Dialectica, 2, issue 3-4, pp.320-324 (1948)

In what follows I shall explain briefly and in an elementary way why I consider the methods of quantum mechanics fundamentally unsatisfactory. I want to say straight away, however, that I will not deny that this theory represents an important, in a certain sense even final, advance in physical knowledge. I imagine that this theory may well become a part of a subsequent one, in the same way as geometrical optics is now incorporated in wave optics: the inter-relationships will remain, but the foundation will be deepened or replaced by a more comprehensive one.

I consider a free particle described at a certain time by a spatially restricted ψ-function (completely described - in the sense of quantum mechanics). According to this, the particle possesses neither a sharply defined momentum nor a sharply defined position. In which sense shall I imagine that this representation describes a real, individual state of affairs? Two possible points of view seem to me possible and obvious and we will weigh one against the other:

(a) The (free) particle really has a definite position and a definite momentum, even if they cannot both be ascertained by measurement in the same individual case. According to this point of view, the ψ-function represents an incomplete description of the real state of affairs. This point of view is not the one physicists accept. Its acceptance would lead to an attempt to obtain a complete description of the real state of affairs as well as the incomplete one, and to discover physical laws for such a description. The theoretical framework of quantum mechanics would then be exploded.

(b) In reality the particle has neither a definite momentum nor a definite position; the description by ψ-function is in principle a complete description. The sharply-defined position of the particle, obtained by measuring the position, cannot be interpreted as the position of the particle prior to the measurement. The sharp localisation which appears as a result of the measurement is brought about only as a result of the unavoidable (but not unimportant) operation of measurement. The result of the measurement depends not only on the real particle situation but also on the nature of the measuring mechanism, which in principle is incompletely known. An analogous situation arises when the momentum or any other observable relating to the particle is being measured. This is presumably the interpretation preferred by physicists at present; and one has to admit that it alone does justice in a natural way to the empirical state of affairs expressed in Heisenberg's principle within the framework of quantum mechanics.

According to this point of view, two ψ-functions which differ in more than trivialities always describe two different real situations (for example, the particle with well-defined position and one with well-defined momentum).

The above is also valid, mutatis mutandis, to describe systems which consist of several particles. Here, too, we assume (in the sense of interpretation Ib) that the ψ-function completely describes a real state of affairs, and that two (essentially) different ψ-functions describe two different real states of affairs, even if they could lead to identical results when a complete measurement is made. If the results of the measurement tally, it is put down to the influence, partly unknown, of the measurement arrangements.

II

If one asks what, irrespective of quantum mechanics, is characteristic of the world of ideas of physics, one is first of all struck by the following: the concepts of physics relate to a real outside world, that is, ideas are established relating to things such as bodies, fields, etc., which claim a 'real existence' that is independent of the perceiving subject - ideas which, on the other hand, have been brought into as secure a relationship as possible with the sense-data. It is further characteristic of these physical objects that they are thought of as arranged in a space-time continuum. An essential aspect of this arrangement of things in physics is that they lay claim, at a certain time, to an existence independent of one another, provided these objects 'are situated in different parts of space'. Unless one makes this kind of assumption about the independence of the existence (the 'being-thus') of objects which are far apart from one another in space which stems in the first place from everyday thinking - physical thinking in the familiar sense would not be possible. It is also hard to see any way of formulating and testing the laws of physics unless one makes a clear distinction of this kind. This principle has been carried to extremes in the field theory by localizing the elementary objects on which it is based and which exist independently of each other, as well as the elementary laws which have been postulated for it, in the infinitely small (four-dimensional) elements of space.

The following idea characterizes the relative independence of objects far apart in space (A and B): external influence on A has no direct influence on B; this is known as the 'principle of contiguity', which is used consistently only in the field theory. If this axiom were to be completely abolished, the idea of the existence of (quasi-) enclosed systems, and thereby the postulation of laws which can be checked empirically in the accepted sense, would become impossible.

III

I now make the assertion that the interpretation of quantum mechanics (according to Ib) is not consistent with principle II. Let us consider a physical system S₁₂ which consists of two part-systems S₁ and S₂. These two part-systems may have been in a state of mutual physical interaction at an earlier time. We are, however, considering them at a time when this interaction is an at end.

Let the entire system be completely described in the quantum mechanical sense by a ψ-function ψ₁₂ of the coordinates q₁,... and q₂,... of the two part-systems (ψ₁₂ cannot be represented as a product of the form ψ₁ ψ₂ but only as a sum of such products). At time t let the two part-systems be separated from each other in space, in such a way that ψ₁₂ only differs from 0 when q₁,... belong to a limited part R₁ of space and q₂, ...belong to a part R₂ separated from R₁.

