Quantum
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Bohr assigned a pivotal role to the act of choosing which experiment to perform. Heisenberg identified the act of measurement to determine, for example, the exact position of an electron as the origin of a disturbance that ruled out a simultaneously precise measurement of its momentum. Bohr agreed that there was a physical disturbance. ‘Indeed, our usual [classical] description of physical phenomena is based entirely on the idea that the phenomena concerned may be observed without disturbing them appreciably’, he said during a lecture delivered in September 1927.69 It was a statement implying that such a disturbance is caused by the act of observing phenomena in the quantum world. A month later he was more explicit when, in a draft of a paper, he wrote ‘that no observation of atomic phenomena is possible without their essential disturbance’.70 However, he believed that the origin of this irreducible and uncontrollable disturbance lay not in the act of measurement but in the experimenter having to choose one side of the wave-particle duality in order to perform that measurement. Uncertainty, Bohr argued, was nature’s price for making that choice.
In the middle of April 1927, as he worked on formulating a consistent interpretation of quantum mechanics within the conceptual framework provided by complementarity, Bohr sent a copy of the uncertainty paper to Einstein at Heisenberg’s request. In the accompanying letter he wrote that it was a ‘very important contribution to the discussion of the general problems of quantum theory’.71 In spite of their ongoing and often heated arguments, Bohr informed Einstein that ‘Heisenberg shows in an exceedingly brilliant manner how his uncertainty relations may be utilized not only in the actual development of quantum theory, but also for the judgement of its visualizable content’.72 He went on to outline some of his own emerging ideas that would throw light on ‘the difficulties of the quantum theory [that] are connected with the concepts, or rather with the words that are used in the customary description of nature, and which always have their origin in the classical theories’.73 Einstein, for some unknown reason, chose not to reply.
If he was hoping to elicit a response from Einstein, then Heisenberg must have been disappointed when he returned to Copenhagen after spending Easter in Munich. It was a much-needed break from the constant pressure to yield to Bohr’s interpretation. ‘So I have come to be in a fight for the matrices and against the waves’, Heisenberg wrote to Pauli on 31 May, the very day his 27-page paper appeared in print. ‘In the ardour of this struggle I have often criticized Bohr’s objections to my work too sharply and, without realizing or intending it, have in this way personally wounded him. When I now reflect on these discussions, I can very well understand that Bohr was angry about them.’74 The reason for such contrition was that two weeks earlier, he had finally admitted to Pauli that Bohr was right.
The scattering of gamma rays into the aperture of the hypothetical microscope was the basis of the uncertainty relation for momentum and position. ‘Thus the relation pqh indeed comes out naturally, but not entirely as I had thought.’75 Heisenberg went on to concede that ‘certain points’ were easier to handle using Schrödinger’s wave description, but he remained utterly convinced that in quantum physics ‘only discontinuities are interesting’ and they could never be emphasised enough. It was still not too late to withdraw the paper, but it was a step too far. ‘All results of the paper are correct after all,’ he told Pauli, ‘and I am also in agreement with Bohr concerning these.’76
As a compromise, Heisenberg added a postscript. ‘After the conclusion of the foregoing paper,’ it began, ‘more recent investigations of Bohr have led to a point of view which permits an essential deepening and sharpening of the analysis of quantum-mechanical correlations attempted in this work.’77 Heisenberg acknowledged that Bohr had brought to his attention crucial points that he had overlooked – uncertainty was a consequence of wave-particle duality. He closed by thanking Bohr, and with the publication of the paper, months of wrangling and ‘gross personal misunderstandings’, though not entirely forgotten, were firmly pushed aside.78 Whatever their differences, as Heisenberg said later, ‘all that mattered now was to present the facts in such a way that despite their novelty they could be grasped and accepted by all physicists’.79
‘I am very ashamed to have given the impression of being quite ungrateful’, Heisenberg wrote to Bohr in the middle of June, not long after Pauli had visited Copenhagen.80 Two months later, still full of remorse, he explained to Bohr how he reflected ‘almost every day on how that came about and am ashamed that it could not have gone otherwise’.81 Future job prospects had been a major determining factor in the rush to publish. When he turned down the Leipzig professorship in favour of Copenhagen, Heisenberg was certain that if he continued producing ‘good papers’, then universities would come calling.82 After the publication of the uncertainty paper, the job offers came. Anxious that Bohr might think otherwise, he was quick to explain that he had not encouraged potential suitors because of their recent dispute over uncertainty. Not yet 26, Heisenberg became Germany’s youngest ordinary professor when he accepted a new offer from Leipzig University. He left Copenhagen at the end of June. By then life at the institute was back to normal, as Bohr continued the painfully slow business of dictating the paper on complementarity and its implications for the interpretation of quantum mechanics.
