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Einstein Philosophy Essay Example

1. Introduction: Was Einstein an Epistemological “Opportunist”?

Late in 1944, Albert Einstein received a letter from Robert Thornton, a young African-American philosopher of science who had just finished his Ph.D. under Herbert Feigl at Minnesota and was beginning a new job teaching physics at the University of Puerto Rico, Mayaguez. He had written to solicit from Einstein a few supportive words on behalf of his efforts to introduce “as much of the philosophy of science as possible” into the modern physics course that he was to teach the following spring (Thornton to Einstein, 28 November 1944, EA 61–573).[1] Here is what Einstein offered in reply:

I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today—and even professional scientists—seem to me like somebody who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is—in my opinion—the mark of distinction between a mere artisan or specialist and a real seeker after truth. (Einstein to Thornton, 7 December 1944, EA 61-574)

That Einstein meant what he said about the relevance of philosophy to physics is evidenced by the fact that he had been saying more or less the same thing for decades. Thus, in a 1916 memorial note for Ernst Mach, a physicist and philosopher to whom Einstein owed a special debt, he wrote:

How does it happen that a properly endowed natural scientist comes to concern himself with epistemology? Is there no more valuable work in his specialty? I hear many of my colleagues saying, and I sense it from many more, that they feel this way. I cannot share this sentiment. When I think about the ablest students whom I have encountered in my teaching, that is, those who distinguish themselves by their independence of judgment and not merely their quick-wittedness, I can affirm that they had a vigorous interest in epistemology. They happily began discussions about the goals and methods of science, and they showed unequivocally, through their tenacity in defending their views, that the subject seemed important to them. Indeed, one should not be surprised at this. (Einstein 1916, 101)

How, exactly, does the philosophical habit of mind provide the physicist with such “independence of judgment”? Einstein goes on to explain:

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, 102)

One is not surprised at Einstein's then citing Mach's critical analysis of the Newtonian conception of absolute space as a paradigm of what Mach, himself, termed the “historical-critical” method of philosophical analysis (Einstein 1916, 101, citing Ch. 2, §§ 6–7 of Mach's Mechanik, most likely the third edition, Mach 1897).

The place of philosophy in physics was a theme to which Einstein returned time and again, it being clearly an issue of deep importance to him. Sometimes he adopts a modest pose, as in this oft-quoted remark from his 1933 Spencer Lecture:

If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don't listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities. (Einstein 1933, 5–6)

More typical, however, is the confident pose he struck three years later in “Physics and Reality”:

It has often been said, and certainly not without justification, that the man of science is a poor philosopher. Why then should it not be the right thing for the physicist to let the philosopher do the philosophizing? Such might indeed be the right thing at a time when the physicist believes he has at his disposal a rigid system of fundamental concepts and fundamental laws which are so well established that waves of doubt can not reach them; but it can not be right at a time when the very foundations of physics itself have become problematic as they are now. At a time like the present, when experience forces us to seek a newer and more solid foundation, the physicist cannot simply surrender to the philosopher the critical contemplation of the theoretical foundations; for, he himself knows best, and feels more surely where the shoe pinches. In looking for a new foundation, he must try to make clear in his own mind just how far the concepts which he uses are justified, and are necessities. (Einstein 1936, 349)

What kind of philosophy might we expect from the philosopher-physicist? One thing that we should not expect from a physicist who takes the philosophical turn in order to help solve fundamental physical problems is a systematic philosophy:

The reciprocal relationship of epistemology and science is of noteworthy kind. They are dependent upon each other. Epistemology without contact with science becomes an empty scheme. Science without epistemology is—insofar as it is thinkable at all—primitive and muddled. However, no sooner has the epistemologist, who is seeking a clear system, fought his way through to such a system, than he is inclined to interpret the thought-content of science in the sense of his system and to reject whatever does not fit into his system. The scientist, however, cannot afford to carry his striving for epistemological systematic that far. He accepts gratefully the epistemological conceptual analysis; but the external conditions, which are set for him by the facts of experience, do not permit him to let himself be too much restricted in the construction of his conceptual world by the adherence to an epistemological system. He therefore must appear to the systematic epistemologist as a type of unscrupulous opportunist: he appears as realist insofar as he seeks to describe a world independent of the acts of perception; as idealist insofar as he looks upon the concepts and theories as free inventions of the human spirit (not logically derivable from what is empirically given); as positivist insofar as he considers his concepts and theories justified only to the extent to which they furnish a logical representation of relations among sensory experiences. He may even appear as Platonist or Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research. (Einstein 1949, 683–684)

