by Manjit Kumar
The fifth Solvay conference ended with Bohr, in the minds of those gathered in Brussels, having successfully argued for the logical consistency of the Copenhagen interpretation, but failing to convince Einstein that it was the only possible interpretation of what was a ‘complete’, closed theory. On his journey home, Einstein travelled to Paris with a small group that included de Broglie. ‘Carry on’, he told the French prince as they parted company. ‘You are on the right road.’64 But de Broglie, disheartened at the lack of support in Brussels, would soon recant and accept the Copenhagen interpretation. When Einstein reached Berlin he was exhausted and subdued. Within a fortnight he wrote to Arnold Sommerfeld that quantum mechanics ‘may be a correct theory of the statistical laws, but it is an inadequate conception of individual elementary processes’.65
While Paul Langevin later said that ‘the confusion of ideas reached its zenith’ at Solvay 1927, for Heisenberg this meeting of minds was the decisive turning point in establishing the correctness of the Copenhagen interpretation.66 ‘I am satisfied in every respect with the scientific results’, he wrote as the conference ended.67 ‘Bohr’s and my views have been generally accepted; at least serious objections are no longer being made, not even by Einstein and Schrödinger.’ As far as Heisenberg was concerned, they had won. ‘We could get anything clear by using the old words and limiting them by the uncertainty relations and still get a completely consistent picture’, he recalled almost 40 years later. When asked whom he meant by ‘we’, Heisenberg replied: ‘I could say that at that time it was practically Bohr, Pauli, and myself.’68
Bohr never used the term the ‘Copenhagen interpretation’, nor did anyone else until Heisenberg in 1955. Yet from a handful of adherents it quickly spread so that for most physicists the ‘Copenhagen interpretation of quantum mechanics’ became synonymous with quantum mechanics. Three factors lay behind this rapid dissemination and acceptance of the ‘Copenhagen spirit’. The first was the pivotal role of Bohr and his institute. Inspired by his stay in Rutherford’s laboratory in Manchester as a young postdoctoral student, Bohr had managed to create an institute of his own with the same zing in the air – the sense that anything was possible.
‘Bohr’s Institute quickly became the world centre of quantum physics, and to paraphrase the old Romans, “all roads lead to Blegdamsvej 17”’, recalled the Russian George Gamov who arrived there in the summer of 1928.69 The Kaiser Wilhelm Institute of Theoretical Physics of which Einstein was the director existed only on paper, and he preferred it that way. While he usually worked alone, or later with an assistant who carried out the calculations, Bohr fathered many scientific children. The first to rise to prominence and positions of authority were Heisenberg, Pauli and Dirac. Though only young men, as Ralph Kronig later recalled, other young physicists did not dare to go against them. Kronig, for one, had not published the idea of electron spin after Pauli ridiculed it.
Secondly, around the time of Solvay 1927 a number of professorships became vacant. Those who had helped create the new physics filled nearly all of these. The institutes they headed quickly began to attract many of best and brightest students from Germany and across Europe. Schrödinger had secured the most prestigious position, as Planck’s successor in Berlin. Immediately after the Solvay conference, Heisenberg arrived in Leipzig to take up his post as professor and director of the institute for theoretical physics. Within six months, in April 1928, Pauli moved from Hamburg to a professorship at the EHT in Zurich. Pascual Jordan, whose mathematical skills had been vital to the development of matrix mechanics, succeeded Pauli in Hamburg. Before long, through regular visits and the exchange of assistants and students between each other and Bohr’s institute, Heisenberg and Pauli established Leipzig and Zurich as centres of quantum physics. With Kramers already installed at the University of Utrecht and Born at Göttingen, the Copenhagen interpretation soon became quantum dogma.
