Reception and Impact of the EPR Paper

Abstract

Probably even the authors did not foresee the impact their 1935 paper would have on the debate about the meaning of quantum theory. Astonishingly, it still influences the debate today. In this chapter we therefore give a historic account of its impact and reception. For two reasons, special attention will be given to Bohr’s reply to EPR’s work. On the one hand, it exemplarily shows the conceptual difficulties associated with the debate.

Probably even the authors did not foresee the impact their 1935 paper would have on the debate about the meaning of quantum theory. Astonishingly, it still influences the debate today. In this chapter we therefore give a historic account of its impact and reception. For two reasons, special attention will be given to Bohr’s reply to EPR’s work. On the one hand, it exemplarily shows the conceptual difficulties associated with the debate. On the other hand, it was historically the most important reaction to EPR’s work, because many physicists considered Bohr to be the authority in the field of quantum theory that was not to be challenged. Many, if not most physicists followed Bohr without criticism and did not really bother to read EPR’s and Bohr’s original works. But as Mara Beller, in particular, has pointed out, Bohr’s ‘victory’ over Einstein is but a legend and not based on facts [17, p. 151f]. According to Arthur Fine, the ‘EPR paradox’ is a paradox first and foremost if one adopts the Copenhagen interpretation of quantum theory [73, p. 4f]. This interpretation, we recall, had been formulated by Heisenberg and especially by Bohr, who thought of himself as this interpretation’s creator, in the years after 1925, and had been dismissed by Einstein as “Heisenberg-Bohr tranquillising philosophy” as early as in 1928 in a letter to Schrödinger.¹ So let us first have a look at Bohr’s paper.

4.1 Reprint of Bohr’s Paper

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? N. Bohr, Physical Review, Volume 48, Page 696–702, published in 1935 by the American Physical Society. Reprinted with permission https://doi.org/10.1103/PhysRev.48.696

4.2 Bohr’s Reply

Bohr was very much alarmed by the EPR paper, which becomes apparent in this short account by his student Léon Rosenfeld [138]:

This onslaught came down upon us as a bolt from the blue. Its effect on Bohr was remarkable. […] as soon as Bohr had heard my report of Einstein’s argument, everything else was abandoned: we had to clear up such a misunderstanding at once. We should reply by taking up the same example and showing the right way to speak about it.

Apparently, Bohr and his devoted student Rosenfeld were not interested in an open discussion, but rather in clearing up what according to them was a misunderstanding in the EPR paper.

At first, Bohr published a short response, only one page long, in Nature [27]. Even on the day of its publication, Schrödinger wrote to Einstein: “I was furious about N. Bohr’s letter to Nature from July 13. He only makes you curious, does not reveal at all what he is talking about, and refers to a paper that is to appear in Physical Review.”² The paper Bohr had announced in Nature was indeed submitted to Physical Review on the same day and was published on October 15, 1935. Comprising six pages in its original version, Bohr’s paper is not long but two pages longer than the paper he criticised.

Bohr’s paper is not a prime example of clarity.³ Mara Beller brought up the following quite amusing fact [16]. Most commentators refer to the reprint of Bohr’s article in the collective volume dealing with the foundations of quantum theory edited by Wheeler and Zurek [164]. In this reprint, however, pages 700 and 699 were interchanged.⁴ Nobody ever noticed. Indeed, when reading the paper in the wrong order of pages, one does not get a significantly different impression than when reading the original. The author seems to have known that his paper was incomprehensible. He later wrote about it: “Rereading these passages, I am deeply aware of the inefficiency of expression which must have made it very difficult to appreciate the trend of the argumentation […].”⁵ Is it still possible to extract the core messages from Bohr’s paper?

Already the introductory lines include two points that were essential to Bohr: EPR’s ‘criterion of physical reality’ and the concept of complementarity , introduced by Bohr. According to the author, the application of complementarity will entail the completeness of the quantum mechanical description. In his paper, Bohr especially attacks EPR’s criterion of reality, although it did not play a central role in the EPR paper as we have seen above. Naturally, Bohr felt especially provoked by the passage “without in any way disturbing a system”. After all, when formulating the earlier version of the Copenhagen interpretation, it was indispensable to assume a necessary disturbance of the measured system by the measurement apparatus. This unavoidable disturbance had followed from Heisenberg’s thought experiments concerning the uncertainty relations.