The ψ-functions of the single part-systems S₁ and S₂ are then unknown to begin with, that is, they do not exist at all. The methods of quantum mechanics, however, allow us to determine ψ₂ of S₂ from ψ₁₂ if a complete measurement of the part-system S₁ in the sense of quantum mechanics is also available. Instead of the original ψ₁₂ of S₁₂, one thus obtains the ψ-function ψ₂ of the part-system S₂.

But the kind of complete measurement, in the quantum theoretical sense, that is undertaken on the part system S₁, that is, which observable we are measuring, is crucial for this determination. For example, if S₁ consists of a single particle, then we have the choice of measuring either its position or its momentum components.

The resulting ψ₂ depends on this choice, so that different kinds of (statistical) predictions regarding measurements to be carried out later on S₂ are obtained, according to the choice of measurement carried out on S₁. This means, from the point of view of the interpretations of Ib, that according to the choice of complete measurement of S₁ a different real situation is being created in regard to S₂, which can be described variously by ψ₂, ψ_2', ψ_2'', etc.

Seen from the point of view of quantum mechanics alone, this does not present any difficulty. For, according to the choice of measurement to be carried out on S₁, a different real situation is created, and the necessity of having to attach two or more different ψ-functions ψ₂, ψ_2', ... to one and the same system S₁ cannot arise.

It is a different matter, however, when one tries to adhere to the principles of quantum mechanics and to principle II, i.e. the independent existence of the real state of affairs existing in two separate parts of space R₁ and R₂. For in our example the complete measurement on S₁ represents a physical operation which only affects part R₁ of space.

Such an operation, however, can have no direct influence on the physical reality in a remote part R₂ of space. It follows that every statement about S₂ which we arrive at as a result of a complete measurement of S₁ has to be valid for the system S₂, even if no measurement whatsoever is carried out on S₁. This would mean that all statements which can be deduced from the settlement of ψ₂ or ψ_2' must simultaneously be valid for S₂. This is, of course, impossible, if ψ₂, ψ_2', etc. should represent different real states of affairs for S₂, that is, one comes into conflict with the Ib interpretation of the ψ-function.

There seems to me no doubt that those physicists who regard the descriptive methods of quantum mechanics as definitive in principle would react to this line of thought in the following way: they would drop the requirement II for the independent existence of the physical reality present in different parts of space; they would be justified in pointing out that the quantum theory nowhere makes explicit use of this requirement.

I admit this, but would point out: when I consider the physical phenomena known to me, and especially those which are being so successfully encompassed by quantum mechanics, I still cannot find any fact anywhere which would make it appear likely that requirement II will have to be abandoned.

I am therefore inclined to believe that the description of quantum mechanics in the sense of Ia has to be regarded as an incomplete and indirect description of reality, to be replaced at some later date by a more complete and direct one.

At all events, one should beware, in my opinion, of committing oneself too dogmatically to the present theory in searching for a unified basis [i.e., a continuous field theory] for the whole of physics.

A. Einstein (This English translation is based on the translation in chapter X of Max Born's 1949 book The Natural Philosophy of Cause and Chance and in the 1964 Born-Einstein Letters, pp.166-170.)

This 1948 article on his view of "reality" was one of Einstein's last attempts to get Born to understand him (if not to agree with him).

Before 1948, the two scientists had jousted over Born's comments on Einstein in an essay for Einstein's Schilpp volume, Albert Einstein: Philosopher-Scientist, Born's review of Einstein's work in Born's Waynflete lectures, Natural Philosophy of Cause and Chance, and Einstein's contribution to the Born volume, Scientific Papers presented to Max Born.

As early as 1944, Einstein recognized that he and Born were completely at odds, repeating his famous remark about the "God who places dice."

We have become Antipodean in our scientific expectations. You believe in the God who plays dice, and I in complete law and order in a world which objectively exists, and which I, in a wildly speculative way, am trying to capture. I firmly believe, but I hope that someone will discover a more realistic way, or rather a more tangible basis than it has been my lot to find. Even the great initial success of the quantum theory does not make me believe in the fundamental dice-game, although I am well aware that our younger colleagues interpret this as a consequence of senility. No doubt the day will come when we will see whose instinctive attitude was the correct one.

(The Born-Einstein Letters, p.146)

In March of 1947, Einstein commented to Born on his contribution to the Schilpp volume

I cannot make a case for my attitude in physics which you would consider at all reasonable. I admit, of course, that there is a considerable amount of validity in the statistical approach which you were the first to recognise clearly as necessary given the framework of the existing formalism.

