The relation between Einstein's epistemology and his critique of quantum mechanics

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The relation between Einstein’s epistemology and his critique

of quantum mechanics

Pauline Baanders

August 26, 2019

Universiteit van Amsterdam

Faculteit der Natuurwetenschappen, Wiskunde en Informatica Institute for Theoretical Physics

Bachelorproject Natuur- en Sterrenkunde (15 EC) Author: Pauline Baanders

Student ID: 10818561

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Abstract

In this paper the relation between Einstein’s epistemology and his critique of quantum mechanics will be examined. It has become a commonplace in the literature that, with the completion of his general theory of relativity, Einstein converted from Machian positivism to a kind of scientific realism (Howard 1993, p. 205; Van Dongen 2010, p.159; Ryckman 2017, p. 341). Here I will diverge from that view. Punctually following the work of Don Howard, I will show that Duhem’s holistic variety of conventionalism better suited the epistemology of Einstein. Generally, the Einstein-Podolsky-Rosen paper Can Quantum-Mechanical Description of Physical Reality be Considered a Complete? is conceived as accurately displaying Einstein’s objections to quantum mechanics (Howard 2007, pp. 57-58). This is not correct — as Einstein reveals in a letter to Schrödinger in 1935 — he did not write the EPR paper and he was dissatisfied with the way it turned out. The critique that Einstein subsequently presents to Schrödinger is remarkably simply. Ein-stein’s objection to quantum mechanics rests upon its denial of the “separation principle,” which holds that spatio-temporally separated systems possess their own, mutually inde-pendent, physical states. Einstein believed this principle was the only conceivable way to objectively divide the world into parts. I suggest that because Einstein held that any body of experience can be accounted for by different theories, the empirical successes of quantum mechanics were not enough to convince him that quantum mechanics was the right theory. He hoped to find a theory that could explain the same results and satisfy his precious “separation principle;” to wit, a unified field theory.

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1 Introduction

With the article Mach, Einstein and the Search for Reality, Holton (1968) sets down what is still the prevailing view with regard to Einstein’s epistemology; in his younger years Einstein was a Machian positivist but, with the completion of his general theory, Einstein became a kind of scientific realist (Howard 1993, p. 205; Van Dongen 2010, p. 159; Ryckman 2017, p. 341). Allegedly, the realization that the point-event ontology of general relativity was incompatible with Machian positivism, formed the motivation for Einstein’s epistemological alteration (Howard 1993, p. 208). If Einstein considerably altered his epistemology, just so that it would better fit his own work, then one might suggest that his critical attitude towards quantum mechanics was due to the fact that it was incompatible with his own work in field theories. Indeed this suggestion has been made (Van Dongen 2010, p. 183).

Section two will be dedicated to Einstein’s philosophy of science. Punctually following the Einstein scholar Don Howard I will object to Holton’s view — arguing that Einstein’s epistemology never was in harmony with Mach’s positivism nor a form of scientific real-ism. Throughout Einstein’s career, Duhem’s holistic variety of conventionalism better suited Einstein’s epistemology. A consequence of Duhem’s holism is that theory choice is under-determined by experiment, a point repeatedly made by Einstein. Moreover, in remarkable similarity to Duhem, Einstein explains the fact that in actuality theory choice seems to be determined by experiment, as the consequence of the influence of the scientific community that the researcher is part of.

Subsequently, I will consider Einstein’s critique of quantum mechanics, in section 3. With regard to Einstein’s critique there exist many misconceptions (Howard 2007, p. 58). Ein-stein’s critique is generally held to be appropriately represented in the Einstein-Podolsky-Rosen (1935) paper, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? (Howard 2007, pp. 57-58). However, it has been shown that Einstein did not write this paper himself, and that he was dissatisfied with the way the argument was set down. Einstein’s concern has not been with the Heisenberg uncertainty relation, but with the “separation principle”. The separation principle states that systems that are spatio-temporally separated possess their own, mutually independent, physical state. In field theories, where each infinitesimal part of the space-time manifold can be viewed as a separate system, this principle is utterly satisfied. Einstein ascribed great importance to this principle because, for him, it was the only objective ground for the individuation of the physical systems that physics is supposed to describe.

Finally I see the relation between Einstein’s epistemology and his persistent rejection of quantum mechanics to be that — because Einstein held there were always different theories conceivable that could accommodate for the same complex of experimental facts — Einstein never gave up on the idea that the recent successes of quantum mechanics could also be explained by a theory that did satisfy his beloved “separation principle.”

2 Einstein’s epistemological opportunism

In this section I will look into Einstein’s epistemology, both before and after the completion of general relativity in 1915. I will show that both before 1915, when Einstein was categorized as an Machian positivist, and after 1915, when he was classified as a (kind of) scientific realist,

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a kind of Duhemian holism is more central to his epistemology.

To begin with I will briefly explain these different movements, I will also discuss the stance of the neo-Kantians; they too play a substantial role in the following analysis.

Subsequently, I will discuss Einstein’s early relation with the work of Mach; showing that there has always been some tightness between Einstein’s epistemology and that of Mach. Moreover, I will place Mach’s work in its own proper historical context, from which we will see then that in Einstein’s time the difference between Mach’s positivism and Duhem’s con-ventionalism was less obvious than it is today; in their time they were seen as allies against the neo-Kantians. One might argue that, even before Einstein had become acquainted with Duhem’s work, Duhem’s epistemology has always better fitted Einstein’s epistemology than Mach’s epistemology did. In contrast with Mach, Duhem was not hostile against deep theory in physics, such as the atomic theory. In Einstein’s correspondence with Schlick, we will see Einstein’s conventionalism come most explicitly to the fore. With these remarks in the back of our mind, we unambiguously recognize Duhem’s holism in Einstein’s later asserted realism. In conclusion, we see that Duhem’s thesis of underdeterminism — that, in principle, any body of experience can be explained by a multitude of different physical theories — is central to Einstein’s epistemology.

