In part 2 we closed with the idea that Bohr seemed to be using general relativity against Einstein to save quantum mechanics! A wonderful story. But is it true?

Einstein seems to have thought that they were arguing about something else. We know this from a letter that Paul Ehrenfest wrote to Bohr in July 1931, after a visit with Einstein in Berlin.  Ehrenfest and Einstein seem to have had a long and thorough chat about the debate with Bohr at the previous fall’s Solvay meeting. Ehrenfest reports to Bohr a most surprising comment from Einstein:
He [Einstein] said to me that, for a very long time already, he absolutely no longer doubted the uncertainty relations, and that he thus, e.g., had BY NO MEANS invented the “weighable light-flash box” (let us call it simply L-F-box) “contra uncertainty relation,” but for a totally different purpose.
(Ehrenfest to Bohr, 9 July 1931, Bohr Scientific Correspondence, Archive for History of Quantum Physics. As quoted in Howard 1990a, 98)

What was that totally different purpose? It was nothing other than an anticipation of Einstein’s later argument for the incompleteness of quantum mechanics.(11)

As Ehrenfest explains to Bohr, Einstein’s idea was this. Let the photon leave the box and be reflected back from a great time and distance, say one-half light year. At about the time when the photon is reflected, we can either weigh the box or check the clock, making possible our predicting either the exact time of the photon’s return or its energy (literally, its color), which is to say that, depending upon which measurement we choose, we ascribe a different theoretical state to the photon, one with definite energy, one entainling a definite time of arrival. Crucial is the fact that the event of performing the measurement on the box–weighing it the second time or checking the clock–is space-like separated from the event of the photon’s distant reflection, because then our choice of a measurement to perform can have no effect on the real state of affairs of the photon, meaning that the photon’s real state of affairs when it returns will be one and the same, regardless of the measurement we performed on the box. This is all just quantum mechanics, in Einstein’s view. But then quantum mechanics has associated two different theoretical states with one real state of affairs, which is possible only if the quantum theory’s state descriptions are incomplete.

If you are unfamiliar with the recent revisionist literature on Einstein’s incompleteness critique of quantum mechanics and are, therefore, saying to yourself that you do not recognize in the immediately foregoing a precursor to the the Einstein, Podolsky, and Rosen (EPR) argument, you are right. But stay tuned, for we will shortly see that Einstein did not write the EPR paper, did not like the argument it contained, and proposed, instead, his own rather different argument for the incompleteness of quantum mechanics,  one that is, indeed, foreshadowed by the argument that Ehrenfest reports to Bohr. That later argument, like the one Ehrenfest describes to Bohr, turns upon the consequences of the space-like separation between two events, this being in both cases the premise for ascribing to the systems involved in each (box and photon in the case of the 1930 Solvay thought experiment) separate, independent, real states of affairs.

What is happening here is that the Einstein who early intimated the deep role that entanglement would play in quantum mechanics and found by 1927 that he could not get rid of the entanglement by a hidden variables interpretation has now come to see in entanglement (still not known by that name) the chief point of difference between quantum mechanics and field theories like general relativity as alternative frameworks for a future fundamental physics and the chief reason for preferring the latter to the former. Einstein will need still a few more years to say exactly why entanglement is unacceptable (again, stay tuned), but that it is unacceptable is something that he seems already clearly to have decided by about 1930.

1935 and Beyond: EPR and Its Aftermath

In the turbulent years between 1930 and 1935 (the triumph of Hitler in Germany, exile, finding a new home in Princeton), Einstein revises and refines his arguments for the incompleteness of quantum mechanics. A note here, a letter there. But finally, in June of 1935, there appears in Physical Review what has since become its most frequently cited paper but also one of most misunderstood papers in history of twentieth-century foundations of physics, the EPR paper.

The outlines of the argument are familiar. EPR assume a completeness condition: “every element of the physical reality must have a counterpart in the physical theory”; and a reality condition: “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” (Einstein, Podolsky, and Rosen 1935, 777).

They consider then a thought experiment involving two previously interacting systems, I and II, whose post-interaction joint state can be written as a superposition over products of either momentum or position eigenstates of I and II. Under these circumstances, measuring the momentum of system I allows one to predict with certainty the momentum of II, and measuring the position of I allows one to predict with certainty the position of II. Thus, according to the reality condition, there exist elements of physical reality corresponding to both the momentum and the position of system II. But since the operators for position and momentum do not commute (Heisenberg indeterminacy), quantum mechanics cannot contain counterparts for these two elements of the physical reality of system II.   Thus, quantum mechanics is incomplete.