But what strikes the “systematic epistemologist” as mere opportunism might appear otherwise when viewed from the perspective of a physicist engaged, as Einstein himself put it, in “the critical contemplation of the theoretical foundations.” The overarching goal of that critical contemplation was, for Einstein, the creation of a unified foundation for physics after the model of a field theory like general relativity. Einstein failed in his quest, but there was a consistency and constancy in the striving that informed as well the philosophy of science developing hand in hand with the scientific project.

Indeed, from early to late a few key ideas played the central, leading role in Einstein's philosophy of science, ideas about which Einstein evinced surprisingly little doubt even while achieving an ever deeper understanding of their implications. For the purposes of the following comparatively brief overview, we can confine our attention to just five topics:

  • The underdetermination of theory choice by evidence.
  • Simplicity and theory choice.
  • Univocalness in the theoretical representation of nature.
  • Realism and separability.
  • The principle theories-constructive theories distinction.

In emphasizing the continuity and coherence in the development of Einstein's philosophy of science, I take issue with an account such as Gerald Holton's (1968), which claims to find a major philosophical break in the mid-1910s, in the form of a turn away from a sympathy for an anti-metaphysical positivism and toward a robust scientific realism. Holton sees this turn being driven by Einstein's alleged realization that general relativity, by contrast with special relativity, requires a realistic ontology. On my view, Einstein was never an ardent “Machian” positivist,[2] and he was never a scientific realist, at least not in the sense acquired by the term “scientific realist” in later twentieth century philosophical discourse (see Howard 1993). Einstein expected scientific theories to have the proper empirical credentials, but he was no positivist; and he expected scientific theories to give an account of physical reality, but he was no scientific realist. Moreover, in both respects his views remained more or less the same from the beginning to the end of his career.

Why Einstein did not think himself a realist (he said so explicitly) is discussed below. Why he is not to be understood as a positivist deserves a word or two of further discussion here, if only because the belief that he was sympathetic to positivism, at least early in his life, is so widespread (for a fuller discussion, see Howard 1993).

That Einstein later repudiated positivism is beyond doubt. Many remarks from at least the early 1920s through the end of his life make this clear. In 1946 he explained what he took to be Mach's basic error:

He did not place in the correct light the essentially constructive and speculative nature of all thinking and more especially of scientific thinking; in consequence, he condemned theory precisely at those points where its constructive-speculative character comes to light unmistakably, such as in the kinetic theory of atoms. (Einstein 1946, 21)

Is Einstein here also criticizing his own youthful philosophical indiscretions? The very example that Einstein gives here makes any such interpretation highly implausible, because one of Einstein's main goals in his early work on Brownian motion (Einstein 1905b) was precisely to prove the reality of atoms, this in the face of the then famous skepticism of thinkers like Mach and Wilhelm Ostwald:

My principal aim in this was to find facts that would guarantee as much as possible the existence of atoms of definite size.… The agreement of these considerations with experience together with Planck's determination of the true molecular size from the law of radiation (for high temperatures) convinced the skeptics, who were quite numerous at that time (Ostwald, Mach), of the reality of atoms. (Einstein 1946, 45, 47)

Why, then, is the belief in Einstein's early sympathy for positivism so well entrenched?

