Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar (2009)

Part III. TITANS CLASH OVER REALITY

Chapter 13. QUANTUM REALITY

'Princeton is a madhouse' and 'Einstein is completely cuckoo', wrote Robert Oppenheimer.1 It was January 1935 and America's leading home-grown theoretical physicist was 31. Twelve years later, after directing the building of the atomic bomb, he would return to the Institute for Advanced Study to take charge of the 'madhouse' and its 'solipsistic luminaries shining in separate and helpless desolation'.2 Einstein accepted that his critical attitude towards quantum mechanics ensured that 'here in Princeton I am considered an old fool'.3

It was a sentiment widely shared by the younger generation of physicists who, having been weaned on the theory, agreed with Paul Dirac's assessment that quantum mechanics explained 'most of physics and all of chemistry'.4That a few old men were fighting about the meaning of the theory was, for them, neither here nor there, given its enormous practical success. By the end of the 1920s, as one problem after another in atomic physics was solved, attention shifted from the atom to the nucleus. During the early 1930s, the discovery of the neutron by James Chadwick in Cambridge, and the work of Enrico Fermi and his team in Rome on the reactions induced by the impact of neutrons on nuclei, opened up the new frontier of nuclear physics.5 In 1932 John Cockcroft and Ernest Walton, Chadwick's colleagues in Rutherford's Cavendish Laboratory, constructed the first particle accelerator and used it to split an atom by breaking apart its nucleus.

Einstein might have moved from Berlin to Princeton, but physics was moving on without him. He knew as much, but felt he had earned the right to pursue the physics that interested him. When he arrived at the institute in October 1933, Einstein was shown to his new office and asked what equipment he needed. 'A desk or table, a chair, paper and pencils', he replied.6 'Oh yes, and a large wastebasket, so I can throw away all my mistakes.' And there were plenty, but Einstein was never disheartened as he sought his holy grail – a unified field theory.

Just as Maxwell had unified electricity, magnetism and light into a single all-encompassing theoretical structure in the nineteenth century, Einstein hoped to unify electromagnetism and general relativity. For him such a unification was the next step, as logical as it was inevitable. It was in 1925 that he undertook the first of his many attempts at constructing such a theory that ended up in the wastebasket. After the discovery of quantum mechanics, Einstein believed that a unified field theory would yield this new physics as a by-product.

In the years following Solvay 1930, there was little direct contact between Bohr and Einstein. A valuable channel of communication ceased with Paul Ehrenfest's suicide in September 1933. In a moving tribute, Einstein wrote of his friend's inner struggle to understand quantum mechanics and 'the increasing difficulty of adaptation to new thoughts which always confronts the man past fifty. I do not know how many readers of these lines will be capable of fully grasping that tragedy.'7

There were many who read Einstein's words and mistook them as a lament at his own plight. Now in his mid-fifties, he knew he was regarded as a relic from a bygone age, refusing, or unable, to live with quantum mechanics. But he also knew what separated him and Schrödinger from most of their colleagues: 'Almost all the other fellows do not look from the facts to the theory but from the theory to the facts; they cannot extricate themselves from a once accepted conceptual net, but only flop about in it in a grotesque way.'8

In spite of these mutual misgivings, there were always young physicists eager to work with Einstein. One was Nathan Rosen, a 25-year-old New Yorker who arrived from MIT in 1934 to serve as his assistant. A few months before Rosen, the 39-year-old Russian-born Boris Podolsky had joined the institute. He had first met Einstein at Caltech in 1931 and they had collaborated on a paper. Einstein had an idea for another paper. It would mark a new phase in his debate with Bohr, as it unleashed a fresh assault on the Copenhagen interpretation.

At Solvay 1927 and 1930, Einstein attempted to circumvent the uncertainty principle to show that quantum mechanics was inconsistent and therefore incomplete. Bohr, aided by Heisenberg and Pauli, had successfully dismantled each thought experiment and defended the Copenhagen interpretation. Afterwards, Einstein accepted that although quantum mechanics was logically consistent it was not the definitive theory that Bohr claimed. Einstein knew he needed a new strategy to demonstrate that quantum mechanics is incomplete, that it does not fully capture physical reality. To this end he developed his most enduring thought experiment.

For several weeks early in 1935, Einstein met Podolsky and Rosen in his office to thrash out his idea. Podolsky was assigned the task of writing the resulting paper, while Rosen did most of the necessary mathematical calculations. Einstein, as Rosen recalled later, 'contributed the general point of view and its implications'.9 Only four pages long, the Einstein-Podolsky-Rosen paper, or the EPR paper as it became known, was completed and mailed by the end of March. 'Can Quantum Mechanical Description of Physical Reality Be Considered Complete?', with its missing 'the', was published on 15 May in the American journal Physical Review.10 The EPR answer to the question posed was a defiant 'No!'. Even before it appeared in print, Einstein's name ensured that the EPR paper generated the kind of publicity nobody wanted.

On Saturday, 4 May 1935, the New York Times carried an article on page eleven under the attention-grabbing headline 'Einstein Attacks Quantum Theory': 'Professor Einstein will attack science's important theory of quantum mechanics, a theory of which he was a sort of grandfather. He concluded that while it is "correct" it is not "complete".' Three days later, the New York Times carried a statement from a clearly disgruntled Einstein. Although no stranger to talking to the press, he pointed out that: 'It is my invariable practice to discuss scientific matters only in the appropriate forum and I deprecate advance publication of any announcement in regard to such matters in the secular press.'11

In the published paper, Einstein, Podolsky and Rosen started by differentiating between reality as it is and the physicist's understanding of it: 'Any serious consideration of a physical theory must take into account the distinction between the objective reality, which is independent of any theory, and the physical concepts with which the theory operates. These concepts are intended to correspond with the objective reality, and by means of these concepts we picture this reality to ourselves.'12 In gauging the success of any particular physical theory, EPR argued that two questions had to be answered with an unequivocal 'Yes': Is the theory correct? Is the description given by the theory complete?