One of the most interesting features of the EPR argument is that in order to prove quantum mechanics incomplete, it employs a thought experiment that some might think was designed to exhibit possible violations of Heisenberg indeterminacy. Of course, Einstein, Podolsky, and Rosen did not assert the direct simultaneous measurability of the position and momentum of system I, and so do not assert the indirect simultaneous measurability of the position and momentum of system II, but the argument is supposed to licence an inference to the simultaneous existence of elements of physical reality corresponding to both the position and the momentum of system II, which one  might take, wrongly, as proof not only of the incompleteness of the quantum mechanical description of system II, but also its incorrectness.

That one might so misinterpret the intended import of the EPR thought experiment reminds one of the fact that Bohr, in his memoir of his debates with Einstein, did so misinterpret or misremember the import of the photon box thought experiment. Bohr thought it was intended to prove quantum mechanics incorrect by exhibiting violations of Heisenberg indeterminacy, but Einstein explained to Ehrenfest that the real point was to prove incompleteness.

Shortly after publication of the EPR paper, Schrödinger wrote to Einstein on 7 June 1935 to congratulate him: “I was very pleased that in the work which just appeared in Phys. Rev. you openly seized dogmatic quantum mechanics by the scruff of the neck, something we had already discussed so much in Berlin” (EA 22-044).   He was no doubt surprised to receive a reply from Einstein, written on 19 June, that began with these words:
I was very pleased with your detailed letter, which speaks about the little essay. For reasons of language, this was written by Podolsky after many discussions. But still it has not come out as well as I really wanted; on the contrary, the main point was, so to speak, buried by the erudition [die Hauptsache ist sozusagen durch Gelehrsamkeit verschüttet].
(EA 22-047)

Einstein went on to sketch an argument strikingly different from the EPR argument. It begins with
what Einstein terms the “separation principle” or “separation hypothesis,” according to which the
real state of affairs in one part of space cannot be affected instantaneously or super-luminally by events in a distant part of space. Consider, then, two quantum mechanical systems, A and B, that collide and separate in a manner that engenders correlations between observables of the two systems, a typical scattering problem in which, say, momentum and energy are conserved. I can choose to measure any of various observables of system A. Depending upon my choice, quantum mechanics tells me to assign different states to B. Of such a situation, Einstein comments:
After the collision, the real state of (AB) consists precisely of the real state A and the real state of B, which two states have nothing to do with one another. The real state of B thus cannot depend upon the kind of measurement I carry out on A. (“Separation hypothesis” from above.) But then for the same state of B there are two (in general arbitrarily many) equally justified ΨB, which contradicts the hypothesis of a one-to-one or complete description of the real states.

(EA 22-047)

No reality condition. No Heisenberg indeterminacy. The quantum theory is incomplete simply because it assigns more than one theoretical state to what is supposed to be one and the same real physical state of affairs. And the latter assumption–that B possess one and the same real state of affairs regardless of what one chooses to measure on A–is guaranteed by nothing but the separation principle. Deny separation principle, affirm the entanglement of systems A and B, and this argument falls to the ground.(12)

Could it be that Einstein preferred this argument for incompleteness because, by avoiding reliance on Heisenberg indeterminacy, it avoided the confusion that might afflict the EPR argument and did afflict the photon box thought experiment? Whatever the reason, this is the version of the  incompleteness argument that Einstein presented in virtually all subsequent published and unpublished discussions of the problem.(13)  Einstein later noted that the separation principle is a conjunction of two logically independent assumptions, today termed separability and locality, and he presented deep philosophical premises for each. But the basic logic of Einstein’s intended incompleteness argument remained the same.

In brief, separability asserts the existence of independent real states of affairs in spatially separated regions, and locality asserts that the real state of affairs in one region of space cannot be affected super-luminally by events in another region. Locality is entailed not only by relativistic locality constraints but also by the requirement that theories be testable, for were locality not to obtain then there would be no principled way to distinguish the falsity of theory’s prediction about the outcome of a measurement from the effects of stray extraneous influences from afar. Separability is defended as a well-nigh necessary, a priori condition for the possibility of the objective individuation of physical systems (more on this below).