The one piece of evidence standardly cited for a youthful flirtation with positivism is Einstein's critique of the notion of absolute distant simultaneity in his 1905 paper on special relativity (Einstein 1905c). Einstein speaks there of “observers,” but in an epistemologically neutral way that can be replaced by talk of an inertial frame of reference. What really bothers Einstein about distant simultaneity is not that it is observationally inaccessible but that it involves a two-fold arbitrariness, one in the choice of an inertial frame of reference and one in the stipulation within a given frame of a convention regarding the ratio of the times required for a light signal to go from one stationary observer to another and back again. Likewise, Einstein faults classical Maxwellian electrodynamics for an asymmetry in the way it explains electromagnetic induction depending on whether it is the coil or the magnet that is assumed to be at rest. If the effect is the same—a current in the coil—why, asks Einstein, should there be two different explanations: an electrical field created in the vicinity of a moving magnet or an electromotive force induced in a conductor moving through a stationary magnetic field? To be sure, whether it is the coil or the magnet that is taken to be at rest makes no observable difference, but the problem, from Einstein's point of view, is the asymmetry in the two explanations. Even the young Einstein was no positivist.

First generation logical empiricists sought to legitimate their movement in part by claiming Einstein as a friend. They may be forgiven their putting a forced interpretation on arguments taken out of context. We can do better.

Einstein's philosophy of science is an original synthesis drawing upon many philosophical resources, from neo-Kantianism to Machian empiricism and Duhemian conventionalism. Other thinkers and movements, most notably the logical empiricists, drew upon the same resources. But Einstein put the pieces together in a manner importantly different from Moritz Schlick, Hans Reichenbach, and Rudolf Carnap, and he argued with them for decades about who was right (however much they obscured these differences in representing Einstein publicly as a friend of logical empiricism and scientific philosophy). Understanding how Einstein puts those pieces together therefore sheds light not only on the philosophical aspect of his own achievements in physics but also upon the larger history of the development of the philosophy of science in the twentieth century.

2. The Underdetermination of Theory Choice by Evidence: The Nature and Role of Conventions in Science

Any philosophy of science must include an account of the relation between theory and evidence. Einstein learned about the historicity of scientific concepts from Mach. But his preferred way of modeling the logical relationship between theory and evidence was inspired mainly by his reading of Pierre Duhem's La Théorie physique: son objet et sa structure (Duhem 1906). Einstein probably first read Duhem, or at least learned the essentials of Duhem's philosophy of science around the fall of 1909, when, upon returning to Zurich from the patent office in Bern to take up his first academic appointment at the University of Zurich, he became the upstairs neighbor of his old friend and fellow Zurich physics student, Friedrich Adler. Just a few months before, Adler had published the German translation of La Théorie physique (Duhem 1908), and the philosophy of science became a frequent topic of conversation between the new neighbors, Adler and Einstein (see Howard 1990a).

Theoretical holism and the underdetermination of theory choice by empirical evidence are the central theses in Duhem's philosophy of science. His argument, in brief, is that at least in sciences like physics, where experiment is dense with sophisticated instrumentation whose employment itself requires theoretical interpretation, hypotheses are not tested in isolation but only as part of whole bodies of theory. It follows that when there is a conflict between theory and evidence, the fit can be restored in a multiplicity of different ways. No statement is immune to revision because of a presumed status as a definition or thanks to some other a priori warrant, and most any statement can be retained on pain of suitable adjustments elsewhere in the total body of theory. Hence, theory choice is underdetermined by evidence.

That Einstein's exposure to Duhem's philosophy of science soon left its mark is evident from lecture notes that Einstein prepared for a course on electricity and magnetism at the University of Zurich in the winter semester of 1910/11. Einstein asks how one can assign a definite electrical charge everywhere within a material body, if the interior of the body is not accessible to test particles. A “Machian” positivist would deem such direct empirical access necessary for meaningful talk of a charge distribution in the interior of a sold. Einstein argues otherwise:

We have seen how experience led to the introd. of the concept of the quantity of electricity. it was defined by means of the forces that small electrified bodies exert on each other. But now we extend the application of the concept to cases in which this definition cannot be applied directly as soon as we conceive the el. forces as forces exerted on electricity rather than on material particles. We set up a conceptual system the individual parts of which do not correspond directly to empirical facts. Only a certain totality of theoretical material corresponds again to a certain totality of experimental facts.

