Uncertainty

by David Lindley

  So it was that the so-called Copenhagen interpretation of quantum mechanics began to gain traction, a circumstance that has vexed not only physicists but also historians and sociologists of science. It has the look of a conspiracy. Despite much internal disagreement, it seems, the Bohr camp publicly united in order to squelch criticism from those not in the inner circle. Heisenberg in particular swallowed his objections, wiped away his tears, and obediently toed the party line.

  Did Heisenberg, as had happened with Kramers, succumb to Bohr’s irresistible force, or collapse in the face of Bohr’s inexhaustible capacity to argue? Or, as some have suggested, did Heisenberg’s fervent desire to win a professorial appointment in Germany necessitate an abdication to Bohr’s views, in order to show that he was a solid, reliable fellow, a team player, not a hot-head or a maverick?

  Neither speculation seems likely. Heisenberg had, after all, shown enough resilience to insist on publishing his uncertainty paper before Bohr had properly blessed it. At the age of twenty-six, he was responsible for the essential insight that created quantum mechanics in the first place and had now worked out one of its most disturbing and far-reaching consequences. Despite fundamental disagreements about physics, he had won the admiration of Einstein and Planck. It is hard to imagine that he felt the need to suppress his own views in order to get a job.

  The simple explanation is not necessarily wrong. After he left Copenhagen, Heisenberg looked back on his behavior and could see that some part of his hostility was little more than amour propre, an unhappiness that Bohr did not see uncertainty exactly as he did. Pauli chided him to give Bohr’s ideas more consideration. The sweeping generality and concomitant vagueness of complementarity may not have been to Heisenberg’s taste, but when it came to explaining how physicists were to make sense of quantum mechanics, he could not deny that Bohr’s strategy captured an important truth. And, simply put, was helpful.

  Heisenberg changed his mind, in short, because he saw that Bohr offered a better way forward. He was a pragmatist. There is no reason to believe he was insincere.

  If the Como meeting was distinctly unmomentous, one reason was the absence of both Einstein and Schrödinger. Sometime in the spring of 1927, Einstein submitted a paper arguing for a realistic—that is, not probabilistic—interpretation of Schrödinger’s waves, only to withdraw it, apparently after corresponding with Heisenberg. He did not like uncertainty, but his attempts to find a counterargument went nowhere. Fretting but frustrated, Einstein remained in Berlin, where Schrödinger would soon join him as a faculty colleague. Planck had officially retired, and the convivial and scientifically conservative Schrödinger came through as the most agreeable replacement.

  On the face of it, Einstein ought to have liked complementarity. As early as 1909, when he alone was arguing for the reality of photons, he had said that theoretical physics must “bring us a new theory of light that can be interpreted as a kind of fusion of the wave and the emission [that is, photon] theory.” And just before Heisenberg unleashed uncertainty, Einstein lectured in Berlin on the need for a synthesis of conflicting views. But such a synthesis, to Einstein, would of necessity make the underlying conflicts go away. Bohr’s complementarity, by contrast, like its creator, seemed positively to revel in contradiction.

  Only a few weeks after the Como meeting broke up, many of the same physicists reconvened in Brussels for the Fifth Solvay Conference on Physics, taking as their theme “Electrons and Photons.” Ernest Solvay was a Belgian chemist and amateur enthusiast of science who had made a fortune on the strength of an industrial process for the manufacture of sodium carbonate. In 1911, intrigued by the emerging physics of atoms and radiation, he had funded an invitation-only meeting at the luxurious Hôtel Métropole in Brussels, where twenty luminaries—including Einstein, Planck, Rutherford, and Mme Curie—could debate in leisurely comfort their most pressing questions.

  So well received was this debut that Solvay decided to make his conference a triennial occurrence. The war interrupted that schedule, but resuming again afterward, the Solvay conferences became the venue for many of the knottiest and most profound scientific discussions of the postwar years. They remained invitation-only events, with no more than twenty or thirty distinguished participants.