2.1 The different epistemological movements in Einstein’s time

Immanuel Kant (1781) had in his Kritik der Reinen Vernuft (Critique of Pure Reason) held that the human intellect possesses particular constructive ordering principles. These ordering principles authorize the synthesis of different sensual impressions into a single perception. Take for example the sensual impressions of round and yellow; Kant stated that the possibility of perceiving a round, yellow object hinges upon these constructive ordering principles. Since these principles form the very possibility for experience, they must precede experience, and cannot be dependent upon it. These principles are hence called a priori. According to Kant, one of these a priori principles was the truth of Euclidean geometry. Particularly this claim led to intense debate in Einstein’s time — for his general theory of relativity employs non-Euclidean geometry.

After Kant died, his work was carried on by the neo-Kantians. After general relativity became widely acknowledged the neo-Kantians tried to reconcile Kant’s epistemology with the new theory. There have been numerous attempts to do so, the one of the philosopher Ernst Cassirer considered the most successful (Howard 1994, p. 53). Cassirer proposed that although Euclidean geometry is not a priori, there does exist a weaker topological structure that is. Evidently Euclidean geometry and Riemann geometry, the one employed by Einstein, had to have this weaker structure in common.

Mach viewed the world of experience as the most fundamental ontology; he conceived any claim about what exists beyond the world of experience as metaphysical speculation. On this basis Mach held the opinion that, ideally, physics only permits concepts that can be directly linked to experience (Howard 1993, p. 213). Consequently, each concept, and hence each proposition, bears its own empirical content.

Conventionalists in general hold that scientific theories are not correlated one-to-one with the world around us. Theories are thus not imposed on us, but rather, there is always an element of choice. For Duhem the conventional character of theories is the consequence of the fact that scientific hypotheses cannot be tested individually. Not only the hypothesis in

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question is put to the test, but also the whole of the theoretical construction that the experi-menter needs to interpret his results, the thesis of (confirmational) holism. The consequence of this thesis is that only theoretical constructs in their entirety can be endowed with empirical content. When an experiment fails to produce the expected outcome, there is a large number of changes one could make to make the theory fit the results. It’s this choice, of which part of the theory should be revised, that gives theories the status of conventions. For Duhem, theory is thus underdetermined by experiment.

Scientific realism is the view that there exist scientific theories independent of our knowl-edge of them. Scientific realism is subdivided in different branches. In direct opposition to positivism, scientific realism regards the totality of concepts in our scientific theories — whether they be observable or not — as the most fundamental ontology. Knowledge about unobservables is thus considered real. Moreover it encompasses that scientific theory are converging the “truth,” which is taken as correspondence between the theory and the “real” world.

2.2 Einstein’s appreciation of Mach

It is beyond doubt that the work of Mach had a great influence on the young Einstein. As he writes himself:

It was Ernst Mach who, in his History of Mechanics, shook this [classical mechanics as firm and final foundation of physics] dogmatic faith; this book exercised a profound influence upon me in this regard while I was a student. I see Mach’s greatness in his incorruptible skepticism and independence; in my younger years, however, Mach’s epistemological posi-tion also influenced me very greatly, a posiposi-tion which today appears to me to be essentially untenable. For he did not place in the correct light the essentially constructive and specu-lative nature of thought and more especially of scientific thought; in consequence of which he condemned theory on precisely those points where its constructive-speculative charac-ter unconcealably comes to light, as for example in the kinetic atomic theory (Einstein 1949, p. 21).

What, precisely, was it in Mach’s epistemological position that influenced the young Einstein but that he repudiated later?

Einstein’s paper on the theory of special relativity in 1905 is generally conceived as an expression of his pre-1915 adherence of Machian positivism. In the paper Einstein denied the Newtonian notions of absolute time and space, which were inextricably linked to the existence of the ether. These Newtonian notions have been emphatically criticized by Mach. However, when the context of both Einstein’s paper of special relativity and his other 1905 papers are considered, the link is less straightforward then one might expect.

This becomes apparent, already when one considers Einstein’s own motivation for rejecting the ether, as expressed in a letter to Maric Mileva:

I am more and more convinced that the electrodynamics of moving bodies as currently presented is not correct, and that it should be possible to present it in a simpler way. The introduction of the term “ether” into theories of electricity and magnetism leads to the notion of a medium of whose motion one can speak without, I believe, being able to associate any physical meaning with such a statement (Einstein 1899 cited in Ryckman 2017, p. 180).

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What is notable here is the relation between the repudiation of the ether and the arbitrariness of the relative motion of electrodynamic bodies. What Einstein means by this, is that the laws of physics should be indifferent with regard to whether a current is induced by a magnetic field, or conversely, that the current induces the magnetic field. Now the important question with respect to Mach is, is whether the notions “current” and, even more so, “field” can really be seen as Machian “elements of sensation;” i.e., whether the chains of thoughts that connect these concepts to their directly observable properties are really as succinct as is generally demanded by Mach and his direct followers.

That the delineation of what might count as an experimental fact is for Einstein more liberate than for Mach is also acknowledged by Holton (Van Dongen 2010, p. 39). However, the question is whether this difference is really a matter of degree; it’s in fact Einstein himself who draws in 1917 — in a letter to Moritz Schlick (discussed below) — a clear, qualitative, distinction between Machian “elements” and what he would call “events.”

As suggested by the letter above Einstein’s own motivation for rejecting the ether was not that it could not be directly observed, but rather that it was a concept devoid of physical meaning. His aim was to show that the ether was a superfluous concept, rather than to prove that it didn’t exist. This is also emphasized by Einstein in the opening of his special relativity paper:

It is known that Maxwell’s electrodynamics—as usually understood at the present time— when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion (Einstein 1905, p. 891).

In 1905 Einstein also published three articles concerning the existence of atoms. Ludwig Boltzmann was of great influence in these works (Ryckman 2017, p. 4). Boltzmann was an ardent defender of the reality of atoms, diametrically opposed to, among others, Mach. How can one assemble the fact that Einstein conforms to such rivaling views? Is this to be explained as an expression of epistemological opportunism, or does this elucidate something about his adherence to Mach? When one considers the above mentioned underlying motivation that Einstein rejected the ether one may argue for the latter.