We find that such an el. continuum is always applicable only for the representation of el. states of affairs in the interior of ponderable bodies. Here too we define the vector of el. field strength as the vector of the mech. force exerted on the unit of pos. electr. quantity inside a body. But the force so defined is no longer directly accessible to exp. It is one part of a theoretical construction that can be correct or false, i.e., consistent or not consistent with experience, only as a whole. (EA 3-007, ECP 3-11, 325)

One can hardly ask for a better summary of Duhem's point of view in application to a specific physical theory.

Explicit citations of Duhem by Einstein are rare (for details, see Howard 1990a). But explicit invocations of a holist picture of the structure and empirical interpretation of theories are not hard to find. An especially interesting example is found in a review that Einstein wrote in 1924 of Alfred Elsbach's Kant und Einstein (1924), one of the flood of books and articles then trying to reconcile the Kantian doctrine of the a priori Euclidean character of space with general relativity's postulate of variable spacetime curvature. Having asserted that relativity theory is incompatible with Kant's doctrine of the a priori, Einstein explains why, more generally, he is not sympathetic with Kant:

This does not, at first, preclude one's holding at least to the Kantian problematic, as, e.g., Cassirer has done. I am even of the opinion that this standpoint can be rigorously refuted by no development of natural science. For one will always be able to say that critical philosophers have until now erred in the establishment of the a priori elements, and one will always be able to establish a system of a priori elements that does not contradict a given physical system. Let me briefly indicate why I do not find this standpoint natural. A physical theory consists of the parts (elements) A, B, C, D, that together constitute a logical whole which correctly connects the pertinent experiments (sense experiences). Then it tends to be the case that the aggregate of fewer than all four elements, e.g., A, B, D, without C, no longer says anything about these experiences, and just as well A, B, C without D. One is then free to regard the aggregate of three of these elements, e.g., A, B, C as a priori, and only D as empirically conditioned. But what remains unsatisfactory in this is always the arbitrariness in the choice of those elements that one designates as a priori, entirely apart from the fact that the theory could one day be replaced by another that replaces certain of these elements (or all four) by others. (Einstein 1924, 1688–1689)

Einstein's point seems to be that while one can always choose to designate selected elements as a priori and, hence, non-empirical, no principle determines which elements can be so designated, and our ability thus to designate them derives from the fact that it is only the totality of the elements that possesses empirical content.

Much the same point could be made, and was made by Duhem himself (see Duhem 1906, part 2, ch. 6, sects. 8 and 9), against those who would insulate certain statements against empirical refutation by claiming for them the status of conventional definitions. Edouard Le Roy (1901) had argued thus about the law of free fall. It could not be refuted by experiment because it functioned as a definition of “free fall.” And Henri Poincaré (1901) said much the same about the principles of mechanics more generally. As Einstein answered the neo-Kantians, so Duhem answered this species of conventionalist: Yes, experiment cannot refute, say, the law of free fall by itself, but only because it is part of a larger theoretical whole that has empirical content only as a whole, and various other elements of that whole could as well be said to be, alone, immune to refutation.

That Einstein should deploy against the neo-Kantians in the early 1920s the argument that Duhem used against the conventionalism of Poincaré and Le Roy is interesting from the point of view of Einstein's relationships with those who were leading the development of logical empiricism and scientific philosophy in the 1920s, especially Schlick and Reichenbach. Einstein shared with Schlick and Reichenbach the goal of crafting a new form of empiricism that would be adequate to the task of defending general relativity against neo-Kantian critiques (see Schlick 1917 and 1921, and Reichenbach 1920, 1924, and 1928; for more detail, see Howard 1994a). But while they all agreed that what Kant regarded as the a priori element in scientific cognition was better understood as a conventional moment in science, they were growing to disagree dramatically over the nature and place of conventions in science. With the help of new logical tools and a more sophisticated verificationist semantics, Schlick and Reichenbach were refining Poincaré's idea of conventional definitional elements in science into the classic logical empiricist view that the moment of convention was restricted to conventional coordinating definitions that endow individual primitive terms and, by extension, the individual synthetic propositions constructed out of them with empirical content. This view worked well as an answer to the neo-Kantian, for it implied that once one fixed one's coordinating definition—as with a conventional choice of a standard measuring rod coordinated with the geometer's concept of a “rigid body”—the question of the curvature of space had an empirically determinate answer. But unless the division is wholly arbitrary, parsing theories thus into coordinating definitions and empirical statements assumes a principled difference in kind between the two categories of statements along the lines of an analytic-synthetic distinction. As had been the case with Duhem before him, the assumption of such a principled difference in kind did not comport well with the holism about theories that Einstein had learned from Duhem.