  Because of the postwar exclusion of German scientists, it was not until the fifth Solvay meeting of 1927 that a truly representative international assembly gathered again. Einstein returned, and Bohr came for the first time, having missed the 1924 meeting because of illness. (Solvay himself had died in 1922.) And at the fifth Solvay there was something large to discuss: quantum mechanics and the uncertainty principle, neither of which had existed three years earlier.

  A striking division into old guard and young Turks emerged, except that Bohr, characteristically, refused to sit quietly in either camp. The young men, notably Heisenberg, Pauli, and Dirac, wanted nothing except to push quantum mechanics forward by applying it to unsolved problems concerning atoms, photons, and radiation. They were impatient of anything that smacked of philosophy, semantics, or pedantry. On the other side, de Broglie tried to restrain the avant-garde by talking up Schrödinger’s invention of a scientifically acceptable form of quantum mechanics, while Schrödinger offered a rather inarticulate defense of his own conception of quantum waves, refusing the probability interpretation. His talk drew sharp criticism from Born and Heisenberg in particular, and Schrödinger kept his head down for the remainder of the meeting.

  Einstein, answering as always to no one’s vision but his own, yet standing also as the chief among traditionalists, gave no formal presentation. He had been invited to speak on his own views of quantum mechanics, but after some hesitation begged off, saying that he hadn’t pondered the matter as thoroughly as he would like and preferred to sit and listen. During the conference talks he mainly bit his tongue, and kept his worries to himself. When he did occasionally rise to speak, he did so apologetically, admitting that perhaps he had not looked closely enough into quantum mechanics to be sure of what he was saying.

  But Einstein made his presence felt nonetheless. Over meals, after hours, long into the evenings, he pushed the advocates of quantum mechanics to say precisely what they believed, and pressed upon them his own reservations—intuitive, philosophical, not wholly rational, but weighty all the same. There was no shortage of miscommunication, with advocates of one point of view failing to digest the objections from other camps. At some point Paul Ehrenfest, one of Boltzmann’s last students and a close friend of Einstein’s, inscribed on a blackboard the verse from Genesis about Babel: “The Lord did there confound the language of all the earth.” Heisenberg and Pauli professed to be unconcerned with the old man’s grumblings. They listened deferentially, said little, but could be heard muttering to themselves that there was nothing to worry about, it would all turn out fine.

  Bohr, on the other hand, both out of personal respect for Einstein and because he too indulged in philosophical worries, could not ignore his old friend’s objections. It was he who took on the task of defending quantum mechanics, as if the others did not really see that it was in any great need of defense. And Bohr admitted in private that he did not entirely understand what it was that Einstein so strongly objected to.

  Einstein put up one of his favorite devices, a thought experiment. He asked his colleagues to imagine something quite simple. Think of a beam of electrons passing through a tiny hole in an opaque screen, he said. Because the electrons have wave characteristics, they will create, on a second screen placed beyond the first to record an image, a so-called diffraction pattern of alternately light and dark rings. (This phenomenon, predicted for light by the French scientist Augustin Fresnel in the early nineteenth century, had been one of the clinching pieces of evidence in favor of the wave theory of light.)

  Quantum mechanics, supposedly, could predict only the probability that each electron would hit the screen in one place or another. Individual electrons passing through the hole and distributing th
emselves in probabilistic fashion would dutifully but independently build up the required diffraction pattern. But think about a single electron, Einstein urged. As soon as it hits the screen in one place, the probability of it hitting anywhere else must fall to zero. The wave function must abruptly change to register the new situation. Does this not imply, Einstein argued, that something instantaneous happened across the screen at the moment of impact?

  Here was the germ of what became Einstein’s perennial objection to quantum mechanics. It implied faster-than-light communication, though admittedly just what was being communicated was hard to fathom. Unfortunately, the only substantial account of the tussle between Einstein and Bohr was written by Bohr himself, some twenty years later. In it, we get a somewhat perplexed glimpse of Einstein’s argument, followed by Bohr’s detailed response, which misses the fundamental point.

