Quantum
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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 probability 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 perhaps in 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 world-view on the foundations of any scientific theory. I
f 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