It was this argument over the nature and place of conventions in science that underlay Einstein's gradual philosophical estrangement from Schlick and Reichenbach in the 1920s. Serious in its own right, the argument over conventions was entangled with two other issues as well, namely, realism and Einstein's famous view of theories as the “free creations of the human spirit” (see, for example, Einstein 1921). In both instances what troubled Einstein was that a verificationist semantics made the link between theory and experience too strong, leaving too small a role for theory, itself, and the creative theorizing that produces it.

If theory choice is empirically determinate, especially if theoretical concepts are explicitly constructed from empirical primitives, as in Carnap's program in the Aufbau (Carnap 1928), then it is hard to see how theory gives us a story about anything other than experience. As noted, Einstein was not what we would today call a scientific realist, but he still believed that there was content in theory beyond mere empirical content. He believed that theoretical science gave us a window on nature itself, even if, in principle, there will be no one uniquely correct story at the level of deep ontology (see below, section 5). And if the only choice in theory choice is one among conventional coordinating definitions, then that is no choice at all, a point stressed by Reichenbach, especially, as an important positive implication of his position. Reichenbach argued that if empirical content is the only content, then empirically equivalent theories have the same content, the difference resulting from their different choices of coordinating definitions being like in kind to the difference between “es regnet” and “il pleut,” or the difference between expressing the result of a measurement in English or metric units, just two different ways of saying the same thing. But then, Einstein would ask, where is there any role for the creative intelligence of the theoretical physicist if there is no room for genuine choice in science, if experience somehow dictates theory construction?

The argument over the nature and role of conventions in science continued to the very end of Einstein's life, reaching its highest level of sophistication in the exchange between Reichenbach and Einstein the Library of Living Philosopher's volume, Albert Einstein: Philosopher-Physicist (Schilpp 1949). The question is, again, whether the choice of a geometry is empirical, conventional, or a priori. In his contribution, Reichenbach reasserted his old view that once an appropriate coordinating definition is established, equating some “practically rigid rod” with the geometer's “rigid body,” then the geometry of physical space is wholly determined by empirical evidence:

The choice of a geometry is arbitrary only so long as no definition of congruence is specified. Once this definition is set up, it becomes an empirical question which geometry holds for physical space.… The conventionalist overlooks the fact that only the incomplete statement of a geometry, in which a reference to the definition of congruence is omitted, is arbitrary. (Reichenbach 1949, 297)

Einstein's clever reply includes a dialogue between two characters, “Reichenbach” and “Poincaré,” in which “Reichenbach” concedes to “Poincaré” that there are no perfectly rigid bodies in nature and that physics must be used to correct for such things as thermal deformations, from which it follows that what we actually test is geometry plus physics, not geometry alone. Here an “anonymous non-positivist” takes “Poincaré's” place, out of respect, says Einstein, “for Poincaré's superiority as thinker and author” (Einstein 1949, 677), but also, perhaps, because he realized that the point of view that follows was more Duhem than Poincaré. The “non-positivist” then argues that one's granting that geometry and physics are tested together contravenes the positivist identification of meaning with verifiability:

Non-Positivist: If, under the stated circumstances, you hold distance to be a legitimate concept, how then is it with your basic principle (meaning = verifiability)? Must you not come to the point where you deny the meaning of geometrical statements and concede meaning only to the completely developed theory of relativity (which still does not exist at all as a finished product)? Must you not grant that no “meaning” whatsoever, in your sense, belongs to the individual concepts and statements of a physical theory, such meaning belonging instead to the whole system insofar as it makes “intelligible” what is given in experience? Why do the individual concepts that occur in a theory require any separate justification after all, if they are indispensable only within the framework of the logical structure of the theory, and if it is the theory as a whole that stands the test? (Einstein 1949, 678).