Einstein certainly aims to provide evidence for the reality of atoms. However, the influence of Mach is being felt; Einstein does not grant atoms more properties than needed for him to explain the empirical evidence. So, in Einstein’s early papers on statistical mechanics his atomic theory boils down to the assumption that the system under consideration holds a finite number of degrees of freedom (Howard 1993, p. 211). Both Einstein and Mach are against metaphysical speculation in physics, but — for Einstein, in opposition to Mach — this does not mean that every concept has to be directly linked to experience.

When Einstein’s earlier works are taken together, one might argue that what Einstein shared with Mach, was not so much the opposition against deep theory but, rather, a discontent for speculation that was not empirically grounded. From this perspective an elucidating connection between the work of Mach and Duhem can be uncovered; a linkage that for the contemporaries of Einstein was more clear than for us today. The reason is that Mach, after the establishment of the logical empiricists, is too often read as its antecedent, with the

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consequence that Mach’s opposition against metaphysical speculation is concealed with his phenomenalism (Howard 1993, p. 212).

The influence Duhem had on Einstein has long been unrecognized (Howard 1990, p. 363). In 1909, Einstein came across the work of Duhem via his new neighbour, Friedrich Adler. Adler and Einstein were often engaged in "questions whose place is generally not understood by the majority of other physicists” (Ardelt 1984 cited in Howard 1990, p. 3t67), as Adler would put it in a letter to his parents. Adler had just translated — partly on insistence of Mach — Duhem’s work La Theoriè Physique to German. In the preface to this work Adler emphasizes Duhem’s holism.

Contemporaries, and supposedly Mach himself, perceived the difference between Duhem and Mach as a matter of degree (Howard 1993, p. 212). For Mach a concept that is not directly linked to experience, is conceived as metaphysical speculation. For Duhem demarcation is more liberate; only the totality of concepts has to be linked to experience, for only the totality of concepts is put to the test.

Now an interesting link can be made to Einstein’s obituary of Mach, in 1916, and the declaration that he “came to realize” that Mach’s epistemological position is not tenable. In particular it may be suggested that Einstein’s turning away from Mach is not to be conceived as a turning away from the views that Einstein, himself, held earlier.

Let’s consider what Einstein says in his obituary:

Concepts that have proven useful in ordering things easily achieve such an authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they come to be stamped as “necessities of thought,” “a priori givens,” etc. The path of scientific advance is often made impassable for a long time through such errors. For that reason, it is by no means an idle game if we become practiced in analyzing the long commonplace concepts and exhibiting those circumstances upon which their justification and usefulness depend, how they have grown up, individually, out of the givens of experience. By this means, their all-too-great authority will be broken. They will be removed if they cannot be properly legitimated, corrected if their correlation with given things be far too superfluous, replaced by others if a new system can be established that we prefer for whatever reason (Einstein 1916 cited in Howard 1993, p. 215).

It can be seen that this appraisal contains hardly any epistemological content. With respect to the justification of concepts Einstein is not very specific; he refers to “properly” legitimated and not “ far too superfluous.” The explicit reference to “a priori givens,” is to be seen as a direct opposition against the (neo-)Kantian epistemology. Indeed the opposition of Duhem and Mach against metaphysical speculation was, for their contemporaries, widely conceived as an opposition against the neo-Kantians. The least one can say is that there is no emphasis on the points that distinguishes Mach from Duhem.

That in effect it might even fit better the work of Duhem is apparent when we consider Mach’s own description of Duhem’s main thesis:

The author shows how physical theory gradually transforms itself from a presumptive explanation on the basis of a vulgar or more or less scientific metaphysics into a system resting on a few principles, a system of mathematical propositions that economically describe and classify our experiences. In this process the explanatory picture changes many times, until finally it falls away entirely [..] Duhem regards the model, like the picture, as a parasitic growth (Mach 1908 cited in Howard 1990, p. 364).

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What Mach stresses here is Duhem’s emphasis on how concepts arise, genetically. This is exactly what is stressed by Einstein in his obituary to Mach. Mach’s emphasizes that is focused on the justification of concepts, on the other hand, is only of secondary importance in Einstein’s obituary. Moreover it seems that Einstein is not very concerned about this, at least not in a Machian sense, that focuses on justification of the individual concepts.

Now, of course we can say that Einstein was an ardent adherent of Mach. In fact even Einstein affirms it. However, when we consider the content of both his contributions to physics and his epistemological expressions, we may come to another conclusion. Undoubtedly Einstein was influenced by Mach; in fact, it’s highly unlikely that Einstein even knew the work of Duhem in 1905 (Howard 1990, p. 368). Notwithstanding we may say, his 1905 papers and obituary to Mach considered, that actually the philosophy of Duhem had been the better fit all along.

Unlike Mach, Einstein had never been concerned with the justification of individual con-cepts — a point that is quite crucial to Mach’s positivism. More than that, Einstein had been a champion of the atomic theory that had been so keenly opposed by Mach. For Duhem only theories in its entirety can be related to experience, hence Duhem does not pose any constraint on the concepts to be used in physical theories. In later remarks we will see that Einstein also adheres explicitly to this point of Duhem.

2.3 Einstein’s conventionalism in his correspondence with Schlick

From 1915 to approximately 1921 the philosopher and physicist Moritz Schlick and Einstein had regular contact (Howard 1993, p. 220). After that period, their philosophical views grew apart, and their contact watered-down. While in 1915 we recognize Duhemian holism in Schlick’s work, in 1917 we see the first signs of the logical empiricism, that Schlick is to be the founder of. From Einstein’s response to this work, we see that what is driving a wedge between him and Schlick, is the way in which they conceive empirically-equivalent theories are related.

In 1915 Schlick’s aim was to jettison, especially neo-Kantian and positivist, misinterpre-tations of relativity that sought in relativity a vindication of their own program. Schlick gave some unprejudiced epistemological implications himself. What Schlick displays in his 1915 essay is indeed an original synthesis of both realistic and conventional characteristics. He writes:

The totality of our scientific propositions, in word and formula, is in fact nothing else but a system of symbols correlated to the facts of reality; and that is equally certain, whether we declare reality to be a transcendent being or merely the totality and interconnection of the immediately “given.” The system of symbols is called “true” however, if the correlation is completely unambiguous [eindeutig ]. Certain features of this symbol system are left to our arbitrary choice; we can select them in this way or that without damaging the unambiguous character [Eindeutigkeit ] of the correlation. It is therefore no contradiction, but lies, rather, in the nature of the matter, that under certain circumstances, several theories may be true at the same time, in that they achieve indeed a different, but each for itself completely unambiguous designation of the facts (Schlick 1916 cited in Howard 1984, p. 617).