'The correctness of the theory is judged by the degree of agreement between the conclusions of the theory and human experience', said EPR. It was a statement that every physicist would accept when 'experience' in physics takes the form of experiment and measurement. To date there had been no conflict between the experiments performed in the laboratory and the theoretical predictions of quantum mechanics. It appeared to be a correct theory. Yet for Einstein it was not enough for a theory to be correct, in agreement with experiments; it also had to be complete.

Whatever the meaning of the term 'complete', EPR imposed a necessary condition for the completeness of a physical theory: 'every element of the physical reality must have a counterpart in the physical theory.'13 This completeness criterion required EPR to define a so-called 'element of reality' if they were to carry through their argument.

Einstein did not want to get stuck in the philosophical quicksand, which had swallowed so many, of trying to define 'reality'. In the past, none had emerged unscathed from an attempt to pinpoint what constituted reality. Astutely avoiding a 'comprehensive definition of reality' as 'unnecessary' for their purpose, EPR adopted what they deemed to be a 'sufficient' and 'reasonable' criterion for designating an 'element of reality': 'If, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.'14

Einstein wanted to disprove Bohr's claim that quantum mechanics was a complete, fundamental theory of nature by demonstrating that there existed objective 'elements of reality' which the theory did not capture. Einstein had shifted the focus of the debate with Bohr and his supporters away from the internal consistency of quantum mechanics to the nature of reality and the role of theory.

EPR asserted that for a theory to be complete there had to be one-to-one correspondence between an element of the theory and an element of reality. A sufficient condition for the reality of a physical quantity, such as momentum, is the possibility of predicting it with certainty without disturbing the system. If there existed an element of physical reality that was unaccounted for by the theory, then the theory was incomplete. The situation would be akin to a person finding a book in a library and when trying to check it out, being told by the librarian that according to the catalogue there was no record of the library having the book. With the book bearing all the necessary markings indicating that it was indeed a part of the collection, the only possible explanation would be that the library's catalogue was incomplete.

According to the uncertainty principle, a measurement that yields an exact value for the momentum of a microphysical object or system excludes even the possibility of simultaneously measuring its position. The question that Einstein wanted to answer was: Does the inability to measure its exact position directly mean that the electron does not have a definite position? The Copenhagen interpretation answered that in the absence of a measurement to determine its position, the electron has no position. EPR set out to demonstrate that there are elements of physical reality, such as an electron having a definite position, that quantum mechanics cannot accommodate – and therefore, it is incomplete.

EPR attempted to clinch their argument with a thought experiment. Two particles, A and B, interact briefly and then move off in opposite directions. The uncertainty principle forbids the exact measurement, at any given instant, of both the position and the momentum of either particle. However, it does allow an exact and simultaneous measurement of the total momentum of the two particles, A and B, and the relative distance between them.

The key to the EPR thought experiment is to leave particle B undisturbed by avoiding any direct observation of it. Even if A and B are light years apart, nothing within the mathematical structure of quantum mechanics prohibits a measurement of the momentum of A yielding information about the exact momentum of B without B being disturbed in the process. When the momentum of particle A is measured exactly, it indirectly but simultaneously allows, via the law of conservation of momentum, an exact determination of the momentum of B. Therefore, according to the EPR criterion of reality, the momentum of B must be an element of physical reality. Similarly, by measuring the exact position of A, it is possible, because the physical distance separating A and B is known, to deduce the position of B without directly measuring it. Hence, EPR argue, it too must be an element of physical reality. EPR appeared to have contrived a means to establish with certainty the exact values of either the momentum or the position of B due to measurements performed on particle A, without the slightest possibility of particle B being physically disturbed.

Given their reality criterion, EPR argued that they had thus proved that both the momentum and position of particle B are 'elements of reality', that B can have simultaneously exact values of position and momentum. Since quantum mechanics via the uncertainty principle rules out any possibility of a particle simultaneously possessing both these properties, these 'elements of reality' have no counterparts in the theory.15 Therefore the quantum mechanical description of physical reality, EPR conclude, is incomplete.

Einstein's thought experiment was not designed to simultaneously measure the position and momentum of particle B. He accepted that it was impossible to measure either of these properties of a particle directly without causing an irreducible physical disturbance. Instead, the two-particle thought experiment was constructed to show that such properties could have a definite simultaneous existence, that both the position and the momentum of a particle are 'elements of reality'. If these properties of particle B can be determined without B being observed (measured), then these properties of B must exist as elements of physical reality independently of being observed (measured). Particle B has a position that is real and a momentum that is real.

EPR were aware of the possible counter-argument that 'two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted'.16 This, however, made the reality of the momentum and position of particle B dependent upon the process of measurement carried out on particle A, which could be light years away and which does not disturb particle B in any way. 'No reasonable definition of reality could be expected to permit this', said EPR.17

Central to the EPR argument was Einstein's assumption of locality – that some mysterious, instantaneous action-at-a-distance does not exist. Locality ruled out the possibility of an event in a certain region of space instantaneously, faster-than-light, influencing another event elsewhere. For Einstein, the speed of light was nature's unbreakable limit on how fast anything could travel from one place to another. For the discoverer of relativity it was inconceivable for a measurement on particle A to affect instantaneously, at a distance, the independent elements of physical reality possessed by particle B.

As soon as the EPR paper appeared, the alarm was raised among the leading quantum pioneers throughout Europe. 'Einstein has once again made a public statement about quantum mechanics, and even in the issue of Physical Review of May 15 (together with Podolsky and Rosen, not good company by the way)', wrote a furious Pauli in Zurich to Heisenberg in Leipzig.18 'As is well known,' he continued, 'that is a disaster whenever it happens.' Pauli nevertheless conceded, as only he could, 'that if a student in one of his earlier semesters had raised such objections, I would have considered him quite intelligent and promising'.19

With the zeal of a quantum missionary, Pauli urged Heisenberg to publish an immediate rebuttal to prevent any confusion or wavering among fellow physicists in the wake of Einstein's latest challenge. Pauli admitted that he had considered, for 'educational' reasons, 'squandering paper and ink in order to formulate those facts demanded by quantum theory which cause Einstein particular intellectual difficulties'.20 In the end it was Heisenberg who drafted a reply to the EPR paper and sent Pauli a copy. But Heisenberg withheld the publication of his paper, as Bohr had already taken up arms in defence of the Copenhagen interpretation.