Two years before the Quine's publication of “Two Dogmas of Empiricism” (1951), Einstein here makes explicit the semantic implications of a thoroughgoing holism.

If theory choice is empirically underdetermined, then an obvious question is why we are so little aware of the underdetermination in the day-to-day conduct of science. In a 1918 address celebrating Max Planck's sixtieth birthday, Einstein approached this question via a distinction between practice and principle:

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 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, 31; my translation)

But why is theory choice, in practice, seemingly empirically determined? Einstein hinted at an answer the year before in a letter to Schlick, where he commended Schlick's argument that the deep elements of a theoretical ontology have as much claim to the status of the real as do Mach's elements of sensation (Schlick 1917), but suggested that we are nonetheless speaking of two different kinds of reality. How do they differ?

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 “elements” can be vastly different. And the two constructions need not agree as regards the “events”; for these surely belong to the conceptual constructions. Certainly on 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.… I would like to recommend a clean conceptual distinction here. (Einstein to Schlick, 21 May 1917, EA 21-618, ECP 8-343)

Why, in practice, are physicists unaware of underdetermination? It is because ours is not the situation of “two different peoples pursu[ing] physics independently of one another.” Though Einstein does not say it explicitly, the implication seems to be that apparent determination in theory choice is mainly a consequence of our all being similarly socialized as we become members of a common scientific community. Part of what it means to be a member of a such a community is that we have been taught to make our theoretical choices in accord with criteria or values that we hold in common.

3. Simplicity and Theory Choice

For Einstein, as for many others, simplicity is the criterion that mainly steers theory choice in domains where experiment and observation no longer provide an unambiguous guide. This, too, is a theme sounded early and late in Einstein's philosophical reflections (for more detail, see Howard 1998, Norton 2000, and van Dongen 2002). For example, the just-quoted remark from 1918 about the apparent determination of theory choice in practice, contrasted with in-principle underdetermination continues:

Furthermore this conceptual system that is univocally coordinated with the world of experience is reducible to a few basic laws from which the whole system can be developed logically. With every new important advance the researcher here sees his expectations surpassed, in that those basic laws are more and more simplified under the press of experience. With astonishment he sees apparent chaos resolved into a sublime order that is to be attributed not to the rule of the individual mind, but to the constitution of the world of experience; this is what Leibniz so happily characterized as “pre-established harmony.” Physicists strenuously reproach many epistemologists for their insufficient appreciation of this circumstance. Herein, it seems to me, lie the roots of the controversy carried on some years ago between Mach and Planck. (Einstein 1918, p. 31)

There is more than a little autobiography here, for as Einstein stressed repeatedly in later years, he understood the success of his own quest for a general theory of relativity as a result of his seeking the simplest set of field equations satisfying a given set of constraints.

Always a leitmotif, Einstein's celebration of simplicity as a guide to theory choice comes clearly to the fore in the early 1930s. Why then? The reason might well be that his faith in simplicity had been vindicated when, seemingly with a sigh of relief, he found that he could drop from the gravitational field equations the cosmological constant that he had introduced in 1917 for the purpose of blocking non-static solutions, for the introduction of the cosmological constant in the first place had represented to him “a considerable renunciation of the logical simplicity of the theory” (Einstein 1949, 684–685). That his faith in simplicity was reaffirmed is clear. Witness what he wrote in his 1933 Herbert Spencer lecture:

If, then, it is true that the axiomatic foundation of theoretical physics cannot be extracted from experience but must be freely invented, may we ever hope to find the right way? Furthermore, does this right way exist anywhere other than in our illusions? May we hope to be guided safely by experience at all, if there exist theories (such as classical mechanics) which to a large extent do justice to experience, without comprehending the matter in a deep way?