Now in the first part of his paper, Bohr covers the example of the double slit, as he did in the discussions during the Solvay Conference of 1927, which has little to do with the EPR paper. Although Bohr accepted their thought experiment, he did not agree with their interpretation, which he then replaced with his own. This happens in the second part of his paper, which is also where his notion of complementarity comes fully into play. While in Como in 1927 Bohr had talked about complementarity of causality and space-time description, he now applied the complementarity to the measurement apparatus. Since the measurements of position and momentum exclude each other, and thus are ‘complementary’ to each other, neither position and momentum of the measured particle, nor the position and momentum of the distant particle as calculated from the information on the first particle, can have simultaneous reality. Bohr wrote (p. 700 of the paper reprinted in this book, italics by Bohr):

Of course there is in a case like that just considered no question of a mechanical disturbance of the system under investigation [Bohr means the second, distant particle, C.K.] during the last critical stage of the measuring procedure. But even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behaviour of the system. 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 argument of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete. […] It is just this entirely new situation as regards the description of physical phenomena, that the notion of complementarity aims at characterising.

Evidently, EPR did not directly claim that position and momentum have simultaneous reality, although this seems to follow implicitly from their argumentation. EPR agreed with Bohr that position and momentum of the first particle cannot be measured simultaneously and that therefore position and momentum of the second particle cannot be calculated simultaneously. EPR only concluded that different wave functions can be ascribed to the same reality, and therefore the description of reality with wave functions is not unique and quantum theory not complete. But Bohr did not mention wave functions at all! So in his reply, Bohr missed the essential message of the EPR paper. Instead, he assigned a word to the situation in question – complementarity.

In her book, Mara Beller attentively analyses Bohr’s paper and sees two contradicting voices coming to light [17, chap. 7]. One voice expresses Bohr’s point of view from before the EPR paper. According to it, a measurement always corresponds to a direct physical disturbance of the measured system by the measurement apparatus. After the publication of the EPR paper, such a point of view could not be maintained, because the second particle, by assumption, cannot be disturbed – at least not mechanically, as Bohr specified in the above quoted section. The second voice expresses a positivist attitude. Only what can be measured simultaneously has simultaneous reality; there is no objective reality independent of observations. It is this second point of view that Bohr would maintain the rest of his life. Beller accurately describes it as the transition of a physical disturbance of the system into a semantic disturbance of a system – the semantic disturbance being the above quoted “influence on the very conditions which define the possible types of predictions regarding the future behaviour of the system.”

What mattered to Bohr in his discussions with Einstein from 1927 to 1930 was to also apply the uncertainty relations to the measurement apparatus. So the measurement apparatus also became a quantum mechanical system. After 1935, Bohr no longer held that opinion. From then on he emphasised the fundamental difference between the nature of atomic objects and the nature of measurement apparatus. The latter always need to be described classically. According to Beller, it was this doctrine of the necessity of classical notions in the macroscopic realm that underlie Bohr’s philosophy of complementarity. For Beller, complementarity is but a metaphor [17, p. 243f]:

Complementarity is not a rigorous guide to the heart of the quantum mystery. Nor do Bohr’s numerous analogies between quantum physics and other domains, such as psychology or biology, withstand close scrutiny. Complementarity does not reveal preexisting similarities; it generates them. Complementarity builds new worlds by making new sets of associations. These worlds are spiritual and poetic, not physical. Complementarity did not result in any new physical discovery – “it is merely a way to talk about the discoveries that have already been made” (interview with Dirac, Archive for the History of Quantum Physics).

Beller was right to point out that the asserted necessity of classical concepts is vague, historically as well as philosophically. According to Beller, this view ignores the huge gap between Aristotle’s direct intuition and the abstract framework of Newton’s (and Einstein’s) physics. Following Fine, Bohr was the more conservative one in the Einstein and Bohr debate, because he absolutely wanted to keep the old (classical) notions, whereas Einstein subjected them to a critical examination; Bohr viewed the world through classical glasses [73, p. 19f]. As Whitaker pointed out, the assumptions underlying the idea of complementarity prohibit the kind of argument that EPR used, because alternative measurements may not be taken into account [165, p. 1335f].

The notion of complementarity in its positivist formulation and the necessity of the classical concepts when describing the measurement apparatus constitute the core of what is known today as the Copenhagen interpretation .⁶ This is why EPR’s argumentation constitutes such a problem for the followers of this interpretation. But other authors had their problems with EPR as well, as we shall see in the next section.