Einstein received Schlick’s essay on 13 December 1915, and he was avid about it, as we can tell from his reply (Howard 1984, p. 618). Einstein liked in particular Schlick’s independent

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view. Also Einstein had high esteem of the opposition against the neo-Kantians and positivists. He begins his letter thus:

Yesterday I received your essay and I have already studied it through completely. It is among the best that have until now been written about relativity. From the philosophical side, nothing appears to have been written on the subject that is at all so clear (EA 21-610 cited in Howard 1984, p. 618).

Later in the letter Einstein compliments Schlick on his analysis of the neo-Kantians and positivists.

In Schlick’s later work, Raum und Zeit in den gegenwärtigen Physik (1917) we read:

It is, however, possible to indicate identically the same set of facts by means of various systems of judgments; and consequently there can be various theories to which the cri-terion of truth applies in the same say, and which then do justice in equal measure to the observed facts and lead to the same predictions. They are just different systems of symbols that are correlated to the same objective reality, different modes of expression that reproduce the same set of facts (Schlick 1917 cited in Howard 1984, p. 617).

It seems that in his essay of 1915, Schlick has not yet formulated how empirically-equivalent theories are related to each other. Here Schlick suggests that they are “different modes of expression.” Empirically-equivalent theories not only reproduce the same set of facts; accord-ing to Schlick, they also “lead to the same predictions.” This implies that such theories are not that different after all, something like linguistically invariants, much like the difference between English and German.

Einstein is again enthusiast about Schlick’s work; but it’s exactly on this one point — on how empirically-equivalent theories are related — that Einstein has a suggestion:

The second point to which I want to refer concerns the reality concept. Your view stands opposed to Mach’s according to the following schema:

Mach: Only impressions are real.

Schlick: Impressions and events (of a phys[ical] nature) are real.

Now it appears to me that the word “real” is taken in different senses, according to whether impressions or events, that is to say, states of affairs in the physical sense, are spoken of. If two different peoples pursue physics independently of one another, they will create systems that certainly agree as regards the impressions (“elements” in Mach’s sense). The mental constructions that the two devise for connecting these “elemenents” can be vastly different. And the two constructions need not agree as regards the “events”; for these surely belong to the conceptual constructions. Certainly only the “elements,” but not the “events,” are real in the sense of being “given unavoidably in experience.”

But if we designate as “real” that which we arrange in the space-time-schema, as you have done in the theory of knowledge, then without doubt the “events,” above all, are real. Now what we designate as “real” in physics is, no doubt, the “spatio-temporally-arranged,” not the “immediately-given.” The immediately-given can be and illusion, the spatio-temporally arranged can be a sterile concept that does not contribute to illuminating the connections between the immediately-given. I would like to recommend a clean conceptual distinction here (EA 21-618 cited in Howard 1984, pp. 219-220).

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Here Einstein’s explains his concept of reality, in lucid terms. The two senses of the word “real” that Schlick does not distinguish is the real in the sense of the immediately given, as opposed to the spatio-temporally-arranged, which is designated as the real in physics. Empirically-equivalent theories certainly describe the same reality taken in the first sense, but not with respect to the second. The physical real, as opposed to the experienced real, arises from a framework that aims to connect the immediately-given. Empirically-equivalent may very well construct a different physical reality, and can thus hardly be seen as “different modes of expression.” It’s a clear form of conventionalism that Einstein displays here, and it’s very similar to later remarks, as we will see below.

What is driving a wedge between Schlick and Einstein, is the way in which they conceive the relation between empirically-equivalent theories. It is suggested, considering both Schlick’s work and Einstein’s reply, that Schlick perceives them as different systems of relations, that ultimately relate the same things — indeed, as different modes of expression to relate the perceived reality (Einstein’s “immediately-given”) to ultimately a singular, deeper, underly-ing reality (Einstein’s “spatio-temporally-arranged”). For Einstein, in rather sharp contrast, physics connects the immediately given and, thereby, designates the physical real. This is exactly the point on which Einstein and Schlick are drifting apart.

2.4 Einstein’s realism in his later realistic remarks

As mentioned above, in his later years Einstein is said to have embraced a form of scientific realism. I will not consider this claim in full depth but I will analyze Einstein’s remarks in his Planck tribute and in his Oxford lecture — which are often referred to in order to substantiate Einstein’s realism (Howard 1993, p. 226) — and show in what way his holistic conventionalism also comes clearly to the light on these occasions.1

On the occasion of Planck’s sixtieth birthday, Einstein speaks as follows:

The supreme task of the physicist is... the search for those most general, elementary laws from which the world picture is to be obtained through pure deduction. No logical path leads to these elementary laws; it is instead just the intuition that rests on an empathic understanding of experience. In this state of methodological uncertainty one can think that arbitrarily many, in themselves equally justified systems of theoretical principles were possible; and this opinion is, in principle, certainly correct. But the development of physics has shown that of all the conceivable theoretical constructions a single one has, at any given time, proved itself unconditionally superior to all the others. No one who has really gone deeply into the subject will deny that, in practice, the world of perceptions determines the theoretical system unambiguously, even though no logical path leads from the perceptions to the basic principles of the theory (Einstein 1918 cited in Howard 1993, pp. 226-227).

Crucially for his expression of realism here is that “the world of perceptions determines the theoretical system unambiguously.” Indeed this sentence could be conceived as a form of realism, and maybe even Platonism. However, when we look to the context of this sentence we can see that this reading is not quite correct. Einstein is saying that although the path from experience to the elementary laws is uncertain — in principle there is more than one path — one theory, that belongs to one of the many paths, “has, at any given time, proved

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itself unconditionally superior to all the others.” From the context one sees that it’s abso-lutely not straightforward that the superiority of this one theory is due to it being in better correspondence with the “reality;” as a realist would argue. But then, what makes that at any given time, one theory is superior? When we assimilate Einstein’s reply to Schlick and his Planck address, the work of Duhem is elucidating.