The EPR 'onslaught came down upon us as a bolt from the blue', recalled Léon Rosenfeld, who was in Copenhagen at the time.21 'Its effect on Bohr was remarkable.' Immediately abandoning everything else, Bohr was convinced that a thorough examination of the EPR thought experiment would reveal where Einstein had gone wrong. He would show them 'the right way to speak about it'.22 Excitedly, Bohr started dictating to Rosenfeld the draft of a reply. But soon he began to hesitate. 'No, this won't do, we must try all over again', Bohr mumbled to himself. 'So it went on for a while, with growing wonder at the unexpected subtlety of the [EPR] argument', recalled Rosenfeld. 'Now and then, he would turn to me and ask: "What can they mean? Do you understand it?"'23 After a while, an increasingly agitated Bohr realised that the argument Einstein had deployed was both ingenious and subtle. A refutation of the EPR paper would be harder than he first thought, and he announced that he 'must sleep on it'.24 The next day he was calmer. 'They do it smartly,' he told Rosenfeld, 'but what counts is to do it right.'25 For the next six weeks, day and night, Bohr worked on nothing else.

Even before he had finished his reply to EPR, Bohr wrote a letter on 29June for publication in the journal Nature. Entitled 'Quantum Mechanics and Physical Reality', it briefly spelled out his counter-attack.26 Once again, the New York Times smelt a story. 'Bohr and Einstein at Odds/ They Begin a Controversy Concerning the Fundamental Nature of Reality' were the headlines of the article that appeared on 28 July. 'The Einstein-Bohr controversy has just begun this week in the current issue of Nature, the British scientific publication,' the paper told its readers, 'with a preliminary challenge by Professor Bohr to Professor Einstein and with a promise by Professor Bohr that "a fuller development of this argument will be given in an article to be published shortly in the Physical Review".'

Bohr had deliberately chosen the same forum as Einstein, and his six-page response, received on 13 July, was also entitled 'Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?'27 Published on 15 October, Bohr's answer was an emphatic 'Yes'. However, unable to identify any error in the EPR argument, Bohr was reduced to arguing that Einstein's evidence for quantum mechanics being incomplete was not strong enough to bear the weight of such a claim. Using a debating tactic with a long and illustrious history, Bohr began his defence of the Copenhagen interpretation by simply rejecting the major component of Einstein's case for incompleteness: the criterion of physical reality. Bohr believed that he had identified a weakness in the EPR definition: the need to conduct a measurement 'without in any way disturbing a system'.28

Bohr hoped to exploit what he described as an 'essential ambiguity when it is applied to quantum phenomena' of the reality criterion, as he publicly retreated from the position that an act of measurement resulted in an unavoidable physical disturbance. He had relied on disturbance to undermine Einstein's previous thought experiments by demonstrating that it was impossible to know simultaneously the exact momentum and position of a particle because the act of measuring one caused an uncontrollable disturbance that ruled out an exact measurement of the other. Bohr knew perfectly well that EPR did not seek to challenge Heisenberg's uncertainty principle, since their thought experiment was not designed to simultaneously measure the position and momentum of a particle.

Bohr acknowledged as much when he wrote that in the EPR thought experiment 'there is no question of a mechanical disturbance of the system under investigation'.29 It was a significant public concession, one he had made in private a few years earlier as he, Heisenberg, Hendrik Kramers and Oskar Klein sat around the fire at his country cottage in Tisvilde. 'Isn't it odd,' said Klein, 'that Einstein should have such great difficulties in accepting the role of chance in atomic physics?'30 It is because 'we cannot make observations without disturbing the phenomena', said Heisenberg; 'the quantum effects we introduce with our observation automatically introduce a degree of uncertainty into the phenomenon to be observed.'31 'This Einstein refuses to accept, although he knows the facts perfectly well.' 'I don't entirely agree with you', Bohr told Heisenberg.32 'In any case,' he continued, 'I find all such assertions as "observation introduces uncertainty into the phenomenon" inaccurate and misleading. Nature has taught us that the word "phenomenon" cannot be applied to atomic processes unless we also specify what experimental arrangement or what observational instruments are involved. If a particular experimental set up has been defined and a particular observation follows, then we can admittedly speak of a phenomenon, but not of its disturbance by observation.'33Yet before, during, and after the Solvay conferences, an act of measurement disturbing the observed object peppered Bohr's writings and was central to his dismantling of Einstein's thought experiments.

Feeling the pressure from Einstein's continued probing of the Copenhagen interpretation, Bohr abandoned his previous reliance on 'disturbance' because he knew that it implied that an electron, for example, existed in a state that could be disturbed. Instead, Bohr now emphasised that any microphysical object being measured and the apparatus doing the measuring formed an indivisible whole – the 'phenomenon'. There simply was no room for a physical disturbance due to an act of measurement. This was why Bohr believed the EPR reality criterion was ambiguous.

Alas, Bohr's response to EPR was less than clear. Years later, in 1949, he admitted to a certain 'inefficiency of expression' when he re-read his paper. Bohr tried to clarify that the 'essential ambiguity' he had alluded to in his EPR rejoinder lay in referring to 'physical attributes of objects when dealing with phenomena where no sharp distinction can be made between the behaviour of the objects themselves and their interaction with the measuring instruments'.34

Bohr did not object to EPR predicting the results of possible measurements of particle B based on knowledge acquired by measuring particle A. Once the momentum of particle A is measured, it is possible to predict accurately the result of a similar measurement of the momentum of particle B as outlined by EPR. However, Bohr argued that that does not mean that momentum is an independent element of B's reality. Only when an 'actual' momentum measurement is carried out on B can it be said to possess momentum. A particle's momentum becomes 'real' only when it interacts with a device designed to measure its momentum. A particle does not exist in some unknown but 'real' state prior to an act of measurement. In the absence of such a measurement to determine either the position or the momentum of a particle, Bohr argued that it was meaningless to assert that it actually possessed either.