4.3 Schrödinger and Entanglement

Erwin Schrödinger, the father of wave mechanics, was especially interested in the conceptual questions raised by EPR. In reaction to the EPR paper, he published a number of articles in 1935 and 1936, detailing his point of view on quantum mechanics [145,146,147]; in a footnote in one of these articles he openly admitted: “The appearance of this work [the EPR paper, C. K.] motivated the present – shall I say lecture or general confession?”⁷

In his general confession, Schrödinger introduced a notion that today is considered to be the central element of quantum theory – entanglement. Modern research areas like quantum information are inconceivable without an extensive discussion of properties of entangled systems. De facto, entangled states had already been discussed before 1935, for example in the above quoted works by Hylleraas [93, 94].

An entanglement between quantum mechanical systems (like the two particles in the EPR paper) generally occurs when these systems interact. The wave function of the combined system cannot be expressed as a product of two wave functions that correspond to one of the subsystems each; this does not change even when the subsystems are being separated by so far a distance that an exchange of information is no longer possible. Schrödinger wrote:

Maximal knowledge of a combined system does not necessarily include maximal knowledge of all its parts, not even when these are fully separated from each other and at the moment are not influencing each other at all.⁸

Following Schrödinger, maximal knowledge of a quantum mechanical system is obtained by knowledge of its wave function ψ, which in the case of an entangled system is known only for the combined system, but nor for the constituting subsystems. Entanglement occurs naturally when two systems interact:

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.⁹

Different to our usage of the term entanglement today, Schrödinger here spoke about an entanglement of knowledge. This is due to his interpretation of the wave function as an ‘expectation-catalog’ and not as the dynamically relevant state that can be understood in a specific realistic sense. For Schrödinger, the entanglement of the subsystems was mainly a correlation of probabilities, as is already highlighted in the titles of his papers [145, 147].

Shortly after the publication of the EPR paper, an intense exchange of letters set in between Schrödinger an Einstein. We already talked about this above (Sect. 2.5). In these letters, some of the topics of Schrödinger’s 1935 papers are anticipated. Most notably they already contained the notorious cat-example, known today as Schrödinger’s cat, that was later printed in Schrödinger [146, p. 812]. In his letter to Einstein on August 19, 1935, Schrödinger wrote:

I am long past the stage where I thought that one can consider the ψ-function as somehow a direct description of reality. […] Confined in a steel chamber is a Geigercounter prepared with a tiny amount of uranium, so small that in the next hour it is just as probable to expect one atomic decay as none. An amplifying relay provides that the first decay shatters a small bottle of prussic acid. This and – cruelly – a cat is also trapped in the steel chamber. According to the ψ-function for the total system, after an hour, sit venia verbo, ¹⁰ the living and dead cat are smeared out in equal measure.¹¹

The situation of Schrödinger’s cat is a macroscopic superposition of quantum states that exhibits non-classical properties. The example with the coupling to a radioactive is meant to illustrate how such states occur naturally when one extends the quantum mechanical formalism to macroscopic areas. To Schrödinger, this thought experiment proves the interpretation of ψ as a mere expectation-catalogue. Only the understanding of the classical limit through decoherence (Sect. 5.4), that was reached much later, shows why the state of Schrödinger’s cat can correspond to reality. Einstein, in a letter to Schrödinger on September 4, 1935, noted in reference to the cat-example:

As for the rest, your cat shows that we are in complete agreement concerning our assessment of the character of the current theory. A ψ-function that contains the living as well as the dead cat just cannot be taken as a description of a real state of affairs. To the contrary, this example shows exactly that it is reasonable to let the ψ-function correspond to a statistical ensemble that contains both systems with live cats and those with dead cats.¹²

Einstein would highlight this point in later letters, too.

In quantum optics one today speaks of ‘cat-states’ when coherent states of ions or atoms are superposed. Serge Haroche (Ecole Normale Supérieure, Paris, France) and David Wineland (National Institute of Standards and Technology, Boulder, USA) are pioneers in this research area and report on it in their Nobel lectures [84, 170].¹³ Preparing this kind of states is an important prerequisite for experiments concerning the behaviour in the classical limit, see Sect. 5.4 further below.