In 1917 Einstein wrote to Schlick that the mental constructions, which two people devise for connecting the sense impressions, can be vastly different — if they pursue physics inde-pendently of one another. When we consider that in actual fact there is always one mental construction that is superior to the others we may suggest that, in actual fact, no two people pursue physics independent of one another. In other words, the determination of the theo-retical system is strongly related to historical and sociological factors that characterize the community that the two people belong to.

In the Planck address, Einstein says it’s “the intuition that rests on an empathic under-standing of experience,” that is key factor to underunder-standing the determination of the theoretical system. But then, what have sociological and historical factors of the scientific community to do with the intuition of the researcher? Indeed, when the question is put this way, the answer suggests itself.

That Einstein would agree that these two are indeed inextricably linked up, is evident in his Oxford lecture of 1933, he writes:

Of course his [of a man who spent his life in striving for the unification of knowledge] view of the past and present history of his subject is likely to be unduly influenced by what he expects from the future and what he is trying to realize to-day. But this is the common fate of all who have adopted a world of ideas as their dwelling-place.

He is just in the same plight as the historian, who also, even though unconsciously, disposes events of the past around ideals that he has formed about human society (Einstein 1933, p. 164).

In Duhem’s La Theoriè Physique the idea that the scientific community has a great influ-ence on the scientific theories it produces, is comprehensibly formulated:

Contemplation of a set of experimental laws does not, therefore, suffice to suggest to the physicist what hypotheses he should choose in order to give a theoretical representation of these laws; it is also necessary that the thought habitual with those among whom he lives and the tendencies impressed on his own mind by his previous studies come and guide him, and restrict the excessively great latitude left to his choice by the rules of logic [..] Logic leaves the physicist who would make a choice of a hypothesis with a freedom that is almost absolute; but this absence of any guide or rule cannot embarrass him, for, in fact, the physicist does not choose the hypothesis on which he will base a theory; he does not choose it any more than a flower chooses the grain of pollen which will fertilize it [..] the physicist is limited to opening his thought through attention and reflection to the idea which is take seed in him without him (Duhem 1906 cited in Howard 1990, pp. 379-380.

Both Einstein and Duhem contrasted the apparent paradox that although theory choice is underdetermined by experimental facts, in practice it appears that theory choice is determined. We further see that this contrast is explained by Duhem, by the fact that the researcher is part of a particular scientific community — in striking similarity with Einstein’s utterances.

Precisely on the basis of this remarkable similarity it is suggested that Einstein’s illustrious “free creations of the human mind” can also be elucidated with Duhem’s flower-seed parable.

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“Free” should be taken to mean “not necessarily the way it is;” after all, the flower could have been fertilized by another seed. Of course theories are created by human minds, but that is not how “creations of the human mind” is to be read on the basis of Duhem. What is crucial is the fact, that on the basis of logic, theory choice is not determined; but then, it follows, there is not a one-to-one correspondence between experience and theory. The human mind is not discovering a link between experience and an underlying ontology, it is creating one. Remember, this is just the nub of what Einstein had pointed out to Schlick in response to Schlick’s Raum und Zeit in den gegenwärtigen Physik of 1917.

It’s clear that Duhem’s holistic variant of conventionalism has substantially influenced Einstein. In Einstein’s early years — when Einstein is considered, also by himself, to be an ardent follower of Mach — his atomic theory shows that, while Einstein had a disdain for metaphysical speculation, he had nothing against deep theory. What really appealed to Ein-stein was not Mach’s positivism, but more generally, Mach’s opposition against metaphysical speculation. In their time, Duhem and Mach were seen as allies in their opposition against empirically ungrounded speculation. However, Duhem’s holism is more accommodating to deep theory; for him only the theory in its whole has to be related to experience. Particular Einstein’s atomic theory of 1905 showed that his epistemology conflicts with that of Mach, and that Duhem’s epistemology would actually have been a better fit.

In his later years — when Einstein was supposedly becoming a realist — we see that Einstein distinctly asserts that although theory choice seems to be determined on the grounds of empirical evidence, in principle, it is not. In principle there are arbitrarily many theories conceivable that join together the same empirical evidence — a thesis diametrically opposed to scientific realism, but remarkably similar to Duhem’s holism.

3 Einstein’s critique of quantum mechanics

For a long time the standard narrative concerning Einstein’s critique of quantum mechanics has been that, from the years 1927 to 1930, he began with inventing thought experiments that violated the Heisenberg uncertainty relations — with Bohr finding fault in each. One such ex-periment would be the photon-box thought exex-periment, which Einstein presented at the Solvay meeting of 1930. After 1930 Einstein supposedly shifted his attention to arguing that quan-tum mechanics was not incorrect but incomplete. When the famous Einstein-Podolsky-Rosen (EPR) paper — that is generally conceived as correctly representing Einstein’s objections — was met by a devastating reply from Bohr, Bohr was seen as the victor and Einstein’s critique was put away as the complaint of an old stubborn man (Howard 2007, pp. 57-58).

That this narrative is seriously flawed became apparent when Fine, in 1981, discovered a letter Einstein wrote to Schrödinger in which he reveals that he had not written EPR, and that he was dissatisfied with the way it turned out (Howard 2007, p. 58). Moreover the photon-box presented at the Solvay meeting of 1930 is best known from Bohr’s (1949) contribution to Albert Einstein: Philosopher-Scientist, but Bohr’s account contradicts contemporary documentary material (Howard 2007, p. 73). Contrary to Bohr’s exposition, Einstein had not intended the photon-box thought experiment to violate the Heisenberg uncertainty principle.