There was much debate in the community around Bohr about who should reply to EPR and how. Heisenberg and Wolfgang Pauli discussed the need for a “pedagogical” reply to counter the harm that might otherwise be done among physics students in the US who could be led astray by Einstein’s prestige. Heisenberg actually drafted a reply, but deferred when he heard that Bohr had written one as well.(14)

Bohr’s reply appeared in the Physical Review in October. The reply is curious in that, while Bohr focuses on the published EPR paper, Einstein’s own intended argument evidently having not yet made its way to him, he does so in a surprising way that targets directly, if not explicitly, the separability assumption that underlay Einstein’s intended argument. The problem, Bohr says, is that there is an “essential ambiguity” in the EPR reality condition. In the EPR thought experiment, the measurement on system (1) produces no classical physical disturbance of system (2), and so the antecedent in the reality condition–“if, without in any way disturbing a system”–seems to be satisfied. But there is, nonetheless, says Bohr, “an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system” (Bohr 1935, 700).

What does this mean? It means that, in choosing to measure one observable rather than another on system (1), we are choosing between different contexts or “experimental procedures” specification of which is necessary for defining “unambiguously” the “complementary classical concepts” that we might apply in describing measurements on system (2). What does this mean? And what does it have to do with separability?

Work is required to elucidate the connections in such typically Bohrian remarks.(15) Here is the short version. As Bohr said in the Como lecture, according to the quantum theory object and instrument form an entangled pair, neither can be ascribed an independent reality. It follows that we cannot speak unambiguously of the measured value of a property of the object all by itself. But in order to speak intelligibly (Bohr says “objectively”) about measurements we must be able to speak of measured values of a property of the object all by itself.

That means that we must pretend, contrary to quantum mechanical fact, that object and instrument are not entangled. Doing that is what Bohr means by a description in terms of “classical concepts.” The descriptions are “classical” simply in the sense that entanglement is denied and separability is affirmed (again, contrary to quantum mechanical fact). But we can give such “classical” descriptions only relative to the specification of a particular experimental context and then only as regards the physical properties of systems measurable in that context.(16)

Such “classical” descriptions are complementary because the contexts necessary for measuring incompatible observables like position and momentum cannot be realized simultaneously.

Demonstrating this last point–that the contexts for measuring incompatible observables cannot be realized simultaneously–was the reason for Bohr’s detailed discussion in the reply to EPR of the “realistic” version of the two-slit diffraction experiment. We can measure the vertical position of the particle traversing the apparatus if the first diaphragm, the one containing the single collimating slit, is firmly bolted to the lab bench. We can measure the particle’s momentum along the vertical axis if the first diaphragm floats suspended from a spring, allowing an inference to the particle’s momentum from the recoil momentum of the diaphragm as the particle passes through it.  But that diaphragm cannot be both bolted to the lab bench and floating freely on a spring.(17)

Here is how Bohr, himself, put many of these ideas together just three years later in what is,
for Bohr, a comparatively lucid way:

The elucidation of the paradoxes of atomic physics has disclosed the fact that the unavoidable interaction between the objects and the measuring instruments sets an absolute limit to the possibility of speaking of a behavior of atomic objects which is independent of the means of observation.

We are here faced with an epistemological problem quite new in natural philosophy, where all description of experience has so far been based on the assumption, already inherent in ordinary conventions of language, that it is possible to distinguish sharply between the behavior of objects and the means of observation.   This assumption is not only fully justified by all everyday experience but even constitutes the whole basis of classical physics. . . . As soon as we are dealing, however, with phenomena like individual atomic processes which, due to their very nature, are essentially determined by the interaction between the objects in question and the measuring instruments necessary for the definition of the experimental arrangement, we are, therefore, forced to examine more closely the question of what kind of knowledge can be obtained concerning the objects. In this respect, we must, on the one hand, realize that the aim of every physical experiment–to gain knowledge under reproducible and communicable conditions–leaves us no choice but to use everyday concepts, perhaps refined by the terminology of classical physics, not only in all accounts of the construction and manipulation of the measuring instruments but also in the description of the actual experimental results. On the other hand, it is equally important to understand that just this circumstance implies that no result of an experiment concerning a phenomenon which, in principle, lies outside the range of classical physics can be interpreted as giving information about independent properties of the objects.

(Bohr 1938, 25-26)

To return to Bohr’s reply to EPR, the issues of separability and entanglement are central.  When Bohr remarks that there is an influence on the conditions defining possible types of predictions regarding system (2), he has in mind the foregoing analysis of the role of the experimental context.  Such attention to context is required only as the means whereby to secure, in an “as if” manner, the kind of “classical” (disentangled) description of measurements required for unambiguous talk of measurement outcomes. And we are forced to this expedient of context-dependent “classical” descriptions only by the circumstance that object and instrument form, strictly speaking, an entangled pair.