Einstein and Schrödinger would go on to discuss these fundamental questions until Einsteins’s death, without ever finding a consensus.¹⁴ For Einstein it was unthinkable that the ψ-function directly describes the physical reality, beyond a purely statistical description. In his last letters to Schrödinger and Born, he emphasised the role of the superposition principle and the resulting ‘fuzziness’ of macroscopic states, herein differing from what he said directly after the EPR paper, also cf. Einstein [61]. On March 22, 1953, Einstein wrote to Schrödinger:

I do not understand at all the analogy between the uncertainty of the general ψ function and the difficulty this creates to consider it a description of physical reality on the one hand, and a thermodynamical description on the other hand.¹⁵ The essence of quantum theory, after all, is that the ψ function obeys a linear equation. This has been explicitly arranged so that the sum of two ψ functions is again a ψ function (a solution). All the solutions obtained by such summations are per se coequal and thus represent, according to your interpretation, possible real cases that are to be treated as coequal in the theory. It therefore seems to me that in such a theory the quasi-sharpness of positions and momenta of a system as a whole cannot exist. Because the superposition of quasi-sharp states creates arbitrarily fuzzy macroscopic systems (ψ functions), in whose real existence, in the sense of your interpretation, no man can believe. I am convinced that only the statistical interpretation can overcome this difficulty.¹⁶

At around the same time, Einstein voiced the same line of reasoning in letters to Max Born [69], who, just like Schrödinger, missed the root of the matter. Applying the superposition principle, according to which the sum of two physically reasonable ψ functions again constitutes a physically reasonable ψ function, necessarily yields ‘fuzzy’ macroscopic states like Schrödinger’s cat that have never been observed. Einstein’s proposition of interpreting the wave function merely statistically offers a way out of this paradox. But we will see further below this way out is not necessary, because the application of quantum theory to realistic systems makes it possible to understand the non-appearance of macroscopic superpositions within the framework of a realistic interpretation of the wave function.

The problem of the macroscopic superpositions also weighed heavy on Wigner’s mind. In his famous paper ‘Remarks on the Mind-Body Question’ he speculated that only the human consciousness is responsible for the wave function collapse and the fact that ‘fuzzy’ states have never been observed. He wrote [168, p. 176]: “It follows that the quantum description of objects is influenced by impressions entering my consciousness.” He later abandoned this thought under the impression of Zeh’s work [173] that showed that macroscopic objects act classically due to unavoidable interactions with their environment, see Wigner [169, p. 240]. This phenomenon called decoherence will play a central role in the debate on the interpretation of quantum theory, see Sect. 5.4.

4.4 Pauli and Heisenberg

Wolfgang Pauli reacted to the EPR paper in his habitual way, i.e., harshly. Already on June 15, 1935, he wrote to Heisenberg:

Einstein once again commented publicly on quantum mechanics, this time in Physical Review on May 15 (together with Podolsky and Rosen – no good company, by the way). As is well known this is a catastrophe every time it happens. “For – he keenly concludes – that which must not, cannot be.” (Morgenstern).

At least I want to concede to him that if an undergraduate student came to me with such objections, I would think him quite intelligent and promising. – Since this publication risks confusing the public opinion – namely in America – , I would suggest to send a reply to Physical Review, something I wish to encourage you to do.¹⁷

As far as Pauli was concerned, the interpretation of quantum mechanics was just about pedagogical questions. In his letter, he fundamentally attacked EPR’s assumption of separability. Because, according to Pauli, you can only assume this if you are dealing with a very special state, namely a state that is a product with respect to the subsystems. He therefore is not surprised that you run into contradictions when neglecting this and instead conceive ‘hidden properties’ of an un-measured system. In the above-quoted excerpt of his letter, Pauli encourages Heisenberg to publish a riposte to the EPR paper in order to clarify those issues.

Heisenberg was willing to write such a riposte. In his response to Pauli on July 2, 1935, he mentioned that Bohr planned an answer to EPR, but that this answer would differ very much from his own points of view [128, p. 407f]. In his summer vacation 1935, Heisenberg wrote a manuscript and sent it to some of his colleagues (among them, Bohr). However, he never published it, maybe due to the fact that in the meantime a whole number of ripostes to the EPR paper had been published. The manuscript’s title reads “Is a deterministic completion of quantum mechanics possible?”. It was published only posthumously in Pauli [128, p. 409–418].¹⁸