  Since Einstein could not countenance faster-than-light phenomena, he insisted (said Bohr) that quantum mechanics could not be the whole story. There must be some way, within a theory grander than mere quantum mechanics, of calculating the behavior of electrons in detail so that you could predict exactly where each and every one would end up. In that case, the probability inherent in quantum mechanics would turn out to be like the probability enshrined in the old kinetic theory of heat. There, atoms have definite properties at all times and behave, in theory, with absolute predictability. But the physicist cannot hope to know precisely what every atom is doing, so is forced to resort to a statistical description. Quantum mechanics ought to work the same way, Einstein insisted. Beneath the surface it ought to be deterministic in the traditional way. And the intrusion of probability would not indicate a fundamental breakdown in physical determinism, only that physicists had not yet figured out the complete picture.

  By way of counterargument, Bohr used the newly minted uncertainty principle to prove that there was no way to extract more information about the electrons in Einstein’s thought experiment—without, that is, destroying the diffraction pattern in the process. You could get details of each electron’s trajectory before it hit the screen, or you could get the diffraction pattern, but you couldn’t get both.

  It’s not hard to imagine Einstein’s exasperation at this response. Of course quantum mechanics can’t give you all the information you would like. That was precisely the problem Einstein wanted to bring into the open. Far from demolishing the difficulty, Bohr had reinforced it. Quantum mechanics couldn’t be the whole story.

  A letter written by Ehrenfest shortly after the Solvay meeting conveys the affair in an enthusiastic, telegraphic style. “Like a chess match,” he reported. “Einstein ever ready with new arguments. Bohr always producing out of a cloud of philosophical smoke the tools for destroying one example after another. Einstein like a jack-in-the-box, every morning jumping up afresh. Oh, it was priceless.” Ehrenfest was chagrined to see Einstein speaking irrationally of quantum mechanics, the way his critics spoke of relativity, and he said so to Einstein’s face. But then he also acknowledged that Einstein’s dissatisfaction made him uneasy too. And although he sided with Bohr, he couldn’t resist complaining about the “awful Bohr incantation terminology. Impossible for anyone else to summarize.”

  Other participants did not recall the meeting in such melodramatic terms. Dirac, whose views were very much in sympathy with Einstein’s, remarked coolly that “I listened to their arguments, but I did not join in them, essentially because I was not very much interested. I was more interested in getting the correct equations.” Complementarity, he said elsewhere, “doesn’t provide you with any equations which you didn’t have before.”

  Their encounter at the fifth Solvay meeting brought happiness neither to Einstein nor to Bohr. Neither had usefully communicated his perspective to the other. Heisenberg and Pauli stood mostly to one side. Much later Heisenberg claimed that the Solvay meeting was important for establishing a consensus view of quantum mechanics, although when pressed he admitted that the consensus consisted of Bohr, Pauli, and himself. Lecturing in Chicago in 1929, he talked admiringly of Bohr’s influence and of der Kopenhagener Geist—the Copenhagen spirit. For both adherents and dissenters, the Copenhagen interpretation was crystallizing into the standard view of quantum mechanics. It has been over the decades as elusive as it has been influential. Those who subscribe to it talk of its profundity and power while acknowledging they can’t easily put it into words. Precisely the problem, say its critics. It has acquired de facto authority even though no one seems to be able to say quite what it is.

  Einstein was not mollified. A year after the fifth Solvay meeting he wrote scornfully but resignedly to Schrödinger that “the soothing Heisenberg-Bohr philosophy—or religion?—is so nicely contrived that for now it offers the true believer a soft pillow from which he is not easily rousted. So let him lie.” It is ironic, of course, that Einstein objected to religious principles in others when his authority for disliking quantum mechanics derived from his direct access to the thoughts of “the Old One.”

  Chapter 14

  NOW THE GAME WAS WON

  Toward the end of the summer of 1928, a young Russian who had just finished a two-month summer school in Göttingen stopped off for a day in Copenhagen, hoping to meet Niels Bohr before he returned to Leningrad. Finding some free time in the afternoon, Bohr listened keenly as the gangling young man, George Gamow, explained how he had worked out an elegant but odd answer to a longstanding puzzle. Bohr asked Gamow how long he intended to stay in Copenhagen. Gamow replied that he had to leave that very day, as the modest amount of money the Soviet authorities had supplied for his trip had run out. If he could arrange for a year’s fellowship at the institute, Bohr asked, would Gamow be willing to stay? Gamow paused, gulped, and said yes.