Lastly, despite their differences, Bohr and his younger associates always presented a united front against all challenges to the Copenhagen interpretation. The one exception was Paul Dirac. Appointed Lucasian Professor of Mathematics at Cambridge University in September 1932, a chair once occupied by Isaac Newton, Dirac was never interested in the question of interpretation. It seemed to him to be a pointless preoccupation that led to no new equations. Tellingly, he called himself a mathematical physicist, whereas neither his contemporaries Heisenberg and Pauli nor Einstein and Bohr ever described themselves as such. They were theoretical physicists to a man, as was Lorentz, the acknowledged elder statesman of the clan who died in February 1928. ‘To me personally,’ Einstein wrote later, ‘he meant more than all the others encountered in my lifetime.’70
Soon Einstein’s own health became a matter of concern. In April 1928 during a short visit to Switzerland he collapsed as he carried his suitcase up a steep hill. At first it was thought that he had suffered a heart attack, but then an enlargement of the heart was diagnosed. Later Einstein told his friend Michele Besso that he had felt ‘close to croaking’, before adding, ‘which of course one shouldn’t put off unduly’.71 Once back in Berlin under Elsa’s watchful eye, visits by friends and colleagues were strictly rationed. She was once more Einstein’s gatekeeper and nurse, as she had been after he had fallen ill following his Herculean effort in formulating the general theory of relativity. This time Elsa needed help and hired a friend’s unmarried sister. Helen Dukas was 32 and became Einstein’s trusted secretary and friend.72
As he recuperated, a paper by Bohr was published in three languages: English, German and French. The English version, entitled ‘The quantum Postulate and the Recent Development of Atomic Theory’, appeared on 14 April 1928. A footnote stated: ‘The content of this paper is essentially the same as that of a lecture on the present state of quantum theory delivered on September 16, 1927, at the Volta celebrations in Como.’73 In truth, Bohr had produced a more refined and advanced exposition of his ideas surrounding complementarity and quantum mechanics than he had presented in either Como or Brussels.
Bohr sent a copy to Schrödinger, who replied: ‘if you want to describe a system, e.g. a mass point by specifying its [momentum] p and [position] q, then you find that this description is only possible with a limited degree of accuracy.’74 What was therefore needed, Schrödinger argued, was the introduction of new concepts with respect to which this limitation no longer applies. ‘However,’ he concluded, ‘it will no doubt be very difficult to invent this conceptual scheme, since – as you emphasize so impressively – the new-fashioning required touches upon the deepest levels of our experience: space, time and causality.’
Bohr wrote back thanking Schrödinger for his ‘not altogether unsympathetic attitude’, but he did not see the need for ‘new concepts’ in quantum theory since the old empirical concepts appeared inseparably linked to the ‘foundations of the human means of visualization’.75 Bohr restated his position that it was not a question of a more or less arbitrary limitation in the applicability of the classical concepts, but an inescapable feature of complementarity that emerges in an analysis of the concept of observation. He ended by encouraging Schrödinger to discuss the contents of his letter with Planck and Einstein. When Schrödinger informed him of the exchange with Bohr, Einstein replied that the ‘Heisenberg-Bohr tranquilizing philosophy – or religion? – is so delicately contrived that for the time being, it provides a gentle pillow for the true believer from which he cannot very easily be aroused. So let him lie there.’76
Four months after collapsing, Einstein was still weak but no longer confined to his bed. To continue his convalescence he rented a house in the sleepy town of Scharbeutz on the Baltic coast. There he read Spinoza and enjoyed being away from the ‘idiotic existence one leads in the city’.77 It was almost a year before he was well enough to return to his office. He would work there all morning before going home for lunch and a rest until three o’clock. ‘Otherwise he was always working,’ recalled Helen Dukas, ‘sometimes all through the night.�
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During the Easter vacation of 1929 Pauli went to see Einstein in Berlin. He found Einstein’s ‘attitude regarding modern quantum physics reactionary’ because he continued to believe in a reality where natural phenomena unfolded according to the laws of nature, independently of an observer.79 Shortly after Pauli’s visit, Einstein made his views perfectly clear as he received the Planck medal from Planck himself. ‘I admire to the highest degree the achievements of the younger generation of physicists which goes by the name quantum mechanics and believe in the deep level of truth of that theory,’ he told the audience, ‘but I believe that the restriction to statistical laws will be a passing one.’80 Einstein had already embarked on his solitary journey in search of a unified field theory that he believed would save causality and an observer-independent reality. In the meantime he would continue to challenge what was becoming the quantum orthodoxy, the Copenhagen interpretation. When they met again in Brussels at the sixth Solvay conference in 1930, Einstein presented Bohr with an imaginary box of light.