Already the manuscript’s title highlights Heisenberg’s intention to focus on the incompleteness of quantum theory that played such a central role in the EPR paper. He goes on to show that such a deterministic completion is impossible, i.e., in contradiction to the experimental successes of quantum mechanics. Heisenberg emphasises that the wave function is defined in a configuration space of higher dimension whereas observations take place in space and time. He therefore asks: “At what place should one draw the cut between the description by wave functions and the classical-anschaulich description?”¹⁹ His answer being: “The quantum mechanical predictions about the outcome of an arbitrary experiment are independent of the location of the cut just discussed.”²⁰ So the place of the Heisenberg cut (later so named) is, to a certain degree, arbitrary; except, it must remain far enough away from the system to be measured in order to avoid coming into conflict with the system’s observed quantum properties, e.g., interference.

Heisenberg then concludes as follows. Let us assume there exist hidden variables that describe the time evolution beyond the cut. At the place of the cut, and only there, they should contain the transition from a description by wave functions to a statistical interpretation. The place of the cut being arbitrary, this cannot be the case, Heisenberg says. Bacciagaluppi and Crull [5] mention that Heisenberg had turned against the concept of hidden variables even earlier than in this manuscript, because their existence would contradict the observed quantum mechanical phenomenon of interference.

In his letter to Pauli, Heisenberg mentioned an essay by philosopher Grete Hermann (1901–1984) on the subject of incompleteness of quantum mechanics, wherein Hermann exposed a circularity in von Neumann’s proof of impossibility of hidden variables [90].²¹ This will be discussed further below.

4.5 Some More Early Responses

Maybe the earliest printed response to the EPR paper is the one by American physicist Edwin C. Kemble (1889–1984), cf. Kemble [102]. Schrödinger noted [158, p. 551f]: “What I understand least is the paper by E. C. Kemble in Physical Review from June 15 – he doesn’t even mention the case that causes us a headache. It’s as if one is saying: It’s bitterly cold in Chicago, and someone’s answering: That’s a false conclusion, it’s very hot in Florida.” Indeed, Kemble’s criticism misses the point of the EPR paper. He simply claims that a merely statistical interpretation of the wave function suffices to avoid paradoxes. Obviously, Einstein himself had concluded this, but was not ready to accept a merely statistical interpretation (i.e., without an explaining ensemble of fundamental physical objects) and therefore concluded the incompleteness of the theory.

In contrast, American physicist Arthur E. Ruark (1899–1979) used another criterion of reality in his response [139]. According to his criterion, a physical property of a physical system only has reality if and when it is measured. In this respect, his position is close to Bohr’s, whose work, however, had not been published yet at the time. Ruark drew the somewhat evasive conclusion, that given current knowledge a decision was impossible, because one could not know which criterion made more sense.

Wendell H. Furry (1907–1984), another American physicist, took Bohr’s side in his response, but made use of wave functions in his argumentation [75]. He formulated an ‘assumption A’, according to which a system, when interacting with another system, non-causally evolves into a state with a definite wave function. Following the interaction, the total system is then represented by a product of two wave functions (one for the first, one for the second system). This separation occurs without measurement and thus has nothing to do with an alleged collapse of the wave function during the measurement, according to which a measurement should, with some given probability, result in a certain state. Furry then showed explicitly that his assumption A contradicts Schrödinger’s equation. In a short supplement to his paper [76], Furry commented on the articles by Schrödinger that had come out in the meantime [145, 146]. Furry underlined, that while Schrödinger’s mathematical approach resembled his own, he had come to opposing conclusions. Schrödinger rejected assumption A and joined in on EPR’s criterion of reality. Furry commented [76]:

Thus there can be no doubt that quantum mechanics requires us to regard the realistic attitude as in principle inadequate.

By this, he meant EPR’s criterion of local reality. Because:

No matter how far apart the particles are when we try to collect one of them, the relative probabilities of finding it in different places are strongly affected by the ‘interference term’ in the cross section; it is not really ‘free’.

In contrast to this, Schrödinger concludes the incompleteness of quantum theory, but in another way than EPR; he sees more of a problem in the fact that the theory only allows predictions for a “sharply-defined time.”²² But Furry had spotted the crucial point: The reality described by quantum theory is non-local. Bohm and Aharonov [25] referred to an actual experiment contradicting Furry’s assumption A (also cf. Whitaker [166, p. 155f]). Assumption A thus holds no solution to the problem EPR had raised; the entanglement between two subsystems after their interaction is real.