also a physicist and a designer of accelorators. CERN’s charmless, colorless campus of box-shaped buildings with protons flying through their foundations became Bell’s intellectual home for the rest of his life, in the green pastureland between Geneva and the mountains. At such a huge and impersonal place, Bell believed, newcomers should be welcomed. He had never seen Bertlmann before, and so he walked up to him and said, his brogue still clear despite almost two decades in Geneva: “I’m John Bell.”

This was a familiar name to Bertlmann—familiar, in fact, to almost anyone who studied the high-speed crashes and collisions taking place under Bell’s and Bertlmann’s feet (in other words, the disciplines known as particle physics and quantum field theory). Bell had spent the last quarter of a century conducting piercing investigations into these flying, decaying, and shattering particles. Like Sherlock Holmes, he focused on details others ignored and was wont to make startlingly clear and unexpected assessments. “He did not like to take commonly held views for granted but tended to ask, ‘How do you know?,’ ” said his professor, Sir Rudolf Peierls, a great physicist of the previous generation. “John always stood out through his ability to penetrate to the bottom of any argument,” an early co-?worker remembered, “and to find the flaws in it by very simple reasoning.” His papers—numbering over one hundred by 1978—were an inventory of such questions answered, and flaws or treasures discovered as a result.

Bertlmann already knew this, and that Bell was a theorist with an almost quaint sense of responsibility who shied away from grand speculations and rooted himself in what was directly related to experiments at CERN. Yet it was this same responsibility that would not let him ignore what he called a “rottenness” or a “dirtiness” in the foundations of quantum mechanics, the theory with which they all worked. Probing the weak points of these foundations—the places in the plumbing where the theory was, as he put it, “unprofessional”—occupied Bell’s free time. Had those in the lab known of this hobby, almost none of them would have approved. But on a sabbatical in California in 1964, six thousand miles from his responsibilities at CERN, Bell had made a fascinating discovery down there in the plumbing of the theory.

Revealed in that extraordinary paper of 1964, Bell’s theorem showed that the world of quantum mechanics—the base upon which the world we see is built—is composed of entities which are either, in the jargon of physics, not locally causal, not fully separable, or even not real unless observed.

If the entities of the quantum world are not locally causal, then an action like measuring a particle can have instantaneous “spooky” effects across the universe. As for separability: “Without such an assumption of the mutually independent existence (the ‘being-?thus’) of spatially distant things...,” Einstein insisted, “physical thought in the sense familiar to us would not be possible. Nor does one see how physical laws could be formulated and tested without such a clean separation.” The most extreme version of nonseparability is the idea that the quantum entities are not independently real: that atoms do not become solid until they are observed, like the proverbial tree that makes no sound when it falls unless a listener is around. Einstein found the implications ludicrous: “Do you really believe the moon is not there if nobody looks?”

Up to that point, the idea of science rested on separability, as Einstein had said. It could be summarized as humankind’s long intellectual journey away from magic (not locally causal) and from anthropocentricism (not independently real). Perversely, and to the consternation of Bell himself, his theorem brought physics to the point where it seemingly had to choose between these absurdities.

Whatever the ramifications, it would become obvious by the beginning of this century that Bell’s paper had caused a sea change in physics. But in 1978 the paper, published fourteen years before in an obscure journal, was still mostly unknown.

Bertlmann looked with interest at his new acquaintance, who was smiling affably with eyes almost shut behind big metal-rimmed glasses. Bell had red hair that came down over his ears—not flaming red, but what was known in his native country as “ginger”—and a short beard. His shirt was brighter than his hair, and he wore no tie.

In his painstaking Viennese-inflected English, Bertlmann introduced himself: “I’m Reinhold Bertlmann, a new fellow from Austria.”

Bell’s smile broadened. “Oh? And what are you working on?”

It turned out that they were both engaged with the same calculations dealing with quarks, the tiniest bits of matter. They found they had come up with the same results, Bell by one method on his desktop calculator, Bertlmann by the computer program he had written.

So began a happy and fruitful collaboration. And one day, Bell happened to notice Bertlmann’s socks.

Three years later, in an austere room high up in one of the majestic stone buildings of the University of Vienna, Bertlmann was curled over the screen of one of the physics department’s computers, deep in the world of quarks, thinking not in words but in equations. His computer—at fifteen feet by six feet by six feet one of the department’s smaller ones—almost filled the room. Despite the early spring chill, the air-conditioning ran, fighting the heat produced by the sweatings and whirrings of the behemoth. Occasionally Bertlmann fed it a new punch card perforated with a line of code. He had been at his work for hours as the sunlight moved silently around the room.

He didn’t look up at the sound of someone’s practiced fingers poking the buttons that unlocked the door, nor when it swung open. Gerhard Ecker, from across the hall, was coming straight at him, a sheaf of papers in hand. He was the university’s man in charge of receiving preprints—papers that have yet to be published, which authors send to scientists whose work is related to their own.

Ecker was laughing. “Bertlmann!” he shouted, even though he was not four feet away.

Bertlmann looked up, bemused, as Ecker thrust a preprint into his hands: “You’re famous now!”

The title, as Bertlmann surveyed it, read:

Bertlmann’s Socks and the Nature of Reality
J. S. Bell
CERN, Geneve, Suisse

The article was slated for publication in a French physics periodical, Journal de Physique, later in 1981. Its title was almost as incomprehensible to Bertlmann as it would be for a casual reader.

“But what’s this about? What possibly—”

Ecker said, “Read it, read it.”

He read.

The philosopher in the street, who has not suffered a course in quantum mechanics, is quite unimpressed by Einstein-Podolsky-Rosen correlations. He can point to many examples of similar correlations in everyday life. The case of Bertlmann’s socks is often cited.