He had been hard at work on it since April, and Oskar Klein, a 32-year-old Swede based at the institute, was the person Bohr turned to for help. As the argument over uncertainty and complementarity raged, Hendrik Kramers, Bohr’s former assistant, warned Klein: ‘Do not enter this conflict, we are both too kind and gentle to participate in that kind of struggle.’83 When Heisenberg first learnt that Bohr was writing a paper aided by Klein on the basis that ‘there exists waves and particles’, he wrote rather disparagingly to Pauli that ‘when one starts like that, then one can of course make everything consistent’.84
As one draft followed another and the title changed from ‘The philosophical foundations of the quantum theory’ to ‘The quantum postulate and the recent development of atomic theory’, Bohr tried hard to finish the paper so he could present it at a forthcoming conference. But it turned out to be yet another draft. For the time being, it would have to do.
The International Physics Congress from 11 to 20 September 1927 in Como, Italy was held to commemorate the 100th anniversary of the death of the Italian Alessandro Volta, the inventor of the battery. With the conference in full swing, Bohr was still finalising his notes until the day of the lecture on 16 September. Among the audience at the Istituto Carducci eager to hear what he had to say were Born, de Broglie, Compton, Heisenberg, Lorentz, Pauli, Planck, and Sommerfeld.
It was impossible for some in the audience to catch every softly spoken word that followed as Bohr outlined for the first time his new framework of complementarity, followed by an exposition of Heisenberg’s uncertainty principle and the role of measurement in quantum theory. Bohr stitched each of these elements together, including Born’s probabilistic interpretation of Schrödinger’s wave function, so that they constituted the foundations of a new physical understanding of quantum mechanics. Physicists would later call this fusion of ideas the ‘Copenhagen interpretation’.
Bohr’s lecture was the culmination of what Heisenberg later described as ‘an intensive study of all questions concerning the interpretation of quantum theory in Copenhagen’.85 At first even the young quantum magician was uneasy with the Dane’s answers. ‘I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair,’ Heisenberg wrote later, ‘and when at the end of the discussion I went alone for a walk in the neighbouring park I repeated to myself again and again the question: Can nature possibly be as absurd as it seemed to us in these atomic experiments?’86 Bohr’s answer was an unequivocal yes. The central role given to measurement and observation vitiated all attempts to unearth regular patterns in nature or any causal connections.
It was Heisenberg, in his uncertainty paper, who first a
dvocated in print the rejection of one of the central tenets of science: ‘But what is wrong in the sharp formulation of the law of causality, “When we know the present precisely, we can predict the future,” is not the conclusion but the assumption. Even in principle we cannot know the present in all detail.’87 Not knowing simultaneously the exact initial position and velocity of an electron, for example, allows only probabilities of a ‘plenitude of possibilities’ of future positions and velocities to be calculated.88 Therefore it is impossible to predict the exact result of any single observation or measurement of an atomic process. Only the probability of a given outcome among a range of possibilities can be precisely predicted.
The classical universe built on the foundations laid down by Newton was a deterministic, clockwork cosmos. Even after Einstein’s relativistic remodelling, if the exact position and velocity of an object, particle or planet, are known at any given moment, then in principle its position and velocity can be completely determined for all time. In the quantum universe there was no room for the determinism of the classical, where all phenomena can be described as a causal unfolding of events in space and time. ‘Because all experiments are subject to the laws of quantum mechanics, and therefore to equation pqh,’ Heisenberg boldly asserted in the last paragraph of his uncertainty paper, ‘it follows that quantum mechanics establishes the final failure of causality.’89 Any hope of restoring it was as ‘fruitless and senseless’ as any lingering belief in a ‘real’ world hidden behind what Heisenberg called ‘the perceived statistical world’.90 It was a view shared by Bohr, Pauli and Born.
At Como two physicists were noticeable by their absence. Schrödinger had only weeks earlier moved to Berlin as Planck’s successor and was busy settling in. Einstein refused to set foot in fascist Italy. Bohr would have to wait just a month before they met in Brussels.
PART III
TITANS CLASH OVER REALITY
‘There is no quantum world. There is only an abstract quantum mechanical description.’
—NIELS BOHR
‘I still believe in the possibility of a model of reality – that is to say, of a theory that represents things themselves and not merely the probability of their occurrence.’
—ALBERT EINSTEIN
Chapter 11
SOLVAY 1927
‘Now, I am able to write to Einstein’, Hendrik Lorentz wrote on 2 April 1926.1 Earlier that day this elder statesman of physics had been granted a private audience with the King of the Belgians. Lorentz had sought and received royal approval for Einstein’s election to the scientific committee of the International Institute of Physics set up by industrialist Ernest Solvay. Once described by Einstein as ‘a marvel of intelligence and exquisite tact’, Lorentz had also obtained the king’s permission to invite German physicists to the fifth Solvay conference scheduled for October 1927.2
‘His Majesty expressed the opinion that, seven years after the war, the feelings which they aroused should be gradually damped down, that a better understanding between peoples was absolutely necessary for the future, and that science could help to bring this about’, reported Lorentz.3 Aware that Germany’s brutal violation of Belgian neutrality in 1914 was still fresh in the memory, the king felt ‘it necessary to stress that in view of all that the Germans had done for physics, it would be very difficult to pass them over’.4 But passed over and isolated from the international scientific community they had been ever since the end of the war.