Chapter 12
EINSTEIN FORGETS RELATIVITY
Bohr was stunned. Einstein smiled.
Over the past three years, Bohr had re-examined the imaginary experiments Einstein had proposed at the Solvay conference in October 1927. Each was designed to show that quantum mechanics was inconsistent, but he had found the flaw in Einstein’s analysis in every case. Not content to rest on his laurels, Bohr devised some thought experiments of his own involving an assortment of slits, shutters, clocks and the like as he probed his interpretation for any weaknesses. He found none. But Bohr never conjured up anything as simple and ingenious as the thought experiment that Einstein had just finished describing to him in Brussels at the sixth Solvay conference.
The theme of the six-day meeting that began on 20 October 1930 was the magnetic properties of matter. The format remained the same: a series of commissioned reports on various topics related to magnetism, each followed by a discussion. Bohr had joined Einstein as a member of the nine-strong scientific committee and both were therefore automatically invited to the conference. After the death of Lorentz, the Frenchman Paul Langevin had agreed to take on the demanding dual responsibilities of presiding over the committee and the conference. Dirac, Heisenberg, Kramers, Pauli and Sommerfeld were among the 34 participants.
As a meeting of minds it was a close second to Solvay 1927, with twelve current and future Nobel laureates present. It was the backdrop to the ‘second round’ of the ongoing struggle between Einstein and Bohr over the meaning of quantum mechanics and the nature of reality. Einstein had travelled to Brussels armed with a new thought experiment designed to deliver a fatal blow to the uncertainty principle and the Copenhagen interpretation. An unsuspecting Bohr was ambushed after one of the formal sessions.
Imagine a box full of light, Einstein asked Bohr. In one of its walls is a hole with a shutter that can be opened and closed by a mechanism connected to a clock inside the box. This clock is synchronised with another in the laboratory. Weigh the box. Set the clock to open the shutter at a certain time for the briefest of moments, but long enough for a single photon to escape. We now know, explained Einstein, precisely the time at which the photon left the box. Bohr listened unconcerned; everything Einstein had proposed appeared straightforward and beyond contention. The uncertainty principle applied only to pairs of complementary variables – position and momentum or energy and time. It did not impose any limit on the degree of accuracy with which any one of the pair could be measured. Just then, with a hint of smile, Einstein uttered the deadly words: weigh the box again. In a flash, Bohr realised that he and the Copenhagen interpretation were in deep trouble.
To work out how much light had escaped locked up in a single photon, Einstein used a remarkable discovery he had made while still a clerk at the Patent Office in Bern: energy is mass and mass is energy. This astonishing spin-off from his work on relativity was captured by Einstein in his simplest and most famous equation: E=mc2, where E is energy, m is mass, and c is the speed of light.
By weighing the box of light before and after the photon escapes, it is easy to work out the difference in mass. Although such a staggeringly small change was impossible to measure using equipment available in 1930, in the realm of the thought experiment it was child’s play. Using E=mc2 to convert the quantity of missing mass into an equivalent amount of energy, it was possible to calculate precisely the energy of the escaped photon. The time of the photon’s escape was known via the laboratory clock being synchronised with the one inside the light box controlling the shutter. It appeared that Einstein had conceived an experiment capable of measuring simultaneously the energy of the photon and the time of its escape with a degree of accuracy proscribed by Heisenberg’s uncertainty principle.