Einstein's reality is a four-dimensional space-time continuum, with none of the instantaneous "action-at-a-distance" he mistakenly thinks is part of quantum mechanics.

I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance. I am, however, not yet firmly convinced that it can really be achieved with a continuous field theory, although I have discovered a possible way of doing this which so far seems quite reasonable. The calculation difficulties are so great that I will be biting the dust long before I myself can be fully convinced of it. But I am quite convinced that someone will eventually come up with a theory whose objects, connected by laws, are not probabilities but considered facts, as used to be taken for granted until quite recently. I cannot, however, base this conviction on logical reasons, but can only produce my little finger as witness, that is, I offer no authority which would be able to command any kind of respect outside of my own hand.

(The Born-Einstein Letters, p.155)

Born used these two letters from Einstein in the final chapter of his book, Natural Philosophy of Cause and Chance. Born does not mention Einstein's central concern, the "spooky action at a distance," instead focusing on Einstein's dislike of Born's statistical interpretation and hope for a return to a continuous field theory with laws that "are not probabilities."

Metaphysical Conclusions

The statistical interpretation which I have presented in the last section is now generally accepted by physicists all over the world, with a few exceptions, amongst them a most remarkable one. As I have mentioned before, Einstein does not accept it, but still believes in and works on a return to a deterministic theory. To illustrate his opinion, let me quote passages from two letters. The first is dated 7 November 1944, and contains these lines:

'In unserer wissenschaftlichen Erwartung haben wir uns zu Antipoden entwickelt. Du glaubst an den würfelnden Gott und ich an volle Gesetzlichkeit in einer Welt von etwas objektiv Seiendem, das ich auf wild spekulativem Weg zu erhaschen suche. Ich hoffe, dass einer einen mehr realistischen Weg, bezw. eine mehr greif bare Unterlage für eine solche Auffassung finden wird, als es mir gegeben ist. Der grosse anfangliche Erfolg der Quantentheorie kann mich doch nicht zum Glauben an das fundamentale Würfelspiel bringen.'

(In our scientific expectations we have progressed towards antipodes. You believe in the dice-playing god, and I in the perfect rule of law in a world of something objectively existing which I try to catch in a wildly speculative way. I hope that somebody will find a more realistic way, or a more tangible foundation for such a conception than that which is given to me. The great initial success of quantum theory cannot convert me to believe in that fundamental game of dice.)

The second letter, which arrived just when I was writing these pages (dated 3 December 1947), contains this passage:

'Meine physikalische Haltung kann ich Dir nicht so begründen, dass Du sie irgendwie vernünftig finden würdest. Ich sehe naturlich ein, dass die principiell statistische Behandlungsweise, deren Notwendigkeit im Rahmen des bestehenden Formalismus ja zuerst von Dir klar erkannt wurde, einen bedeutenden Wahrheitsgehalt hat. Ich kann aber deshalb nicht ernsthaft daran glauben, weil die Theorie mit dem Grundsatz unvereinbar ist, dass die Physik eine Wirklichkeit in Zeit und Baum darstellen soll, ohne spukhafte Fernwirkungen.... Davon bin ich fest uberzeugt, dass man schliesslich bei einer Theorie landen wird, deren gesetzmassig verbundene Dinge nicht Wahrscheinlichkeiten, sondern gedachte Tatbestande sind, wie man es bis vor kurzem als selbstverstandlich betrachtet hat. Zur Begründung dieser Überzeugung kann ich aber nicht logische Gründe, sondern nur meinen kleinen Finger als Zeugen beibringen, also keine Autoritat, die ausserhalb meiner Haut irgendwelchen Respekt einflossen kann.'

(I cannot substantiate my attitude to physics in such a manner that you would find it in any way rational. I see of course that the statistical interpretation (the necessity of which in the frame of the existing formalism has been first clearly recognized by yourself) has a considerable content of truth. Yet I cannot seriously believe it because the theory is inconsistent with the principle that physics has to represent a reality in space and time without phantom actions over distances.... I am absolutely convinced that one will eventually arrive at a theory in which the objects connected by laws are not probabilities, but conceived facts, as one took for granted only a short time ago. However, I cannot provide logical arguments for my conviction, but can only call on my little finger as a witness, which cannot claim any authority to be respected outside my own skin.)