  What grabbed Bohr’s attention was Gamow’s explanation of the old puzzle about radioactive decay, the enigma that Marie Curie had remarked on as long ago as 1898 and that Rutherford and Soddy had demonstrated quantitatively in 1902. Decay, they all saw, followed a truly random course: any unstable nucleus has a constant probability, in a given time, of disintegrating. Although this had been the first instance in physics of a truly unpredictable phenomenon, its significance had not immediately leaped to physicists’ attention. Even in 1916, when Einstein remarked that electron jumps in the Bohr atom also followed the same law of probability, physicists did not entirely grasp that a new and awkward phenomenon had entered the theoretical arena. Still less could they perceive the source of any connection between radioactivity and electron jumps.

  When Gamow met Bohr, little was understood of nuclear physics. The proton was known, and there was a growing belief that it must have a neutral partner. But it was 1932 before the discovery of the neutron confirmed that suspicion. Physicists had no idea what kept a nucleus in one piece: electrostatic repulsion ought to cause a tightly packed collection of positively charged protons, with or without neutral companions, to fly instantly and forcefully apart.

  Necessarily, Gamow could conjure up only an exceedingly simple model of alpha radioactivity. He imagined that alpha particles, known to be identical to the nuclei of helium atoms, preexisted inside heavy, unstable nuclei, and he assumed that whatever force held the nucleus together also stopped these alphas, most of the time, from popping out. Looking at this picture with a quantum eye, he came to a conclusion both surprising and satisfying.

  Classically, a force strong enough to retain alphas within the nucleus will keep them tucked inside forever. Think of a marble rolling around inside a shallow bowl. If it has enough energy to fly over the bowl’s rim, it will do so promptly, but if it doesn’t have enough speed to get to the edge, it can never get out. There’s a clear demarcation between the two cases.

  But Gamow used Schrödinger’s equation to depict one of the alphas inside a nucleus as a quantum wave rather than an old-fashioned particle. For mathematical reasons, he found, this wave could not vanish abruptly at the boundary of the nucleus. It had to extend beyond, trailing o
ff into the distance. But if the wave existed outside the nucleus, Gamow realized, then there must be some measurable probability that the particle could actually be outside the nucleus. According to Gamow’s quantum analysis, an alpha particle can’t exist strictly and only within the nucleus.

  In other words, an alpha particle has some fixed and constant probability of showing up outside the nucleus—and once it does, electrostatic repulsion will take over and send it zooming away. Gamow’s simpleminded model not only gave a reason why alpha decay occurs but explained too the probability law that Rutherford and Soddy had found a quarter of a century earlier.

  By the time he got to Copenhagen, Gamow had already sent off a paper for publication. As it happened, two American physicists, Edward Condon and Ronald Gurney, independently came up with the same idea and published their work too in 1928.

  This model of alpha decay is usually cited as the first example of a general quantum phenomenon known as tunneling: the alpha particle can sneak through what is in classical terms an impenetrable barrier created by the confining force. But “tunneling” is an awkward attempt to translate a classically impossible phenomenon into familiar language. It suggests an image of a particle rolling around in its prison until, spontaneously, it slips through the wall and gets clear away. But in pure quantum terms—consistent with either Schrödinger’s waves or Heisenberg’s uncertainty—the alpha never has the definite position or momentum this classical image implies. Instead, it maintains a sort of constant but fractional existence beyond the boundaries of the nucleus.

  And that raises a tricky question. If the alpha particle has at all times a certain probability of existing beyond the nucleus, why in fact does it slip away at one moment and not another?

  “How does an electron decide?” Rutherford had asked Bohr all those years ago, failing to see why it would jump to a new orbit at one moment rather than another. And now the same question arose in alpha decay. How does the nucleus decide when to split?