by Manjit Kumar
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 dra
ft 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 29 June 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.’33 Yet 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 a
nd 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.