Were there no entanglement, were object and instrument or the coupled systems in the EPR thought experiment separable, as Einstein assumes, then there would be no question of an influence on the conditions defining possible types of predictions regarding system (2).

Others might struggle to understand Bohr’s point. Einstein did not. Einstein saw exactly what Bohr was saying. Writing about the debate over the incompleteness of quantum mechanics fourteen years after EPR, he remarked:

Of the “orthodox” quantum theoreticians whose position I know, Niels Bohr’s seems to me to come nearest to doing justice to the problem. Translated into my own way of putting it, he argues as follows:

If the partial systems A and B form a total system which is described by its Ψ-function Ψ(AB), there is no reason why any mutually independent existence (state of reality) should be ascribed to the partial systems A and B viewed separately, not even if the partial systems are spatially separated from each other at the particular time under consideration. The assertion that, in this latter case, the real situation of B could not be (directly) influenced by any measurement taken on A is, therefore, within the framework of quantum theory, unfounded and (as the paradox shows) unacceptable.

(Einstein 1949, 681-682)

Others understood as readily as did Einstein. That is why, prodded by his correspondence with Einstein in the wake of EPR, Schrödinger set about producing, later in 1935, the series of three papers in which he coined the term “entanglement” and developed the details of the quantum mechanical interaction formalism (Schrödinger 1935a, 1935b, 1936). Schrödinger shared Einstein’s convictions about the alleged incompleteness of quantum mechanics, but that it assumed entanglement and that the latter assumption enjoyed at least indirect confirmation from the predictive successes of quantum were facts well known to the Schrödinger who first given us the formal tools for describing entanglement when he introduced wave mechanics ten years earlier.


After 1935, Einstein and Bohr returned many times to the question of the quantum theory’s
completeness and the role of entanglement in securing it.(18)

There is a certain repetitiveness in Bohr’s later rehearsals of the debate. By contrast, Einstein seemed more open to new reflections. Under the press of Bohr’s repeated critiques, Einstein dove steadily deeper in his understanding of the roots of his commitment to separability. In a 1948 article he pointed out that field theories like general relativity assume separability in the most extreme possible form, since, in effect, they regard each point of the space-time manifold as a separable physical system, endowed with its own, independent physical state in the form of, say, the value of the metric tensor at that point (Einstein 1948, 321).

He finally got to the bottom of the matter in remarks to Max Born also in 1948. The ostensible
subject is Einstein’s belief in a robust conception of physical reality. Einstein wrote:

I just want to explain what I mean when I say that we should try to hold on to physical reality. We are, to be sure, all of us aware of the situation regarding what will turn out to be the basic foundational concepts in physics: the point-mass or the particle is surely not among them; the field, in the Faraday-Maxwell sense, might be, but not with certainty. But that which we conceive as existing (“real”) should somehow be localized in time and space. That is, the real in one part of space, A, should (in theory) somehow “exist”independently of that which is thought of as real in another part of space, B. If a physical system stretches over the parts of space A and B, then what is present in B should somehow have an existence independent of what is present in A. What is actually present in B should thus not depend upon the type of measurement carried out in the part of space, A; it should also be independent of whether or not, after all, a measurement is made in A.

If one adheres to this program, then one can hardly view the quantum-theoretical description as a complete representation of the physically real. If one attempts, nevertheless, so to view it, then one must assume that the physically real in B undergoes a sudden change because of a measurement in A. My physical instincts bristle at that suggestion.  However, if one renounces the assumption that what is present in different parts of space has an independent, real existence, then I do not at all see what physics is supposed to describe. For what is thought to be a “system” is, after all, just conventional, and I do not see how one is supposed to divide up the world objectively so that one can make statements about the parts.

(Einstein to Born, March 1948, Born 1969, 223-224)

Einstein’s point seems to be that only if one adopts a “joints everywhere” view does one have the guarantee of an objective scheme for the individuation of physical systems. If any spatial separation, even an infinitesimal one, suffices to mark two systems as separable, the we can, by convention, carve up the universe any way we wish, confident in the knowledge that we have thereby objectively specified the basis of our physical ontology.