For Bohr, the role of the measuring apparatus was pivotal in defining EPR's elements of reality. Thus, once a physicist sets up the equipment to measure the exact position of particle A, from which the position of particle B can be calculated with certainty, it excludes the possibility of measuring the momentum of A and hence deducing the momentum of B.

If, as Bohr conceded to EPR, there is no direct physical disturbance of particle B, then its 'elements of physical reality', he argued, must be defined by the nature of the measuring device and the measurement made on A.

For EPR, if the momentum of B is an element of reality, then a momentum measurement on particle A cannot affect B. It merely allows the calculation of the momentum that particle B has independently of any measurement. EPR's reality criterion assumes that if particles A and B exert no physical force on each other, then whatever happens to one cannot 'disturb' the other. However, according to Bohr, since A and B had once interacted before travelling apart, they were forever entwined as parts of a single system and could not be treated individually as two separate particles. Hence, subjecting A to a momentum measurement was practically the same as performing a direct measurement on B, leading instantly to it having a well-defined momentum.

Bohr agreed that there was no 'mechanical' disturbance of particle B due to an observation of particle A. Like EPR, he too excluded the possibility of any physical force, a push or pull, acting at a distance. However, if the reality of the position or momentum of particle B is determined by measurements performed on particle A, then there appears to be some instantaneous 'influence' at a distance. This violates locality, that what happens to A cannot instantaneously affect B, and separability, that A and B exist independently of each other. Both concepts lay at the heart of the EPR argument and Einstein's view of an observer-independent reality. However, Bohr maintained that a measurement of particle A somehow instantaneously 'influences' particle B.35 He did not expand on the nature of this mysterious 'influence on the very conditions which define the possible types of predictions regarding the further behaviour of the system'.36 Bohr concluded that since 'these conditions constitute an inherent element of the description of any phenomenon to which the term "physical reality" can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete'.37

Einstein mocked Bohr's 'voodoo forces' and 'spooky interactions'. 'It seems hard to look into the cards of the Almighty', he wrote later.38 'But I won't for one minute believe that he throws dice or uses "telepathic" devices (as he is being credited with by the present quantum theory).' He told Born that 'physics should represent reality in time and space, free from spooky action at a distance'.39

The EPR paper expressed Einstein's view that the Copenhagen interpretation of quantum theory and the existence of an objective reality were incompatible. He was right and Bohr knew it. 'There is no quantum world. There is only an abstract quantum mechanical description', argued Bohr.40 According to the Copenhagen interpretation, particles do not have an independent reality, they do not possess properties when they are not being observed. It was a view that was later concisely summarised by the American physicist John Archibald Wheeler: no elementary phenomenon is a real phenomenon until it is an observed phenomenon. A year before EPR, Pascual Jordan took the Copenhagen rejection of an observer-independent reality to its logical conclusion: 'We ourselves produce the results of measurement.'41

'Now we have to start all over again,' said Paul Dirac, 'because Einstein proved that it does not work.'42 He initially believed that Einstein had delivered a fatal blow against quantum mechanics. But soon, like most physicists, Dirac accepted that Bohr had once more emerged victorious from a battle with Einstein. Quantum mechanics had long proved its worth, and few were interested in examining Bohr's reply to the EPR argument too closely, for it was obscure even by his own standards.

Shortly after the EPR paper appeared in print, Einstein received a letter from Schrödinger: 'I was very happy that in the paper just published in P.R. you have evidently caught dogmatic q.m. by the coat-tails.'43 After offering an analysis of some of the finer points of the EPR paper, Schrödinger explained his own reservation concerning the theory he had done so much to create: 'My interpretation is that we do not have a q.m. that is consistent with relativity theory, i.e. with a finite transmission speed of all influences. We have only the analogy of the old absolute mechanics … The separation process is not at all encompassed by the orthodox scheme.'44 As Bohr struggled to formulate his response, Schrödinger believed that the central role of separability and locality in the EPR argument meant that quantum mechanics was not a complete description of reality.

In his letter Schrödinger used the term 'verschränkung', later translated into English as 'entanglement', to describe the correlations between two particles that interact and then separate, as in the EPR experiment. He accepted, like Bohr, that having interacted, instead of two one-particle systems, there was just a single two-particle system and therefore any changes to one particle would affect the other, despite the distance that separated them. 'Any "entanglement of predictions" that takes place can obviously only go back to the fact that the two bodies at some earlier time formed in a true sense one system, that is were interacting, and have left behind traces on each other', he wrote in a famous paper published later in the year.45 'If two separated bodies, each by itself known maximally, enter a situation in which they influence each other, and separate again, then there occurs regularly that which I have just called entanglement of our knowledge of the two bodies.'46

Although he did not share Einstein's intellectual and emotional commitment to locality, Schrödinger was not prepared to reject it. He put forward an argument for undoing the entanglement. Any measurement on either separated part A or B of an entangled two-particle state breaks the entanglement and both are once more independent of each other. 'Measurements on separated systems,' he concluded, 'cannot directly influence each other – that would be magic.'

Schrödinger must have been surprised when he read the letter, dated 17 June, that arrived from Einstein. 'From the point of view of principles,' he wrote, 'I absolutely do not believe in a statistical basis for physics in the sense of quantum mechanics, despite the singular success of the formalism of which I am well aware.'47 This Schrödinger already knew, but Einstein declared: 'This epistemology-soaked orgy ought to come to an end.' Even as he wrote the words, Einstein knew how he sounded: 'No doubt, however, you smile at me and think that, after all, many a young heretic turns into an old fanatic, and many a young revolutionary becomes an old reactionary.'