In this section I will discuss the photon-box thought experiment, the EPR paper, and Einstein’s reply to Schrödinger’s letter, in which Einstein reveals that he had not written EPR. We will see that Einstein’s own argument differs from the argument in the EPR paper

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in three fundamental ways (1) Einstein’s own argument makes no reference to the Heisenberg uncertainty principle, (2) in his own argument Einstein does not make (either explicitly or implicitly) any assertion about the epistemological nature of measurement; in EPR the “cri-terion of physical reality” implicitly invokes such a commitment, and (3) the logical structure of Einstein’s own argument differs fundamentally from that in EPR; Einstein’s own argument indirectly proves, whereas the EPR paper directly proves, the incompleteness of quantum mechanics. We will see that Einstein’s own argument rests upon the “separation principle,” which asserts that two systems that are spatio-temporal separated possess their own, mutual independent, physical real state. At the end of the section I will touch upon why Einstein was under the impression that this principle was so fundamental to physical theory.

3.1 Quantum mechanics formalism

To understand the arguments presented here little technical knowledge of quantum mechanics is required. However, as the history has shown, it’s important to have some fundamentals clearly distinguished.

In quantum mechanics the state of a system is represented by the wave function, generally labeled Ψ. According to quantum mechanics we cannot simultaneously measure observables that are incompatible. In particular, and that is what concerns us now, position and mo-mentum are incompatible observables. Given a wave function Ψ one can either expand it in eigenstates, each with a corresponding eigenvalue i.e. possible measurement outcome, of the momentum operator; or expand it in eigenstates of the position operator. What it means for operators to be incompatible is precisely that they do not share a common set of eigen-states, or in more familiar language, they do not share the same set of possible measurement outcomes. Moreover, quantum mechanics asserts that the very act of measurement forces the wave function into one of the eigenstates of the observable we measure, a process today known as the collapse of the wave function.

The incompatibility of the position and momentum operator, and the collapse of the wave function are the more general features of quantum mechanics from which the Heisenberg principle can be derived. It’s also important to note, that when the incompleteness of quantum mechanics is considered, the usage of the word “state” is not unambiguous. In fact the usage of the word “state” begs the question of incompleteness; for when quantum mechanics is incomplete we may distinguish the “real state” of affairs, as opposed to the “physical state” that quantum mechanics ascribes to it.

3.2 Einstein’s photon-box thought experiment of 1930

As mentioned above the photon-box thought experiment is described by Bohr (1949) in his contribution to Albert Einstein: Philosopher-Scientist. However, a letter that Ehrenfest wrote to Bohr shows that Bohr does not present the thought experiment in the way that Einstein had intended it. In this section I will discuss the general idea of the photon-box, the way Bohr has presented it, and how Einstein had intended the thought experiment, as Ehrenfest explained it in his letter to Bohr (Howard 2007, p. 75).

In short, Bohr tells us that Einstein intended to violate the Heisenberg uncertainty prin-ciple and that Ehrenfest had told him that Einstein had discerned new aspects regarding the thought experiment, which Bohr subsequently presents in an obscure way (Howard 2007,

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p. 75). The letter from Ehrenfest shows us that Ehrenfest had written to Bohr something else; that Einstein had never intended the photon-box thought experiment as to violate the Heisenberg uncertainty principle (Howard 2007, p. 75). In his letter Ehrenfest explains that Einstein had intended the thought experiment to show that in quantum mechanics one real state can be correlated to two different physical states, and Einstein thus concludes that quantum mechanics is incomplete.

The idea of the photon-box thought experiment starts out with a box equipped with a switch in the wall, through which a photon can be emitted (Figure 1). The photon is reflected over a great distance, say a fraction of a light year, and is absorbed by the box at its return. At the moment the photon is released a timer, attached to a clock, is activated which makes it possible to accurately determine the time of emission (Howard 2007, p. 74). The box is suspended in a spring balance which enables us to measure, with arbitrary precision, the mass of the box before and after the emission of the photon, and thus the mass of the photon. By invoking the mass-energy equivalence principle, E = mc2, this enables us to accurately determine the energy of the photon.

Figure 1: Visualization of the photon-box thought experiment. The timer attached to the clock is activated when the photon is emitted, which makes an accurate measurement of the time of emission possible. The spring balance enables us (indirectly) to measure the mass of the photon, and hence its energy (Bohr 1949, p. 227, Figure 8).

In Bohr’s account of the photon-box thought experiment we read:

If, in the beginning, the box contained a certain amount of radiation and the clock was set to open the shutter for a very short interval at a chosen time, it could be achieved that a single photon was released through the hole at a moment known with as great accuracy as desired. Moreover, it would apparently also be possible, by weighing the whole box before and after this event, to measure the energy of the photon with any accuracy wanted, in

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definite contradiction to the reciprocal indeterminacy of time and energy quantities in quantum mechanics (Bohr 1949, pp. 225-226).

Bohr’s description of Einstein’s intention with the photon-box is quite clear; yet another attempt of Einstein to violate the Heisenberg uncertainty principle. Bohr’s memoir continues by explaining that, although at first he was struck by Einstein’s argument, he soon realized that Einstein was wrong. Ironically, it’s general relativity that saves Bohr. When the photon is emitted, the mass of the box changes, with the result that the box moves vertically in the gravitational field of the earth. This vertical movement in the gravitational field of the earth induces a change in the rate of the clock that guarantees satisfaction of the Heisenberg uncertainty principle (Bohr 1949, pp. 227-228).

Subsequently Bohr tells us about Ehrenfest’s letter:

but shortly before his [Ehrenfest’s] deeply deplored death in 1933 he told me that Einstein was far from satisfied and with his usual acuteness had discerned new aspects of the situation (Bohr 1949, p. 228).

A letter that dates from 1931 suggests that Ehrenfest told Bohr something else:

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 “weigh-able 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 cited in Howard 2007, p. 75).2

Bohr’s account is fundamentally different from what Ehrenfest writes in his letter. Moreover, if Bohr is referring to something else than this letter, when this letter is considered it is very plausible to suggest that Bohr must have misunderstood Ehrenfest — much like he had earlier misunderstood Einstein’s intention with the photon-box thought experiment.