My socks? What is he talking about? And EPR correlations? It’s a big joke, John Bell is playing a big published joke on me.

“EPR”—short for the paper’s authors, Albert Einstein, Boris Podolsky, and Nathan Rosen—was, like Bell’s 1964 theorem, which it inspired thirty years later, something of an embarrassment for physics. To the question posed by their title, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?,” Einstein and his lesser-known cohorts answered no. They brought to the attention of physicists the existence of a mystery in the quantum theory. Two particles that had once interacted could, no matter how far apart, remain “entangled”—the word Schrödinger coined in that same year—1935—to describe this mystery. A rigorous application of the laws of quantum mechanics seemed to force the conclusion that measuring one particle affected the state of the second one: acting on it at a great distance by those “spooky” means. Einstein, Podolsky, and Rosen therefore felt that quantum mechanics would be superseded by some future theory that would make sense of the case of the correlated particles.

Physicists around the world had barely looked up from their calculations. Years went by, and it became more and more obvious that despite some odd details, ignored like the eccentricities of a general who is winning a war, quantum mechanics was the most accurate theory in the history of science. But John Bell was a man who noticed details, and he noticed that the EPR paper had not been satisfactorily dealt with.

Bertlmann felt like laughing in confusion. He looked at Ecker, who was grinning: “Read on, read on.”

Dr. Bertlmann likes to wear two socks of different colors. Which color he will have on a given foot on a given day is quite unpredictable. But when you see (Fig. 1) that the first sock is pink...

What is Fig. 1? My socks?

Bertlmann ruffled through the pages and found, appended at the end, a little line sketch of the kind John Bell was fond of doing: But when you see that the first sock is pink you can be already sure that the second sock will not be pink. Observation of the first, and experience of Bertlmann, give immediate information about the second. There is no accounting for tastes, but apart from that there is no mystery here. And is not the EPR business just the same?

Bertlmann imagined John’s voice saying this, conjured up his amused face. For three years we worked together every day and he never said a thing.

Ecker was laughing. “What do you think?”

Bertlmann had already dashed past him, out the door, down the hall to the phone, and with trembling fingers was calling CERN.

Bell was in his office when the phone rang, and Bertlmann came on the line, completely incoherent. “What have you done? What have you done?”

Bell’s clear laugh alone, so familiar and matter-?of-?fact, was enough to bring the world into focus again. Then Bell said, enjoying the whole thing: “Now you are famous, Reinhold.”

“But what is this paper about? Is this a big joke?”

“Read the paper, Reinhold, and tell me what you think.”

A tigress paces before a mirror. Her image, down to the last stripe, mimics her every motion, every sliding muscle, the smallest twitch of her tail. How are she and her reflection correlated? The light shining down on her narrow slinky shoulders bounces off them in all directions. Some of this light ends up in the eye of the beholder: either straight from her fur, or by a longer route, from tiger to mirror to eye. The beholder sees two tigers moving in perfectly opposite synchrony.

Look closer. Look past the smoothness of that coat to see its hairs; past its hairs to see the elaborate architectural arrangements of molecules that compose them, and then the atoms of which the molecules are made. Roughly a billionth of a meter wide, each atom is (to speak very loosely) its own solar system, with a dense center circled by distant electrons. At these levels—molecular, atomic, electronic—we are in the native land of quantum mechanics.

The tigress, though large and vividly colored, must be near the mirror for a watcher to see two correlated cats. If she is in the jungle, a few yards’ separation would leave the mirror showing only undergrowth and swinging vines. Even out in the open, though, at a certain distance the curvature of the earth would rise up to obscure mirror from tigress and decouple their synchrony. But the entangled particles Bell was talking about in his paper can act in unison with the whole universe in between.

Quantum entanglement, as Bell would go on to explain in his paper, is not really like Bertlmann’s socks. No one puzzles over how he always manages to pick different-colored socks, or how he pulls the socks onto his feet. But in quantum mechanics there is no idiosyncratic brain “choosing” to coordinate distant particles, and it is hard not to compare how they do it to magic.

In the “real world,” correlations are the result of local influences, unbroken chains of contact. One sheep butts another—there’s a local influence. A lamb comes running to his mother’s bleat after waves of air molecules hit each other in an entirely local domino effect, starting from her vocal cords and ending when they beat the tiny drum in the baby’s ear in a pattern his brain recognizes as Mom. Sheep scatter at the arrival of a coyote: the moving air has carried bits of coyote musk and dandruff into their nostrils, or the electromagnetic waves of light from the moon have bounced off the coyote’s pelt and into the retinas of their eyes. Either way, it’s all local, including the nerves firing in each sheep’s brain to say danger, and carrying the message to her muscles.

Grown up, sold, and separated on different farms, twin lambs both still chew their cud after eating, and produce lambs that look eerily similar. These correlations are still local. No matter how far the lambs ultimately separate, their genetic material was laid down when they were a single egg inside their mother’s womb.

Bell liked to talk about twins. He would show a photograph of the pair of Ohio identical twins (both named “Jim”) separated at birth and then reunited at age forty, just as Bell was writing “Bertlmann’s Socks.” Their similarities were so striking that an institute for the study of twins was founded, appropriately enough at the University of Minnesota in the Twin Cities. Both Jims were nail-biters who smoked the same brand of cigarettes and drove the same model and color of car. Their dogs were named “Toy,” their ex-wives “Linda,” and current wives “Betty.” They were married on the same day. One Jim named his son James Alan, his twin named his son James Allen. They both liked carpentry—one made miniature picnic tables and the other miniature rocking chairs.