Einstein's Greatest Mistake

by David Bodanis

  That certainty about the universe was what these new findings seemed to be undermining—in Bohr’s view quite definitively. Causality of an absolute, classical sort didn’t exist. We might think there were exact sequences of events that must follow one another—kick a soccer ball hard, for instance, and it will spring forward—but that’s just because we’re seeing the averaged results of a vast number of submicroscopic encounters, each one operating by chance. The electrons on a player’s boot get very close to the electrons on the leather surface of a soccer ball as he swings his leg forward. That we can see; that we can know. But which of those electrons will repel one another, sending the ball flying away, can never—not even in principle—be entirely known.

  The uncertainty principle proved that these subatomic goings-on were unknowable, Bohr insisted. The micro-world really was different from the ordinary large-scale world we’re used to. On the smallest scale, chaos and indeterminacy ruled how the electrons and other particles that make up our bodies and planet operated. Clarity at the micro level did not exist.

  Einstein had come to know the shambolic, brilliant Bohr very well over the years. At their first meeting, in Berlin in 1920, Bohr had brought along Danish cheese and butter, which was much appreciated in a city still suffering from the recent British blockades. At another meeting, in Copenhagen, they’d been so caught up in conversation—admittedly, much of which must have been Einstein waiting as Bohr paused to put together his intense whispers—that they’d far overshot the streetcar stop for Bohr’s home, turned around, and then overshot the stop coming back as well. They were the two wise men in their field, and they also liked each other. “Not often in life has a human being caused me such joy by his mere presence,” Einstein once wrote to Bohr. He wasn’t going to insult his old friend by mocking this most fundamental of new beliefs in public.

  Only outside the main sessions, after Bohr had publicly said his piece, did Einstein begin to argue back.

  Einstein and Bohr in a reflective mood, probably at their friend Paul Ehrenfest’s house, late 1920s

  BOHR PRESENTED A SHAMBLING FRONT, and took even longer than Einstein to get a pipe lit and keep the tobacco burning. (He carried an extra-large box of matches with him to help.) But he was committed to physics, and in a certain sense to the cause of Professor Niels Bohr. His parents were prosperous and distinguished, and with the confidence from growing up with their connections, he’d arranged—despite the lumbering appearance, he was the most skilled of bureaucratic operators—for the Carlsberg Foundation to support a great research institute under his direction in Copenhagen. Through scholarships, grants, and publications, that institute was doing everything it could to support the view that Bohr took of Heisenberg’s and Born’s results. It would be embarrassing if he were to be proved wrong. Instead of the leader of a new breakthrough in thought, he would look like a middle-aged professor who had jumped on the latest bandwagon simply to seem up-to-date.

  It still seemed possible, however, that Einstein would be able to prove Bohr wrong. All Einstein had to do was show how to construct one machine that could operate in contradiction to the uncertainty principle. If he did that, Bohr’s support of the uncertainty principle would be shown to be empty. The possibility that Einstein could accomplish this was very real. Einstein was, after all, the man whose thought experiments about a falling elevator had led to startling yet fully accurate predictions about starlight swerving near the sun; who had, in 1916, as just one of the more minor of his other thought experiments, envisaged a machine that could amplify light on call—the machine that would eventually become our laser. Who was to say that he could not solve this puzzle, too?

  Yet Einstein, like Bohr, had a lot on the line. At forty-eight years old, Einstein knew that he was nearing the point where physicists often go from creating fresh ideas to disparaging whatever is new. He had certainly been on the receiving end of that latter disposition when he was younger. His whole self-definition depended on not being like that. He was a revolutionary. He thought independent thoughts; he went wherever the truth led; he didn’t want to be constrained by the heavy bourgeois style of the Berlin apartment he lived in with Elsa, or by the worst of her social-climbing friends. He had made his own light and airy refuge up in the attic; he wore loose sweaters and often went barefoot around the house, regardless of whether visitors thought such casual behavior beneath him; he was limited only by what he understood as the minimal true structure of the universe.

  What he needed was one successful construction. It didn’t even have to be built; it would be enough if he could describe it in words and show Bohr and Heisenberg that it worked. If he could do that, he’d be back where he knew he belonged—at the forefront, consolidating the truth, not anxiously trying to hold on to the past simply because that happened to be what he was familiar with. And he knew in his bones that the universe had to have causality in its deepest structure; he was convinced of it. How, then, to show that was true?

  It helped that he could make almost any mechanical device work. He’d had years of practical experience analyzing the most complex of devices in his Patent Office days. That would be his approach here.

  Heisenberg later recalled how Einstein went about launching his attack. They were all staying at the same hotel, he said, and Einstein had the habit of telling the others at breakfast about experiments he had thought up that would, he felt, undermine quantum mechanics. As Bohr, Einstein, and Heisenberg walked to the conference hall together, they would make a start on analyzing the assumptions behind Einstein’s latest proposal. Heisenberg picks up:

  “In the course of the day, Bohr, [Wolfgang] Pauli and I would frequently discuss Einstein’s proposal, so that already by dinner-time we could prove that his thought-experiments were consistent with the uncertainty relations, and so could not be used to refute them. Einstein admitted this, but next morning brought along to breakfast a new thought-experiment.” Each time, the new thought experiment was more complicated than the previous one, but each time—by dinner—the other men had managed to disprove it. “And so it went on for several days.”