I have quoted these letters because I think that the opinion of the greatest living physicist, who has done more than anybody else to establish modern ideas, must not be by-passed. Einstein does not share the opinion held by most of us that there is overwhelming evidence for quantum mechanics. Yet he concedes 'initial success' and 'a considerable degree of truth'. He obviously agrees that we have at present nothing better, but he hopes that this will be achieved later, for he rejects the 'dice-playing god'. I have discussed the chances of a return to determinism and found them slight. I have tried to show that classical physics is involved in no less formidable conceptional difficulties and had eventually to incorporate chance in its system. We mortals have to play dice anyhow if we wish to deal with atomic systems. Einstein's principle of the existence of an objective real world is therefore rather academic. On the other hand, his contention that quantum theory has given up this principle is not justified, if the conception of reality is properly understood. Of this I shall say more presently.

Einstein's letters teach us impressively the fact that even an exact science like physics is based on fundamental beliefs. The words ich glaube appear repeatedly, and once they are underlined. I shall not further discuss the difference between Einstein's principles and those which I have tried to extract from the history of physics up to the present day. But I wish to collect some of the fundamental assumptions which cannot be further reduced but have to be accepted by an act of faith.

Causality is such a principle, if it is defined as the belief in the existence of mutual physical dependence of observable situations. However, all specifications of this dependence in regard to space and time (contiguity, antecedence) and to the infinite sharpness of observation (determinism) seem to me not fundamental, but consequences of the actual empirical laws.

Another metaphysical principle is incorporated in the notion of probability. It is the belief that the predictions of statistical calculations are more than an exercise of the brain, that they can be trusted in the real world. This holds just as well for ordinary probability as for the more refined mixture of probability and mechanics formulated by quantum theory.

(Natural Philosophy of Cause and Chance, p.122-124)

In March of 1948, Einstein complained to Born about errors in these quotations from his letters. Einstein sent his criticisms as marginal comments. Notice that there is no mention here of determinism.

Remark: you should not interpret the omission of marginal comments in the latter part of your article as agreement. The whole thing is rather sloppily thought out, and for this I must respectfully clip your ear. I just want to explain what I mean when I say that we should try to hold on to physical reality. We all of us have some idea of what the basic axioms in physics will turn out to be. The quantum or the particle will surely not be amongst them; the field, in Faraday's and Maxwell's sense, could possibly be, but it is not certain. But whatever we regard as existing (real) should somehow be localised in time and space. That is, the real in part of space A should (in theory) somehow 'exist' independently of what is thought of as real in space B. When a system in physics extends over the parts of space A and B, then that which exists in B should somehow exist independently of that which exists in A. That which really exists in B should therefore not depend on what kind of measurement is carried out in part of space A; it should also be independent of whether or not any measurement at all is carried out in space A. If one adheres to this programme, one can hardly consider the quantum-theoretical description as a complete representation of the physically real. If one tries to do so in spite of this, one has to assume that the physically real in B suffers a sudden change as a result of a measurement in A. My instinct for physics bristles at this. However, if one abandons the assumption that what exists in different parts of space has its own, independent, real existence, then I simply cannot see what it is that physics is meant to describe. For what is thought to be a 'system' is, after all, just a convention, and I cannot see how one could divide the world objectively in such a way that one could make statements about parts of it.

(The Born-Einstein Letters, pp.161-62)

A month later, in April 1948, Einstein sent Born the above article "Quantum Mechanics and Reality," which had been recommended by Wolfgang Pauli for publication in the new Swiss journal, Dialectica. Here is Einstein's accompanying note to Born, hoping that Born would overcome his objections enough to understand Einstein's argument (by Born's own later admissions, he perhaps never did.) For his part, Einstein never came to accept the non-separability of entangled particles, for which Born gives him the too-simple example of a beam-splitter and a stream of polarized photons. Niels Bohr reports* that Einstein had very early and frequently called attention to the case of a single photon split and then reflected back on itself to interfere. This was perhaps the earliest case of the two-slit experiment.

* "Discussions with Einstein," in Albert Einstein: Philosopher-Scientist, Schilpp, p.222

Here is Born's reply.

Dear Einstein

I am very sorry not to have replied at once to your letter of April 5th with the manuscript...I am pleased that you seem to attach some importance to my opinion. I have the feeling that I hardly deserve it. But, if you like, you shall hear what came into my mind while reading your manuscript.

Einstein himself had given a simple example of two particles leaving a center with equal and opposite velocities. Measure one and you know the other by conservation of momentum.
He did not like it

Let me begin with an example. A beam of light falls on to a plate of doubly refracting crystal, and is split into two beams. The direction of polarisation of one of the beams is determined by measurement: it is then possible to deduce that that of the second beam is perpendicular to the first. In this way one has been able to make a statement about a system in a certain part of space as a result of a measurement carried out on a system in another part of space. That this is possible depends on the knowledge that both beams have originated from one beam which has passed through a crystal; in the language of optics, that they are coherent. It seems to me that this case is closely related to your abstract example, which is apparently connected with collision theory. But it is simpler and shows that such things happen within the framework of ordinary optics. All quantum mechanics has done is to generalise it.