‘The only German invited is Einstein who is considered for this purpose to be international’, Rutherford told a colleague before the third Solvay conference in April 1921.5 Einstein decided not to attend because Germans were excluded, and instead went on a lecture tour of America to raise funds for the founding of the Hebrew University in Jerusalem. Two years later he said he would decline any invitation to the fourth Solvay conference because of the continuing prohibition on German participation. ‘In my opinion it is not right to bring politics into scientific matters,’ he wrote to Lorentz, ‘nor should individuals be held responsible for the government of the country to which they happen to belong.’6
Unable to attend the 1921 conference because of ill health, Bohr too declined an invitation to Solvay 1924. He feared that to go might be interpreted by some as tacit approval of the policy to exclude the Germans. When Lorentz became president of the League of Nations’ Committee on Intellectual Cooperation in 1925, he saw little prospect of the ban on German scientists from international conferences being lifted in the near future.7 Then, unexpectedly in October that same year, the door barring them was unlocked if not yet opened.
In an elegant palazzo in the small Swiss resort of Locarno, on the northern tip of Lake Maggiore, treaties were ratified that many hoped would ensure the future peace of Europe. Locarno was the sunniest place in Switzerland and an apt setting for such optimism.8 It had taken months of intense diplomatic negotiations to arrange the meeting so that emissaries of Germany, France and Belgium could settle their post-war borders with one another. The Locarno treaties paved the way for Germany’s acceptance, in September 1926, into the League of Nations, and membership brought with it an end to the exclusion of her scientists from the international stage. When the King of Belgium gave his consent, prior to the final moves on the diplomatic chessboard, Lorentz wrote to Einstein asking him attend the fifth Solvay conference and to accept his election to the committee responsible for planning it. Einstein agreed, and in the coming months the participants were selected, the agenda finalised, and the coveted invitations sent out.
All those invited fell into one of three groups. The first were members of the scientific committee: Hendrik Lorentz (president), Martin Knudsen (secretary), Marie Curie, Charles-Eugène Guye, Paul Langevin, Owen Richardson and Albert Einstein.9 The second group consisted of a scientific secretary, a Solvay family representative, and three professors from the Free University of Brussels, invited as a matter of courtesy. The American physicist Irving Langmuir, due to visit Europe at the time, would be present as a guest of the committee.
The invitation made clear that the ‘conference will be devoted to the new quantum mechanics and to questions connected with it’.10 This was reflected in the composition of the third group: Niels Bohr, Max Born, William L. Bragg, Léon Brillouin, Arthur H. Compton, Louis de Broglie, Pieter Debye, Paul Dirac, Paul Ehrenfest, Ralph Fowler, Werner Heisenberg, Hendrik Kramers, Wolfgang Pauli, Max Planck, Erwin Schrödinger and C.T.R. Wilson.
The old masters of quantum theory and the young turks of quantum mechanics would all travel to Brussels. Sommerfeld and Jordan were the most prominent of those not invited to what looked like the physicists’ equivalent of a theological council convened to settle some disputed point of doctrine. During the conference, five reports would be presented: William L. Bragg on the intensity of X-ray reflection; Arthur Compton on disagreements between experiment and the electromagnetic theory of radiation; Louis de Broglie on the new dynamics of quanta; Max Born and Werner Heisenberg on quantum mechanics; and Erwin Schrödinger on wave mechanics. The last two sessions of the conference would be devoted to a wide-ranging general discussion concerning quantum mechanics.
Two names were missing from the agenda. Einstein had been asked, but decided he was ‘not competent’ enough to present a report. ‘The reason,’ he told Lorentz, ‘is that I have not been able to participate as intensively in the modern development of quantum theory as would be necessary for that purpose. This is in part because I have on the whole too little receptive talent for fully following the stormy developments, in part also because I do not approve of the purely statistical way of thinking on which the new theory is founded.’11 It was not an easy decision, since Einstein had wanted to ‘contribute something of value in Brussels’, but he confessed: ‘I have now given up that hope.’12
In fact Einstein had closely monitored ‘the stormy developments’ of the new physics, and indirectly stimulated and encouraged the work of de Broglie and Schrödinger. However, from the v
ery beginning he doubted that quantum mechanics was a consistent and complete description of reality. Bohr’s name was also missing. He too had played no direct part in the theoretical development of quantum mechanics, but had exerted his influence through discussions with the likes of Heisenberg, Pauli and Dirac who did.
All those invited to the fifth Solvay conference on ‘Electrons and Photons’ knew it was designed to address the most pressing problem of the day, more philosophy than physics: the meaning of quantum mechanics. What did the new physics reveal about the nature of reality? Bohr believed he had found the answer. For many he arrived in Brussels as king of the quantum, but Einstein was the pope of physics. Bohr was anxious ‘to learn his reaction to the latest stage of the development which, to our view, went far in clarifying the problems which he had himself from the outset elicited so ingeniously’.13 What Einstein thought mattered deeply to Bohr.
So it was in a mood of great expectancy that most of the world’s leading quantum physicists assembled at 10am on a grey, overcast Monday on 24 October 1927, at the Institute of Physiology in Léopold Park for the start of the first session. The conference had taken eighteen months to arrange and required the consent of a king and the ending of Germany’s pariah status.