To these questions, I answer with complete confidence, that, in my opinion, the right way exists, and that we are capable of finding it. Our experience hitherto justifies us in trusting that nature is the realization of the simplest that is mathematically conceivable. I am convinced that purely mathematical construction enables us to find those concepts and those lawlike connections between them that provide the key to the understanding of natural phenomena. Useful mathematical concepts may well be suggested by experience, but in no way can they be derived from it. Experience naturally remains the sole criterion of the usefulness of a mathematical construction for physics. But the actual creative principle lies in mathematics. Thus, in a certain sense, I take it to be true that pure thought can grasp the real, as the ancients had dreamed. (Einstein 1933, p. 183; my translation)

Another consideration reinforcing Einstein's conviction that the theoretical physicist must trust simplicity is that physics is moving steadily into domains ever further removed from direct contact with observation and experiment. Before the 1960s, general relativity, itself, rested on a famously thin empirical footing, and empirical evidence provided even less of a guide in Einstein's search for a unified field theory. One year after the Herbert Spencer lecture, at a time when he was immersed in work on unified field theory, Einstein wrote:

The theory of relativity is a beautiful example of the basic character of the modern development of theory. That is to say, the hypotheses from which one starts become ever more abstract and more remote from experience. But in return one comes closer to the preeminent goal of science, that of encompassing a maximum of empirical contents through logical deduction with a minimum of hypotheses or axioms. The intellectual path from the axioms to the empirical contents or to the testable consequences becomes, thereby, ever longer and more subtle. The theoretician is forced, ever more, to allow himself to be directed by purely mathematical, formal points of view in the search for theories, because the physical experience of the experimenter is not capable of leading us up to the regions of the highest abstraction. Tentative deduction takes the place of the predominantly inductive methods appropriate to the youthful state of science. Such a theoretical structure must be quite thoroughly elaborated in order for it to lead to consequences that can be compared with experience. It is certainly the case that here, as well, the empirical fact is the all-powerful judge. But its judgment can be handed down only on the basis of great and difficult intellectual effort that first bridges the wide space between the axioms and the testable consequences. The theorist must accomplish this Herculean task with the clear understanding that this effort may only be destined to prepare the way for a death sentence for his theory. One should not reproach the theorist who undertakes such a task by calling him a fantast; instead, one must allow him his fantasizing, since for him there is no other way to his goal whatsoever. Indeed, it is no planless fantasizing, but rather a search for the logically simplest possibilities and their consequences. (Einstein 1954, 238–239; my translation)

What warrant is there for thus trusting in simplicity? At best one can do a kind of meta-induction. That “the totality of all sensory experience can be ‘comprehended’ on the basis of a conceptual system built on premises of great simplicity” will be derided by skeptics as a “miracle creed,” but, Einstein adds, “it is a miracle creed which has been borne out to an amazing extent by the development of science” (Einstein 1950, p. 342).

But for all that Einstein's faith in simplicity was strong, he despaired of giving a precise, formal characterization of how we assess the simplicity of a theory. In 1946 he wrote about the perspective of simplicity (here termed the “inner perfection” of a theory):

This point of view, whose exact formulation meets with great difficulties, has played an important role in the selection and evaluation of theories from time immemorial. The problem here is not simply one of a kind of enumeration of the logically independent premises (if anything like this were at all possible without ambiguity), but one of a kind of reciprocal weighing of incommensurable qualities.… I shall not attempt to excuse the lack of precision of [these] assertions … on the grounds of insufficient space at my disposal; I must confess herewith that I cannot at this point, and perhaps not at all, replace these hints by more precise definitions. I believe, however, that a sharper formulation would be possible. In any case it turns out that among the “oracles” there usually is agreement in judging the “inner perfection” of the theories and even more so concerning the degree of “external confirmation.” (Einstein 1946, pp. 21, 23).

As in 1918, so in 1946 and beyond, Einstein continues to be impressed that the “oracles,” presumably the leaders of the relevant scientific community, tend to agree in their judgments of simplicity. That is why, in practice, simplicity seems to determine theory choice univocally.