Their letters had crossed in the post. Two days after having written his, Einstein received Schrödinger's on the EPR paper and replied immediately. 'What I really intended has not come across very well,' Einstein explained, 'on the contrary the main point was, so to speak, buried by erudition.'48 The EPR paper written by Podolsky lacked the clarity and style that characterised Einstein's published work in German. He was unhappy that the fundamental role of separability, that the state of one object cannot depend upon the kind of measurement made on another spatially separated object, had been obscured in the paper. Einstein wanted the separation principle to be an explicit feature of the EPR argument and not as it appeared, on the last page, as some sort of afterthought. He wanted to draw out the incompatibility of separability and the completeness of quantum mechanics. Both could not be true.

'The actual difficulty lies in the fact that physics is a kind of metaphysics', he told Schrödinger; 'physics describes reality; we know it only through its physical description.'49 Physics was nothing less than a 'description of reality', but that description, Einstein wrote, 'can be "complete" or "incomplete"'. He attempted to illustrate what he meant by asking Schrödinger to imagine two closed boxes, one of which contains a ball. Opening the lid of a box and looking inside is 'making an observation'. Prior to looking inside the first box, the probability that it contains the ball is ½, in other words there is a 50 per cent chance that the ball is inside the box. After the box is opened, there is either a probability of 1 (the ball is in the box) or 0 (the ball is not in the box). But, says Einstein, in reality the ball was always in one of the two boxes. So, he asks, is the statement 'The probability is ½ that the ball is in the first box' a complete description of reality? If no, then a complete description would be 'The ball is (or is not) in the first box'. If before the box is open is deemed to be a complete description, then such a description would be 'The ball is not in one of the two boxes'. The ball's existence in a definite box occurs only when one of the boxes is opened. 'In this way arises the statistical character of the world of experience or its empirical systems of laws', concluded Einstein. So he poses the question, is the state before the box is opened completely described by the pro ability ½?

To decide, Einstein brought in the 'separation principle' – the second box and its contents is independent of anything that happens to the first box. Therefore, according to him, the answer is no. Assigning the probability of ½ that the first box contains the ball is an incomplete description of reality. It was Bohr's violation of Einstein's separation principle that resulted in the 'spooky action at a distance' in the EPR thought experiment.

On 8 August 1935, Einstein followed up his ball-in-the-box with a more explosive scenario to demonstrate to Schrödinger the incompleteness of quantum mechanics because the theory could only offer probabilities where there was certainty. He asked Schrödinger to consider a keg of unstable gunpowder that spontaneously combusts at some time during the next year. At the beginning the wave function describes a well-defined state – a keg of unexploded gunpowder. But after a year the wave function 'describes a sort of blend of not-yet and of already-exploded systems'.50 'Through no art of interpretation can this wave-function be turned into an adequate description of a real state of affairs,' Einstein told Schrödinger, '[for] in reality there is just no intermediary between exploded and not-exploded.'51 Either the keg had exploded or it had not. It was, said Einstein, a 'crude macroscopic example' that exhibited the same 'difficulties' as encountered in the EPR thought experiment.

The flurry of letters he exchanged with Einstein between June and August 1935 had inspired Schrödinger to scrutinise the Copenhagen interpretation. The fruit of this dialogue was a three-part essay published between 29 November and 13 December. Schrödinger said he did not know whether to call 'The Present Situation in Quantum Mechanics' a 'report' or a 'general confession'. Either way, it contained a single paragraph about the fate of a cat that was to have a lasting impact:

'A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhapsin the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The wave function of the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.'52

According to Schrödinger and common sense, the cat is either dead or alive, depending on whether or not there has been a radioactive decay. But according to Bohr and his followers, the realm of the subatomic is an Alice in Wonderland sort of place: because only an act of observation can decide if there has been a decay or not, it is only this observation that determines whether the cat is dead or alive. Until then the cat is consigned to quantum purgatory, a superposition of states in which it is neither dead nor alive.

Although he chided Schrödinger for choosing to publish in a German journal while there remained German scientists prepared to tolerate the Nazi regime, Einstein was delighted. The cat shows, he told Schrödinger, 'that we agree completely with respect to the character of the present theory'. A wave function that contains a living and a dead cat 'cannot be considered to describe a real state'.53 Years later, in 1950, Einstein inadvertently blew up the cat, as he forgot that it was he who devised the exploding gunpowder keg. Writing to Schrödinger about 'contemporary physicists', he could not conceal his dismay at their insistence 'that the quantum theory provides a description of reality, and even a complete description'.54 Such an interpretation, Einstein told Schrödinger, was 'refuted most elegantly by your system of radioactive atom + Geiger counter + amplifier + charge of gunpowder + cat in a box, in which the wave function of the system contains the cat both alive and blown to bits'.55

Schrödinger's famous feline thought experiment also highlighted the difficulty of where to draw the line between the measuring apparatus, which is part of the macro world of the everyday, and the object being measured, which is part of the micro world of the quantum. For Bohr, there was no sharp 'cut' between the classical and quantum worlds. To explain his point about the unbreakable bond between observer and observed, Bohr offered the example of a blind man with a cane. Where, he asked, was the break between the blind man and the unseen world in which he lived? The blind man is inseparable from his cane, argued Bohr; it is an extension of him, as he uses it to get information about the world around him. Does the world start at the tip of the blind man's cane? No, said Bohr. Through the tip of his cane the blind man's sense of touch reaches into the world, and the two are inextricably bound together. Bohr suggested that the same applies when an experimenter attempts to measure some property of a microphysical particle. The observer and the observed are entwined in an intimate embrace through the act of measurement such that it is impossible to say where one begins and the other ends.

Nevertheless, the Copenhagen view assigns a privileged position to the observer, be it human or a mechanical device, in the construction of reality.

But all matter is made up of atoms and therefore subject to the laws of quantum mechanics, so how can the observer or measuring apparatus have a privileged position? This is the measurement problem. The Copenhagen interpretation's assumption of the prior existence of the classical world of the macroscopic measuring device appears circular and paradoxical.