Bohr continues by displaying Einstein’s “discerned new aspects of the situation," we read:

Without in any way interfering with the photon between its escape and its later inter-action with other suitable measuring instruments, we are, thus, able to make accurate predictions pertaining either to the moment of its arrival or to the amount of energy liberated by its absorption. Since, however, according to the quantum-mechanical formal-ism, the specification of the state of an isolated particle cannot involve both a well-defined connection with the time scale and an accurate fixation of the energy, it might thus ap-pear as if this formalism did not offer the means of an adequate description (Bohr 1949, p. 229).

Bohr presents the argument here as if the fact that we can “make accurate predictions pertain-ing either to the moment of its arrival or to the amount of energy liberated by its absorption," together with the Heisenberg uncertainty principle, forces Einstein’s conclusion — that quan-tum mechanics is incomplete. Bohr misses, again, Einstein’s crucial point. In the way Bohr tells the story, it is suggested that Einstein here implicitly invokes the “criterion of physi-cal reality” of the EPR paper, which will be discussed below. This criterion was considered 2_{In Jammer (1974) the key passage of this letter’s translation is flawed. Jammer translates "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.” Howard (2007, p. 75) suggest that this has significantly contributed to the situation that it has been overlooked for so long, that Einstein’s photon-box was never intended to exhibit a violation of the Heisenberg uncertainty relations.

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very problematical by critics; and Bohr now makes Einstein’s photon-box thought experiment susceptible to the same criticism.

As Ehrenfest had explained later in the above mentioned letter to Bohr, what was crucial for Einstein was the assertion that, since the measurement on the box was made when the photon was spatially separated, the measurement could not possibly affect the real state of the photon (Howard 2007, p. 75). This point is in no way treated in Bohr’s account; clearly Bohr must have missed the crux of Einstein’s photon-box thought experiment.

Einstein’s fundamental assertion was that the measurement of the box could not influence the real state of the spatially separated photon. Meaning that the real state of the photon, when it returns, is the same — independent of the measurement that is made on the box. However, whether we choose to check the clock or measure the weight of the box after emission, quantum mechanics ascribes two different physical states to the returned photon. By checking the clock we could accurately predict the moment of arrival, and the physical state of the returned photon would be in an eigenstate of the position operator. When, instead, we weigh we can predict the energy of the photon; in which case the physical state of the returned photon would be in an eigenstate of the energy operator or Hamiltonian.

The situation, then, is that there are two different descriptions, or physical states, corre-lated to one real state. When we have two different descriptions for one and the same thing, it follows that these descriptions are incomplete. For, if the descriptions entail everything there is to know about the thing they describe, they would be the same. It’s this consequence — that there are two different physical states correlated to one real state — that is quintessence of the photon-box thought experiment; it’s the reason why Einstein concludes that quantum mechanics is incomplete, and it turns upon his separation principle.

As we will see in the next section, the argument of the photon-box thought experiment differs fundamentally from the argument that is presented in the EPR paper. But, remem-ber, the EPR paper was not written by Einstein himself. This is revealed in the letter to Schrödinger; and the argument Einstein presents there is, in fact, very similar to the argu-ment in the photon-box thought experiargu-ment. In 1930 Einstein supposes, without further ado, that the real state of the photon is not effected by the measurement of the spatially sepa-rated box. In 1935, in the letter to Schrödinger, he poses this supposition as the “separation principle," but his argument has not changed.

3.3 The EPR paper of 1935

The reassessment of the Bohr-Einstein debate started with Fine’s discovery, in 1981, of a letter Einstein wrote to Schrödinger (Howard 2007, p. 78). In the letter Einstein reveals that he had not written the EPR paper himself, and that he was dissatisfied about the way it turned out. Subsequently he presents Schrödinger his own argument for the incompleteness of quantum mechanics. In this section I will discuss the argument of the EPR paper and compare it to Einstein’s own argument, as he had put it in the letter to Schrödinger.

However unfortunate, Einstein’s critique of quantum mechanics is best known from the Einstein-Podolsky-Rosen paper published in 1935. By means of a thought experiment the paper is supposed to directly prove the incompleteness of quantum mechanics; a necessary condition for completeness is posed and it’s shown that this condition is not satisfied in the special case under consideration.

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every element of the physical reality must have a counterpart in the physical theory (Einstein, Podolsky & Rosen cited in Howard 1985, p. 174).

However in order to invoke this condition it must be clear what is meant by “physical reality.” EPR thus poses the notorious and highly controversial “criterion for physical reality:”

If, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity (Einstein, Podolsky & Rosen 1935 cited in Howard 1985, p. 174).

Now the thought experiment runs as follows. Let the real state of affairs be two spatially separated particles whose physical states have become correlated through interaction. Suppose we could perform one of two measurements on system 1; we could either measure its position or momentum. When we would measure the position of system 1 we could, with certainty, the position of system 2. In the case we measure the momentum of system 1 we are able to predict the momentum of system 2. When the systems are far enough apart, the measurement on system 1 can be done without disturbing system 2, so that the premise of the criterion for physical reality is satisfied. Thus, by invoking the criterion, we can conclude that there exist elements of physical reality pertaining to the position and momentum of system 2. At this point the Heisenberg uncertainty principle is invoked; quantum mechanics does not have counterparts corresponding to both elements of physical reality, i.e., quantum mechanics prohibits for system 2 to have both a well-defined position and a well-defined momentum. Thereby it’s shown that the condition of completeness is not satisfied. Consequently, quantum mechanics is dubbed incomplete.

The argument in EPR is not solid. What is considered especially problematic is the inter-ference, from the possibility of measuring either the position or the momentum of system 1, to the simultaneous existence of elements of physical reality corresponding to the position and momentum of system 2.3 To vindicate this interference additional assumptions are required, and they are not to be found in the EPR paper. But Einstein’s own opinion of the EPR paper was not good either; his own argument is more considerate and not in need for extra assumptions.

The EPR paper was published on 15 May 1935. On June 7 Schrödinger wrote Einstein a detailed letter concerning the paper, in which we read:

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 (Schrödinger to Einstein, 7 June 1935 cited in Howard 1985, p. 175).

On 19 June Einstein replied, and his letter opens with an unexpected remark:

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 (Einstein to Schrödinger, 19 June 1935 cited in Howard 1985, p. 175).