Born is quite right. If ψ₁₂ is separable into ψ₁ and ψ₂, the off-diagonal interference terms vanish and coherence is lost.

It seems to me that your axiom of the 'independence of spatially separated objects A and B', is not as convincing as you make out. It does not take into account the fact of coherence; objects far apart in space which have a common origin need not be independent. I believe that this cannot be denied and simply has to he accepted. Dirac has based his whole book on this. You say: The methods of quantum mechanics enable one to determine ψ₂ of S₂ from ψ₁₂ provided a complete measurement, in the quantum mechanical sense, of the spatial system S₂ exists as well. You evidently assume that ψ₁₂ is already known. Therefore a measurement in S₂ does not really give any information about events occurring in far distant S₂, but only in association with the information about ψ₁₂, that is, with the help of additional earlier measurements. In the optical example, we have the information that both partial beams are produced from one single beam by one crystal.

Your example is too abstract for me and insufficiently precise to be useful as a beginning. 'Measurement' is often loosely defined in quantum mechanics. It means either the determination of the possible eigenvalues of a quantity, or the determination of the actual state corresponding to the particular eigenvalue of a system, or, more generally, the determination of the weight | a_n | ² corresponding to the different eigenvalues n = 1,2, ... in the mixture ψ (x,y) = Σ a_n ψ_n(x). It is not clear to me what you mean by 'measurement' in your example. I would find it more convenient to consider a real collision process, in which two originally independent particles collide and are deflected. The wave functions after the collision would then correspond to your ψ₁ and ψ₂...

(The Born-Einstein Letters, pp.170-71)

Born added further remarks in the late 1960's:

The root of the difference of opinion between Einstein and me was the axiom that events which happen in different places A and B are independent of one another, in the sense that an observation of the state of affairs at B cannot teach us anything about the state of affairs at A. My argument against this assumption is taken from optics, and is based on the concept of coherence. When a beam of light is split in two by reflection, double-refraction, etc., and these two beams take different paths, one can deduce the state of one of the beams at a remote point B from an observation at point A. It is curious that Einstein did not admit this objection to his axiom as valid, although he had been one of the first theoreticians to recognize the significance of de Broglie's work on wave mechanics and had drawn our attention to it. The axiom certainly does not apply to light; but if the movement of matter can be described as 'wave motion' - and it was Einstein himself, after all, who supplied some powerful arguments for this - then the concept of coherence can be applied to beams of matter from this it follows that, as in the case of light, one can under certain circumstances draw conclusions about the state at B by determining the state at A. Einstein declared that any theory which could lead to such conclusions was incomplete. Therefore, in his eyes, the theory of light must be considered to be incomplete as well. He looked forward to the creation of a more profound theory which would do away with this state of imperfection. So far his hopes have not been realized, and physicists have good reasons for believing this to be impossible, based mainly on studies carried out by J. von Neumann.

(The Born-Einstein Letters, p.173)

Einstein replied in June 1948, perhaps somewhat hurt.

Your letter about the interpretation of the quantum theory goes into quite a lot of detail but does not keep to my logical system, so that I am unable to reply without fatiguing you with tiresome repetitions. Perhaps one day we will have that personal discussion after all. I should just like to add that I am by no means mad about the so-called classical system, but I do consider it necessary to do justice to the principle of general relativity in some way or other, for its heuristic quality is indispensable to real progress.

(The Born-Einstein Letters, p.175)

And Born commented later (1960's), after Einstein's death, and a few years after John Bell and his theorem. Bell's work made Einstein's claims about "spooky actions at a distance," nonlocality and nonseparability famous. The tests of Bell's Theorem led to Erwin Schrödinger's concept of entanglement becoming the basis of the "second revolution" in quantum mechanics, leading to today's quantum cryptography and quantum computing.

As regards Einstein's remarks about physics at the conclusion of his letter, his reproach that I had not kept to his logical system seems to me quite unjustified. He was so thoroughly convinced that his ideas were right that he could not accept any different method, while he for his part reproached me for doing the same. We had come to different philosophical points of view between which there could be no bridge. But, even so, I believe that I followed the teaching of the young Einstein, as defined by him in his obituary for Ernst Mach...

(The Born-Einstein Letters, p.175)

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