Einstein and Schrödinger believed it to be a glaring indication of the incompleteness of quantum mechanics as a total world-view, and Schrödinger tried to highlight it with his cat-in-a-box. Measurement in the Copenhagen interpretation remains an unexplained process, since there is nothing in the mathematics of quantum mechanics that specifies how or when the wave function collapses. Bohr 'solved' the problem by simply declaring that measurements can indeed be made, but never offered an explanation of how.

Schrödinger met Bohr while in England in March 1936 and reported the encounter to Einstein: 'Recently in London spent a few hours with Niels Bohr, who in his kind, courteous way repeatedly said that he found it "appalling", even found it "high treason" that people like Laue and I, but in particular someone like you, should want to strike a blow against quantum mechanics with the known paradoxical situation, which is so necessarily contained in the way of things, so supported by experiment. It is as if we are trying to force nature to accept our preconceived conception of "reality". He speaks with the deep inner conviction of an extraordinarily intelligent man, so that it is difficult for one to remain unmoved in one's position.' Yet Einstein and Schrödinger both remained steadfast in their opposition to the Copenhagen interpretation.56

In August 1935, two months before the EPR paper was published, Einstein finally bought a house. There was nothing to distinguish 112 Mercer Street from its neighbours, but because of its owner it became one of the most famous addresses in the world. It was conveniently located within walking distance of his office at the Institute for Advanced Study, although he preferred to work in his study at home. Located on the first floor, a large table covered with the usual paraphernalia of the scholar dominated the centre of the study. On the walls there were portraits of Faraday and Maxwell, later joined by one of Gandhi.

The small clapboard house with its green shutters was also home to Elsa's younger daughter Margot, and Helen Dukas. All too soon the domestic tranquillity was shattered as Elsa was diagnosed with heart disease. As her condition worsened, Einstein became 'miserable and depressed', Elsa wrote to a friend.57 She was pleasantly surprised: 'I never thought he was so attached to me. That, too, helps.'58 She died aged 60 on 20 December 1936. With two women to look after him, Einstein quickly came to terms with his loss.

'I am settling down splendidly here', he wrote to Born.59 'I hibernate like a bear in its cave, and really feel more at home than ever before in all my varied existence.' He explained that this 'bearishness has been accentuated still further by the death of my mate, who was more attached to human beings than I'. Born found Einstein's almost casual announcement of Elsa's death 'rather strange' but unsurprising. 'For all his kindness, sociability, and love of humanity,' Born said later, 'he was nevertheless totally detached from his environment and the human beings included in it.'60 Almost. There was one person to whom Einstein was deeply attached, his sister Maja. She came to live with him in 1939 after Mussolini's racial laws forced her to leave Italy, and stayed until her death in 1951.

After Elsa's death, Einstein established a routine that as the years passed varied less and less. Breakfast between 9 and 10 was followed by a walk to the institute. After working until 1pm he would return home for lunch and a nap. Afterwards he would work in his study until dinner between 6.30 and 7pm. If not entertaining guests, he would return to work until he went to bed between 11 and 12. He rarely went to the theatre or to a concert, and unlike Bohr, hardly ever watched a movie. He was, Einstein said in 1936, 'living in the kind of solitude that is painful in one's youth but in one's more mature years is delicious'.61

In early February 1937, Bohr arrived in Princeton, together with his wife and their son Hans, for a week-long stay as part of a six-month world tour. It was the first opportunity that Einstein and Bohr had had to meet face-to-face since the publication of the EPR paper. Could Bohr finally convince Einstein to accept the Copenhagen interpretation? 'The discussion on quantum mechanics was not at all heated', recalled Valentin Bargmann, who later served as one of Einstein's assistants.62 'But to the outside observer, Einstein and Bohr were talking past each other.' Any meaningful discussion, he believed, required 'days and days'. Alas, during the encounter he witnessed, 'So many things were left unsaid'.63

What was left unsaid between them each man already knew. Their debate about the interpretation of quantum mechanics came down to a philosophical belief about the status of reality. Did it exist? Bohr believed that quantum mechanics was a complete fundamental theory of nature, and he built his philosophical worldview on top of it. It led him to declare: 'There is no quantum world. There is only an abstract quantum mechanical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.'64 Einstein, on the other hand, chose the alternative approach. He based his assessment of quantum mechanics on his unshakeable belief in the existence of a causal, observer-independent reality. Consequently he could never accept the Copenhagen interpretation. 'What we call science,' Einstein argued, 'has the sole purpose of determining what is.'65

For Bohr the theory came first, then the philosophical position, the interpretation constructed to make sense of what the theory says about reality. Einstein knew that it was dangerous to build a philosophical worldview on the foundations of any scientific theory. If the theory is found wanting in the light of new experimental evidence, then the philosophical position it supports collapses with it. 'It is basic for physics that one assumes a real world existing independently from any act of perception', said Einstein. 'But this we do not know.'66

Einstein was a philosophical realist and knew that such a position could not be justified. It was a 'belief' concerning reality that was not susceptible to proof. While that may be so, for Einstein 'it is existence and reality that one wishes to comprehend'.67 'I have no better expression than "religious" for confidence in the rational nature of reality insofar as it is accessible to human reason', he wrote to Maurice Solovine. 'Wherever this feeling is absent, science degenerates into uninspired empiricism.'68

Heisenberg understood that Einstein, and Schrödinger, wanted 'to return to the reality concept of classical physics or, to use a more general philosophic term, to the ontology of materialism'.69 The belief in an 'objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them', was for Heisenberg a throw-back to 'simplistic materialist views that prevailed in the natural sciences of the nineteenth century'.70 Heisenberg was only partly right when he identified that Einstein and Schrödinger wanted 'to change the philosophy without changing the physics'.71 Einstein accepted that quantum mechanics was the best theory available, but it was 'an incomplete representation of real things, although it is the only one which can be built out of the fundamental concepts of force and material points (quantum corrections to classical mechanics)'.72

Einstein was desperately seeking to change the physics as well; for he was not the conservative relic many thought. He was convinced that the concepts of classical physics would have to be replaced by new ones. Since the macroscopic world is described by classical physics and its concepts, Bohr agued that even to seek to go beyond them was a waste of time. He had developed his framework of complementarity in order to save classical concepts. For Bohr there was no underlying physical reality that exists independently of measuring equipment, and that meant, as Heisenberg pointed out, 'we cannot escape the paradox of quantum theory, namely, the necessity of using the classical concepts'.73 It is the Bohr-Heisenberg call to retain classical concepts that Einstein called a 'tranquilizing philosoph'.74

Einstein never abandoned the ontology of classical physics, an observer-independent reality, but he was prepared to make a decisive break with classical physics. The view of reality endorsed by the Copenhagen interpretation was all the evidence he needed of the necessity to do so. He wanted a revolution more radical than the one offered by quantum mechanics. It was hardly surprising that Einstein and Bohr left so much unsaid.