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As we have seen above, in the way that it is presented by Bohr, it seems that Einstein is making precisely this interference in his photon-box thought experiment.

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Einstein didn’t write the paper and he was of the opinion that the main point was “buried by the erudition." Well then, what is the main point, according to Einstein? The remainder of Einstein’s reply is devoted to answering this question.

Einstein begins by sketching a non quantum mechanical thought experiment (Howard 1985, p. 178). He considers two boxes, one of which has a ball in it. By opening one of the boxes we “measure” in which box the ball is. Einstein now poses the question whether the state description — “The probability of the ball being in the first box is 1₂” — is complete. He distinguishes three attitudes towards this question; “Born’s”, “Schrödinger’s” and that of the “talmudist.” 4

A follower of the “Born” interpretation would answer the question with “No;” a complete description of the state of the first box would be either that the ball is in the box, or that it is not. “Schrödinger,” on the other hand, would answer the question with “Yes;” before the measurement the ball is not really in one of the two boxes, it’s the observation that forces the ball in one of the two boxes. The “talmudist,” Einstein says:

doesn’t give a hoot for ‘reality’, which he regards as a hobgoblin of the naive, and he declares that the two points of view differ only as to their mode of expression (Einstein to Schrödinger, 19 June 1935 cited in Howard 1985, p. 178).

What is Einstein’s own attitude? He says:

My way of thinking is now this: properly considered, one cannot get at the talmudist if one does not make use of a supplementary principle: the ‘separation principle’. That is to say: ‘the second box, along with everything having to do with its contents, is independent of what happens with regard to the fist box (separated partial systems).’ If one adheres to the separation principle, then one thereby excludes the second (‘Schrödinger’) point of view, and only the Born point of view remains, according to which the above state description is an incomplete description of reality, or of the real states (Einstein to Schrödinger, 19 June 1935 cited in Howard 1985, pp. 177-178).

Here we see just how essential the ‘separation principle’ is to Einstein’s argument. Without the principle the very question of completeness is devoid of meaning; the two stances can be seen as different modes of expression, i.e., there is no actual difference. Stick to the ‘separation principle’ and the conclusion is fixed; we must conclude the description to be incomplete.

Einstein continues by revisiting the EPR thought experiment. Instead of system 1 and 2, Einstein now talks of system A and B. Now, on behalf of the “separation principle,” the measurement on system A cannot affect the real state of the spatially separated system B. However, depending on the measurement on system A, we ascribe different ψ-functions to system B. It is solely this feature — that the ψ_B-function is not unique — that is important to Einstein. Whether the different ψ_B-functions are eigenstates of incompatible observables is irrelevant; the Heisenberg uncertainty principle has nothing to do with Einstein’s argument.

We see that the argument of the photon-box thought experiment, as it was put in the letter of Ehrenfest to Bohr, is remarkably similar to both the new argument and to the review

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That the “talmudist” is supposed to represent Bohr’s view can be inferred from a letter that Einstein wrote to Schrödinger, on 9 August 1939, where he writes: “Es gibt auch noch den Mystiker, der ein Fragen nach etwas unabhängiges vom Beobachten Existierenden, ... überhaupt als unwissenschaftlich verbietet (Bohr). Dann fliessen beide Auffassungen in einen weichen Nebel zusammen, in dem ich mich aber auch nicht besser fühle als in einer der vorgenannten Auffassungen, die zum Realitätsbegriff Stellung nehmen” (Howard 1985, p. 178).

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of the EPR thought experiment in Einstein’s letter to Schrödinger.We can thus conclude that the EPR paper wrongly displays Einstein’s objections to quantum mechanics.

It’s remarkable that in Einstein’s own formulation there is no reference, in any way, to the Heisenberg’s uncertainty relation. Moreover, while the EPR paper poses the “criterion of physical reality” — that implicitly seems to invoke some epistemological commitment as to the nature of measurement — no such criterion or epistemological commitment is posed by Einstein himself. Finally, in the EPR paper the incompleteness of quantum mechanics is proved directly, whereas in Einstein’s own argument it only follows when one sticks to the “separation principle.” If one is of the opinion that the violation of this principle is of no concern, than indeed one doesn’t have to be concerned with Einstein’s argument.

The question arises, what was the reason that the “separation principle” was so important to Einstein? Einstein believed that the separation principle provided the only conceivable way to objectively divide the world into the physical systems that form the content of the physical laws — in his own words:

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 he parts (Born 1969 cited in in Howard 1993, p. 235).

4 Conclusion

Einstein has never been a positivist pur sang. Already in his 1905 papers there is a tension between Einstein’s works in physics and Mach’s positivism — that aimed at eliminating, from physical theory, all entities endowed with properties that could not be directly measured, such as atoms. In his correspondence with Schlick, Einstein’s conventionalism comes most clearly and explicitly to the light. With this remarks in the back of our mind we can clearly recognize, even in Einstein’s most conspicuous comments linked to his realism, conventionalism that greatly resembles the philosophy of Duhem. Einstein observes that in the practical states of affairs there has always been a physical theory that was superior to all others. However, he also acknowledges again and again that, on the basis of logic, there are always infinitely many theories possible that can accommodate for the same body of empirical facts. The thesis that theory choice is underdetermined by experimental facts is at right angles to that of scientific realism; which asserts that science is characterized by convergence, the thesis that with the progress of time scientific theories are converging to a single ultimate theory.

Einstein’s vigorous critique of quantum mechanics turned upon its denial of, as Einstein termed it, the “separation principle,” which states that systems that are spatio-temporal arated possess their own, mutually independent physical states. The importance of the sep-aration principle is obscure in the famous Einstein, Podolsky & Rosen experiment; but this paper was not written by Einstein himself, and he was dissatisfied with the way it turned out. I suppose that because Einstein held that any body of experience can be explained by arbitrarily many theories — i.e., because of his holistic variety of conventionalism — the experimental successes of quantum mechanic where not enough for Einstein to embrace the theory. Einstein kept looking to explain the same results with an alternative theory — to wit, unified field theory — that would satisfy his precious “principle of separation.”

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The relation between Einstein's epistemology and his critique of quantum mechanics