But if quantum mechanics and its descendants, like quantum field theory, are well confirmed, as they so far seem to be, then the entanglement that they take as fundamental seems likewise to be well established, which means that Einstein was wrong. But then the burden falls upon the defenders of quantum mechanics to explain how, while denying separability, quantum mechanics nevertheless rests on an objective ontological foundation.(19)

Einstein was a stubborn defender of the separability principle that he regarded as fundamental to field theories like general relativity and as necessary for our having a coherent ontological foundation for physics. Bohr was a stubborn defender of the quantum theory’s integrity, seeing in entanglement not a source of incoherence but the clue to the deep philosophical lesson of complementarity. Theirs was not a clash between a dogmatic bully and a senile old man. Theirs was a clash between two determined seekers after truth. They both knew that a deep truth was to be discovered where separability and entanglement came into conflict.

A Concluding, Personal Remark

The issues discussed in this paper were regular topics of conversation between Mara Beller and me over a period of more than fifteen years. A complete record of my intellectual debt to her would require a footnote at the end of every paragraph thanking Mara for this or that insightful point or for pressing me to seek greater clarity about this or that aspect of an argument. Let this note, instead, do the work of acknowledging that the influence of Mara’s always friendly, always constructive, while always tough-minded philosophical spirit is felt as every word makes its way to the page. I miss those conversations with Mara. I am the poorer for want of them. I am the better for having been graced by her friendship.

Reprinted with permission from Iyyun: The Jerusalem Philosophical Quarterly,Volume 56, January 2007


11. That Einstein had never intended the photon box thought experiment as an objection to indeterminacy has been overlooked in part because Jammer mistranslated the crucial clause in this letter. Where Ehrenfest says to Bohr that Einstein told him that he “had BY NO MEANS invented the ‘weighable light-flash box’ . . . ‘contra uncertainty relation’” [“Er sagte mir, daß er schon sehr lange absolut nicht mehr an die Unsicherheitsrelation zweifelt und dass er also z.B. den ‘wägbaren Lichtblitz-Kasten’ (lass ihn kurz L-W-Kasten heissen) DURCHAUS nicht ‘contra Unsicherheits-Relation’ ausgedacht hat, sondern für einen ganz anderen Zweck.”], Jammer paraphrases Ehrenfest thus: “Einstein, continued Ehrenfest in his letter to Bohr, no longer intends to use the box experiment as an argument ‘against the indeterminacy relations’ but for a completely different purpose.”  There is a major difference between saying that the photon box thought experiment “had by no means been invented” to refute indeterminacy and saying that one “no longer intends” that it be used thusly. See Jammer 1974, 171-172, and 1985, 134-135.

Fine was the first person to draw attention the fact that Einstein’s intended incompleteness argument differed in important ways from the published EPR argument, drawing attention, in particular, to Einstein’s June 19, 1935 letter to Schrödinger. See Fine 1981.

A detailed accounting of the later history is found in Howard 1985 and 1990a.

The exchange between Heisenberg and Pauli and Heisenberg’s manuscript are to be found in Pauli 1985, 402-405, 407-418.

For an attempt at such an elucidation, see again Howard 1994 and 2004.

16. A technical result underpins this conceptual point. Assume that we are concerned with observables with discrete spectra. Give me a pure entangled joint state for two interacting systems and specify a “context” in the form of a set of co-measurable joint observables. I will then write down a mixed state that reproduces for those observables (but not, in general, observables incompatible with those constituting the context) exactly the same statistical predictions as were provided by the original pure entangled joint state. Such mixed states are factorizable, allowing one to describe the situation as if object and instrument were not entangled. For details, see Howard 1994. For a generalization to observables with continuous spectra, see Halvorson 2004.

17. See Howard 1994 for details.

18. A reasonably complete survey of these later discussions will be found in Howard 1985.

19. Of course Bohmian critics of orthodox quantum mechanics argue that the solution is easy, since quantum mechanics in its Bohmian formulation is a separable theory. There are some interestingtechnical problems to be addressed in determining whether and how the notion of separability applies in the Bohmian framework. It might seem obvious that Bohmian mechanics is separable, whereas orthodox quantum mechanics is not, simply because Bohmian mechanics assumes that individual physical systems always follow well-defined, space-time trajectories. But it is not often enough noted that, for multi-particle systems, the quantum potential is non-separable. There is also the worry that Bohmian mechanics manages to be a separable theory only at the cost of relativistic non-localities at the level of the hidden variables. Opinion varies on whether this is a failing or a virtue, though there is something more like consensus about the fact that, absent control over distributions of hidden variables in an ensemble of systems, non-locality at the level of the hidden variables cannot be made manifest at the macroscopic level. For a helpful discussion of some of these questions, see Belousek 1999. For thoughts on another approach to fixing an objective quantum ontology, see Howard 1997.


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