In January 1939, Bohr returned to Princeton and stayed for four months as a visiting professor at the institute. Although the two men still enjoyed a warm, friendly relationship, their ongoing dispute over quantum reality had inevitably led to a cooling. 'Einstein was only a shadow of himself', recalled Rosenfeld, who had accompanied Bohr to America.75 They did meet, usually at formal receptions, but they no longer talked about the physics that mattered so much to them. During Bohr's stay Einstein gave only one lecture, on his search for a unified field theory. With Bohr in the audience, he expressed the hope that quantum physics would be derivable from such a theory. But Einstein had already made it known that he would rather not discuss the issue further. 'Bohr was profoundly unhappy about this', said Rosenfeld.76 With Einstein unwilling to talk about quantum physics, Bohr found that there were plenty of others in Princeton eager to discuss the latest developments in nuclear physics, given the ominous events in Europe that would lead once again to a world at war.

'No matter how deeply one immerses oneself in work,' Einstein wrote to Queen Elizabeth of Belgium, 'a haunting feeling of inescapable tragedy persists.'77 The letter was dated 9 January 1939, two days before Bohr sailed for America and brought with him the news of a discovery that others had made: the splitting apart of a large nucleus into smaller nuclei, with an accompanying release of energy – nuclear fission. It was during the voyage that Bohr realised it was the uranium-235 isotope that undergoes nuclear fission when it is bombarded by slow-moving neutrons, and not uranium238. At the age of 53, it was Bohr's last major contribution to physics. With Einstein unwilling to debate the nature of quantum reality, Bohr concentrated on working out the details of nuclear fission with the American John Wheeler from Princeton University.

After Bohr returned to Europe, Einstein sent a letter, dated 2 August, to President Roosevelt urging him to examine the feasibility of developing an atomic bomb, given that Germany had stopped the sale of uranium ore from mines it now controlled in Czechoslovakia. Roosevelt replied in October, thanking Einstein for his letter and informing him that he had set up a committee to investigate the issues raised. In the meantime, on 1 September 1939, Germany attacked Poland.

Still a pacifist, Einstein was prepared to compromise until Hitler and the Nazis were defeated. In a second letter, dated 7 March 1940, he urged Roosevelt that more needed to be done: 'Since the outbreak of the war, interest in uranium has intensified in Germany. I have now learned that research there is carried out in great secrecy.'78 Unknown to Einstein, the man in charge of the German atomic bomb programme was Werner Heisenberg. Once again, the letter failed to solicit much of a response. Bohr's discovery that it was uranium-235 that underwent fission was far more important to the creation of the atom bomb than anything achieved by Einstein's two letters to Roosevelt. The American government did not seriously begin thinking about developing an atomic bomb, codenamed the Manhattan Project, until October 1941.

Even though Einstein had become an American citizen in 1940, the authorities considered him a security risk because of his political views. He was never asked to work on the atomic bomb. Bohr was. On 22 December 1943 he stopped off at Princeton on his way to Los Alamos in New Mexico, where the bomb was being built. He had dinner with Einstein and Wolfgang Pauli, who had joined the Institute for Advanced Study in 1940. Much had happened since the last time Bohr met Einstein.

In April 1940, German forces had occupied Denmark. Bohr chose to remain in Copenhagen, hoping that his international reputation would provide some semblance of protection to others at his institute. And it did until August 1943, when the illusion of Danish self-rule was finally shattered as the Nazis declared martial law after the government rejected a demand that a state of emergency be declared and acts of sabotage be punishable by death. Then on 28 September, Hitler ordered the deportation of Denmark's 8,000 Jews. A sympathetic German official informed two Danish politicians that the round-up was to begin at 9pm on 1 October. As word quickly spread of the Nazi plan, almost every Jew disappeared, hidden in the homes of fellow Danes or finding sanctuary in churches, or disguised as patients in hospitals. The Nazis managed to round up fewer than 300 Jews. Bohr, whose mother had been Jewish, managed to escape to Sweden with his family. From there he flew to Scotland in a British bomber, almost dying from a lack of oxygen because he was travelling in the bomb-bay and had an ill-fitting oxygen mask. After meeting British politicians he soon travelled to America, where after his fleeting visit to Princeton he worked on the atomic bomb under the alias 'Nicholas Baker'.

After the war, Bohr returned to his institute in Copenhagen, and Einstein said he felt 'no friendship for any real German'.79 Yet he had abiding sympathy for Planck, who outlived all four children from his first marriage. The death of his youngest son was the bitterest of all the blows Planck endured in his long life. Erwin, an undersecretary of state in the Reich Chancellery before the Nazis came to power, was a suspect in an attempt to assassinate Hitler in July 1944. He was arrested and tortured by the Gestapo and found guilty of complicity in the assassination plot. At one point there was a glimmer of hope as Planck set, in his words, 'Heaven and Hell in motion' to have the death penalty commuted to a prison sentence.80 Then, without warning, Erwin was hanged in Berlin in February 1945. Planck had been denied the opportunity to see his son one last time: 'He was a precious part of my being. He was my sunshine, my pride, my hope. No words can describe what I have lost with him.'81

When he heard the news that Planck had died, aged 89, following a stroke on 4 October 1947, Einstein wrote to his widow of the 'beautiful and fruitful time' he had been privileged to spend with him. As he offered his condolence, Einstein recalled that the 'hours which I was permitted to spend at your house, and the many conversations which I conducted face to face with that wonderful man, will remain among my most beautiful recollections for the rest of my life'.82 It was something, he reassured her, which could not 'be altered by the fact that a tragic fate tore us apart'.