  Einstein’s close friend Paul Ehrenfest, from the Netherlands, was also at the 1927 conference, and shortly afterward he told his Leyden students about it. He loved listening to the dialogue between Bohr and Einstein. Einstein “was like a chess player,” he felt, coming up with ever new examples. “He was a perpetual motion machine, intent on breaking through uncertainty.” But there also was Bohr, who “out of a cloud of philosophical smoke” would lean forward, musing and musing until he came up with the tools that could undermine Einstein’s new examples. Sometimes, when Einstein had devised an especially puzzling “demonstration” of why quantum mechanics had to be wrong, Bohr would keep Ehrenfest up nearly all night as he thought out loud until he found the flaw.

  THE CONFERENCE ENDED in a draw. Einstein had failed to find a counterexample that would refute Bohr, but Bohr remained apprehensive that this new theory on which he’d staked so much might still be undercut.

  On the way back to Berlin, Einstein consoled himself with the thought that the argument wasn’t simply one of youth against age, with all young physicists on Heisenberg’s side and only old ones on his own. It helped that he shared the first part of the journey, to Paris, with Louis de Broglie, a dignified French physicist a decade younger than him, who’d done fundamental work laying out the principles behind quantum mechanics, yet who had the same doubts Einstein did. De Broglie too was convinced that Heisenberg’s explanation was just a provisional step and that somehow a core of certainty would eventually be found underpinning everything we saw. (De Broglie had personal reasons to feel benevolent, for Einstein had ensured that his Ph.D. dissertation, in which he had set out those ideas, had been accepted.)

  The calculated results from quantum mechanics that Heisenberg and others had come up with were quite accurate, both Einstein and de Broglie agreed, but as Einstein repeated, “I believe that the limitation to statistical laws wil
l be a temporary one.” On the Gare du Nord platform in Paris, engaged in one of those long talks travelers have when neither wants their shared journey to end, Einstein repeated his points. De Broglie agreed, and as he left, Einstein called after him, “Carry on! You’re on the right track!”

  In the two years following the 1927 conference, however, Einstein began seeing that his side in the quantum debate was losing popularity. More and more experimental demonstrations seemed to show that quantum mechanics worked. De Broglie himself only held out till 1928 before joining the consensus that Bohr, Heisenberg, and the others on their side must be right. It was becoming a trend. The Austrian Erwin Schrödinger, soon to receive the Nobel Prize, was one of the few scientists to remain on Einstein’s side.

  By 1929, however, Einstein had good reason to be more confident, despite his diminishing support. He was genuinely a modest man, who knew his intellectual gifts weren’t as extraordinary as the general public believed. Grossmann in Zurich, Born in Göttingen, and many others were stronger mathematicians. If he, Einstein, did have good physical insights, that was because his family had raised him in such a distinctive way: open-minded enough to be critical of received opinion, yet grounded in the solid reality of lightbulbs, electric generators, and all the other whirring apparatuses his father’s and uncle’s income had depended on. Lurking behind his insights may also have been his ancestors’ only semi-forgotten religious beliefs, and especially the assumption that there had to be a waiting order and certainty, which at selected moments we were lucky enough to see. And from that mix, of which he had merely been the lucky beneficiary, he also knew that he had been able to probe beyond surface appearances to underlying principles that only much later had experimentalists found to be true.

  Einstein’s E=mc2 equation was now almost universally accepted. But there was something even better. During the 1927 conference, and despite Lemaître’s claims, it had still seemed likely to Einstein that the lambda addition to his other great equation was necessary: that astronomers had been right and his magnificently pure G=T had to be discarded; that his belief in the power of sheer intuition was wrong. But just this year, in 1929, Hubble and Humason had published their new work showing that Einstein’s original, beautiful equation had been right after all.

  To Einstein, Hubble and Humason’s findings changed everything. What they’d discovered with their great 100-inch telescope—that the lambda term wasn’t necessary—showed that his original intuition there, too, had been right—that what he’d seen in 1915 about “things” altering geometry, and altered geometry guiding “things,” had been absolutely, 100 percent true. Experimental results—all the assumptions of the world’s astronomers—had seemed to show otherwise, but if Einstein had held out, he would have been proved right.

  Clearly, he believed, he could hold out—and be proved right—again. He had already been disposed to believe that the universe had to be fundamentally knowable. His experience with lambda—showing that his initial intuition had been justified—provided an extra boost.