‘It was quite a shock for Bohr’, recalled the Belgian physicist Léon Rosenfeld, who had recently begun what turned into a long-term collaboration with the Dane.1 ‘He did not see the solution at once.’ While Bohr was desperately worried by Einstein’s latest challenge, Pauli and Heisenberg were dismissive. ‘Ah, well, it will be all right, it will be all right’, they told him.2 ‘During the whole evening he was extremely unhappy, going from one to the other and trying to persuade them that it couldn’t be true, that it would be the end of physics if Einstein were right,’ recalled Rosenfeld, ‘but he couldn’t produce any refutation.’3
Rosenfeld was not invited to Solvay 1930, but had travelled to Brussels to meet Bohr. He never forgot the sight of the two quantum adversaries heading back to the Hotel Metropole that evening: ‘Einstein, a tall majestic figure, walking quietly, with a somewhat ironical smile on his face, and Bohr trotting near him, very excited, ineffectually pleading that if Einstein’s device would work, it would mean the end of physics.’4 For Einstein it was neither an end nor a beginning. It was nothing more than a demonstration that quantum mechanics was inconsistent and therefore not the closed and complete theory that Bohr claimed. His latest thought experiment was simply an attempt to rescue the kind of physics that aimed to understand an observer-independent reality.
A photograph shows Einstein and Bohr walking together, but slightly out of step. Einstein is just ahead as if trying to flee. Bohr, mouth open, is hurrying to keep pace. He leans towards Einstein, desperate to make himself heard. Despite having his coat draped over his left arm, Bohr gestures with his left forefinger to emphasise whatever point he is trying to make. Einstein’s hands are by his side, one clutching a briefcase and the other a possible victory cigar. As he listens, Einstein’s moustache fails to hide the half-knowing smile of a man who thinks he has just gained the upper hand. That evening, said Rosenfeld, Bohr looked ‘like a dog who has received a thrashing’.5
Bohr spent a sleepless night examining every facet of Einstein’s thought experiment. He took the imaginary box of light apart to find the flaw that he hoped existed. Einstein did not picture, even in his mind’s eye, either the details of the inner workings of the light box or how to weigh it. Bohr, desperate to get to grips with the device and the measurements that would have to be made, drew what he called a ‘pseudorealistic’ diagram of the experimental set-up to help him.
Figure 18: Bohr’s later rendition of Einstein’s 1930s light box (Niels Bohr Archive, Copenhagen)
Given the need to weigh the light box before the shutter is opened at a pre-set time and after the photon has escaped, Bohr decided to focus on the weighing process. With mounting anxiety and little time, he chose the simplest possible method. He suspended the light box from a spring fixed to a supporting frame. To turn it into a weighing scale, Bohr attached a pointer to the light box so its position could be read on a scale attached to the vertical arm of what resembled a hangman’s gallows. To ensure that the pointer was positioned at zero on the scale, Bohr attached a small weight to the bottom of the box. There was nothing whimsical in the construction, as Bohr included even the nuts and bolts used to fix the frame to a base, and drew the clockwork mechanism controlling th
e opening and closing of the hole through which the photon was to escape.
The initial weighing of the light box is simply the configuration with the attached weight chosen to ensure that the pointer is at zero. After the photon escapes, the light box is lighter and is pulled upwards by the spring. To reposition the pointer at zero, the attached weight has to be replaced by a slightly heavier one. There is no time limit on how long the experimenter can take to change the weights. The difference in the weights is the mass lost due to the escaped photon, and from E=mc2 the energy of the photon can be calculated precisely.
From the arguments he deployed at Solvay 1927, Bohr held that any measurement of the position of the light box would lead to an inherent uncertainty in its momentum, because to read the scale would require it to be illuminated. The very act of measuring its weight would cause an uncontrollable transfer of momentum to the light box because of the exchange of photons between the pointer and the observer causing it to move. The only way to improve the accuracy of the position measurement was to carry out the balancing of the light box, the positioning of the pointer at zero, over a comparatively long time. However, Bohr argued that this would lead to a corresponding uncertainty in the momentum of the box. The more accurately the position of the box was measured, the greater the uncertainty attached to any measurement of its momentum.