After the war, Bohr was made a permanent non-resident member of the Institute for Advanced Study and could come and stay whenever he wanted to. His first trip in September 1946 was brief, as he came to take part in the bicentennial celebrations of the founding of Princeton University. Then in 1948 he arrived in February and stayed until June. This time Einstein was willing to talk physics. Abraham Pais, a young Dutch physicist who helped Bohr during his visit, later described the occasion when the Dane came bursting into his office 'in a state of angry despair', saying, 'I am sick of myself'.83 When Pais asked what was wrong, Bohr replied that he had been to see Einstein and they had got into an argument about the meaning of quantum mechanics.

The renewal of their friendship was signalled by the fact that Einstein let Bohr use his office. One day Bohr was dictating a draft of a paper in honour of Einstein's 70th birthday to Pais. Stuck on what to say next, Bohr stood looking out of the window, every now and then muttering Einstein's name aloud. At that moment Einstein tiptoed into the office. His doctor had banned him from buying any tobacco, but had said nothing about stealing it. Pais later recounted what happened next: 'Always on tiptoes, he made a beeline for Bohr's tobacco pot, which stood on the table at which I was sitting. Bohr, unaware, was standing at the window, muttering, "Einstein … Einstein …" I was at a loss what to do, especially because I had at that moment not the faintest idea of what Einstein was up to. Then Bohr, with a firm "Einstein", turned around. There they were, face to face, as if Bohr had summoned him forth. It is an understatement to say that for a moment Bohr was speechless. I myself, who had seen it coming, had distinctly felt uncanny for a moment, so I could well understand Bohr's own reaction. A moment later the spell was broken when Einstein explained his mission. Soon we were all bursting with laughter.'84

There were other visits to Princeton, but Bohr never managed to get Einstein to change his mind on quantum mechanics. Nor did Heisenberg, who saw him only once after the war during a lecture tour of the United States that overlapped with Bohr's last visit in 1954. Einstein invited Heisenberg to his home and, over coffee and cakes, they chatted for most of the afternoon. 'Of politics we said nothing', recalled Heisenberg.85 'Einstein's whole interest focused on the interpretation of quantum theory, which continued to disturb him, just as it had done in Brussels twenty-five years before.' Einstein remained resolute. '"I don't like your kind of physics", he said.'86

'The necessity of conceiving of nature as an objective reality is said to be superannuated prejudice while the quantum theoreticians are vaunted', Einstein had once written to his old friend Maurice Solovine.87 'Men are even more susceptible to suggestion than horses, and each period is dominated by a mood, with the result that most men fail to see the tyrant who rules over them.'

When Chaim Weizmann, the first president of Israel, died in November 1952, the prime minister David Ben-Gurion felt compelled to offer Einstein the presidency. 'I am deeply moved by the offer from our state of Israel, and at once saddened and ashamed because I cannot accept it', said Einstein.88 He highlighted the fact that he lacked 'both a natural aptitude and the experience to deal properly with people and to exercise official functions'. 'For these reasons alone,' he explained, 'I should be unsuited to fulfil the duties of high office, even if advancing age was not making increasing inroads on my strength.'

Ever since the summer of 1950 when doctors discovered that his aortic aneurysm, a bulge in the aorta, was getting larger, Einstein knew he was living on borrowed time. He wrote his will and made it clear that he wanted to be cremated after a private funeral. He lived to celebrate his 76th birthday, and one of his last acts was to sign a declaration written by the philosopher Bertrand Russell calling for nuclear disarmament. Einstein wrote to Bohr asking him to sign it. 'Don't frown like that! This has nothing to do with our old controversy on physics, but rather concerns a matter on which we are in complete agreement.'89 On 13 April 1955, Einstein experienced severe chest pains, and two days later he was taken to hospital. 'I want to go when I want', he said, refusing surgery. 'It is tasteless to prolong life artificially; I have done my share, it is time to go.'90

As fate would have it, his step-daughter Margot was staying in the same hospital. She saw Einstein twice and they chatted for a few hours. Hans Albert, who had arrived in America with his family in 1937, rushed from Berkeley in California to his father's bedside. For a while Einstein seemed better and asked for his notes, unable to abandon his search for a unified field theory even at the end. Shortly after 1am on 18 April, the aneurysm burst. After saying a few words in German that the night nurse could not understand, Einstein died. Later that day he was cremated, but not before his brain was removed and his ashes scattered at an undisclosed location. 'If everyone lived a life like mine there would be no need for novels', Einstein once wrote to his sister. The year was 1899 and he was twenty.91

'Except for the fact that he was the greatest physicist since Newton,' said Banesh Hoffmann, one of Einstein's Princeton assistants, 'one might almost say that he was not so much a scientist as an artist of science.'92 Bohr paid his own heartfelt tribute. He recognised Einstein's achievements to be 'as rich and fruitful as any in the whole history of our culture', and said that 'mankind will always be indebted to Einstein for the removal of the obstacles to our outlook which were involved in the primitive notions of absolute space and time. He gave us a world picture with a unity and harmony surpassing the boldest dreams of the past.'93

The Einstein-Bohr debate did not end with Einstein's death. Bohr would argue as if his old quantum foe were still alive: 'I can still see Einstein's smile, both knowing, humane and friendly.'94 Often his first thought when thinking about some fundamental issue in physics was to wonder what Einstein would have said about it. On Saturday, 17 November 1962, Bohr gave the last of five interviews concerning his role in the development of quantum physics. After lunch on Sunday, Bohr went to take his usual nap. When he called out, his wife Margrethe rushed to the bedroom and found him unconscious. Bohr, aged 77, had suffered a fatal heart attack. The last drawing on the blackboard in his study, made the night before as he replayed the argument over once more, was of Einstein's light box.