  Admittedly there was a great danger here. The English essayist Macaulay once said of himself—accurately, if not modestly—that he had an excellent writing style, but it was close to a very bad style indeed. This meant, he warned, that few of his readers should try to copy it, for if they got it even a little bit wrong, they would fail entirely. Einstein increasingly was taking a similar risk. Advancing from a belief that his intuition was right is what had made him the greatest scientist of the modern era. Yet holding only to that approach meant that his self-confidence could easily cross the line to sheer dogmatism. What’s more, he was less constrained than ever in these issues. During his university years in Zurich he’d had to be responsive to the best wisdom of the past, and during the years with Grossmann he’d had to defer to a friend’s superior mathematical talents, but now he found himself unshackled from these constraints—and more than a little untethered.

  Unless, of course, Einstein really was right. No one yet knew for sure.

  THE WORLD’S TOP physicists only assembled in Brussels every few years. Since the 1927 conference had ended in a draw, when the next one arrived, in October 1930, everyone’s attention was on Einstein and Bohr. They were the two intellectual giants of their generation. Would they clash again, as they had at the last meeting?

  Einstein knew this was the last opportunity he would have to keep the community of physicists on his side, especially the young generation, with whom he’d identified for so long. Yet in 1930, as at the previous conference, he remained quiet in the main meetings; once again he would only bring his objections to Bohr in the relative privacy outside those plenary sessions. In the meantime, the Dane worried.

  Bohr knew something big was coming, but how could he prepare? He simply had to believe that the newly developed science of quantum mechanics would be strong enough to stand against anything. Heisenberg steeled himself, too. Like chess grandmasters before a match, he and Bohr and others had tried to plan every defense.

  Einstein, too, must have spent a long time preparing, puffing on his pipe in his Berlin study or at his country house, for what he came up with was tremendous.

  At the heart of quantum mechanics was Heisenberg’s uncertainty principle, which seemed to put a limit on the detail we could hope to see on the micro level. Without that detail, we could never be sure, entirely, just what was going to happen next. Heisenberg had first presented his principle as saying that one couldn’t get complete accuracy in measuring a particle’s momentum and position at the same time. It was, as the future Nobel laureate Wolfgang Pauli put it, as if we could see an object’s momentum by looking out our left eye, and its location by looking out of our right eye, but would be stuck with a blur if we tried to keep both eyes open at once.

  Previous attempts to get around Heisenberg’s principle had failed for the same reason that attempts to use a tire pressure gauge fail to give fully accurate readings: the very act of using the gauge lets air hiss out, and so changes the pressure inside the tire that you’re trying to measure. Einstein’s new idea was to step back and view the “tire” from farther away: not using any sort of gauge or other device that would disturb it.

  Einstein’s approach was akin to simply weighing the tire, instead of measuring any air going out of it. He came up with a way to do this because recent work had also shown that Heisenberg’s principle meant that one could measure a particle’s energy or the exact time at which it had that energy, but not the two at once. This new finding about the uncertainty principle allowed Einstein to mount the most vigorous attack against it yet.

  For his new thought experiment in Brussels, Einstein came up with a device that would have done his old Patent Office supervisor Herr Haller proud. After they’d strolled away from the main meeting sessions, he told Bohr to imagine a box that had a fine cloud of radiation—think of it as a cloud of light particles, or photons—floating inside it. There’s a tiny shutter in one wall, controlled by a very precise clock. The whole apparatus is supported on a scale, so it can be weighed. When the clock strikes a particular time, the shutter opens, one photon is let out, and then the shutter closes. The box is weighed before and after, and that way it’s obvious how much mass has been lost.

  Doing this, we know how much energy that lost photon carries: the scale tells us (because mass and energy are equivalent). We also know what time it is when the photon flies out: the clock tells us. This was something that should never happen if Heisenberg’s uncertainty principle were true. Since the clock has no connection with the scale—unlike a tire pressure gauge, where measurement interferes with accuracy—Heisenberg’s argument is ruined. Certainty is possible. The classical world of cause and effect is saved.

  Bohr knew that he thought more slowly—albeit more deeply—than most others. But he was used to getting at least some feeling of what the solution to a problem might be. For Einstein’s light-filled box, however, he could imagine no solution at all. The photon flies out through th
e shutter. The clock records the time. The scale moves. The clock and the scale are nowhere near each other.

  How could that be reconciled with Heisenberg’s uncertainty?

  Einstein’s thought experiment overwhelmed Bohr. As one contemporary recalled, “[Bohr] was extremely unhappy, all through the evening, walking from one person to another, trying to persuade them all that this could not be true . . . But he could think of no refutation. I will never forget the sight of the two opponents leaving the university club: Einstein, a majestic figure, walking calmly with a faint ironic smile, and Bohr trotting along by his side, extremely upset.”

  Einstein and Bohr at the 1930 Brussels conference, photographed by Paul Ehrenfest, probably the day Einstein proposed his box+clock experiment but before Bohr had analyzed it.

  It was Einstein’s last moment of glory. Bohr stayed up almost all night—no doubt dragooning graduate students or anyone else unlucky enough to be nearby for help—as he tried to mumble his way to a solution. Heisenberg had earlier described the way that once Bohr was focused on a problem, “he would not give up, even after hours of struggling.” So it was here.