Experience justifies our trusting that nature is the realization of the simplest that is mathematically conceivable. Can we say anything more about why this might be so? A hint is provided by Einstein's enthusiastically positive response to Schlick's first essay on the philosophical significance of relativity (Schlick 1915). At this early stage in his philosophical career, Schlick regarded himself as a realist and defended a version of the underdetermination thesis grounded in his view of truth as the unambiguous many-to-one coordination of propositions to facts (Schlick 1910). Theories being sets of propositions, several theories could likewise be unambiguously coordinated with a given set of facts and thus count as equally true representations of those facts. When he took up the question of simplicity, Schlick derided those who would justify simplicity as a criterion of theory choice by arguing that we should choose simple theories because nature itself is simple. As Schlick rightly pointed out, this is a circular argument, for our only cognitive access to nature is via our theories (note that Einstein argues not that nature, itself, is simple, but that nature is a realization of simple theoretical constructions, a crucial difference). Schlick similarly derides a defense grounded in considerations of mental economy, which he terms “intellectual indolence.” Why then choose simple theories? Schlick's answer is that “the greater simplicity of a theory depends on its containing fewer arbitrary elements.” Why is it better to choose theories with fewer “superfluous,” arbitrary elements? Because only the non-arbitrary elements are likely to correspond to reality, so in choosing the simpler theory “we are then sure of diverging from reality at least no further than is necessitated by the bounds of our knowledge as such” (Schlick 1915, 154–155). As an example of an arbitrary element in theory that does not correspond to reality, Schlick cited the ether frame in Lorentzian electrodynamics (Schlick 1917, 60).

Einstein does not explicitly commend Schlick's defense of simplicity, but he also in no way objects in the course of a long correspondence during the late 1910s, wherein he strongly commends Schlick's general philosophical orientation and carefully records all points of disagreement (for more detail, see Howard 1984). Moreover the principle underlying Schlick's defense of simplicity, the idea that it is the non-arbitrary elements of our theories that represent the real, played a deep and enduring role in Einstein's philosophy of science.

4. Univocalness in the Theoretical Representation of Nature

In the physics and philosophy of science literature of the late nineteenth and early twentieth centuries, the principle according to which scientific theorizing should strive for a univocal representation of nature was widely and well known under the name that it was given in the title of a widely-cited essay by Joseph Petzoldt, “The Law of Univocalness” [“Das Gesetz der Eindeutigkeit”] (Petzoldt 1895). An indication that the map of philosophical positions was drawn then in a manner very different from today is to found in the fact that this principle found favor among both anti-metaphysical logical empiricists, such as Carnap, and neo-Kantians, such as Cassirer. It played a major role in debates over the ontology of general relativity and was an important part of the background to the development of the modern concept of categoricity in formal semantics (for more on the history, influence, and demise of the principle of univocalness, see Howard 1992 and 1996). One can find no more ardent and consistent champion of the principle than Einstein.

The principle of univocalness should not be mistaken for a denial of the underdetermination thesis. The latter asserts that a multiplicity of theories can equally well account for a given body of empirical evidence, perhaps even the infinity of all possible evidence in the extreme, Quinean version of the thesis. The principle of univocalness asserts (in a somewhat anachronistic formulation) that any one theory, even any one among a set of empirically equivalent theories, should provide a univocal representation of nature by determining for itself an isomorphic set of models. The unambiguous determination of theory choice by evidence is not the same thing as the univocal determination of a class of models by a theory.

The principle of univocalness played a central role in Einstein's struggles to formulate the general theory of relativity. When, in 1913, Einstein wrongly rejected a fully generally covariant theory of gravitation, he did so in part because he thought, wrongly, that generally covariant field equations failed the test of univocalness. More specifically, he reasoned wrongly that for a region of spacetime devoid of matter and energy—a “hole”—generally covariant field equations permit the construction of two different solutions, different in the sense that, in general, for spacetime points inside the hole, they assign different values of the metric tensor to one and the same point (for more on the history of this episode, see Stachel 1980 and Norton 1984). But Einstein's “hole argument” is wrong, and his own diagnosis of the error in 1915 rests again, ironically, on a deployment of the principle of univocalness. What Einstein realized in 1915 was that, in 1913, he was wrongly assuming that a coordinate chart sufficed to fix the identity of spacetime manifold points. The application of a coordinate chart cannot suffice to individuate manifold points precisely because a coordinate chart is not an invariant labeling scheme, whereas univocalness in the representation of nature requires such invariance (see Howard and Norton 1993 and Howard 1999 for further discussion).

Here is how Einstein explained his change of perspective in a letter to Paul Ehrenfest of 26 December 1915, just a few weeks after the publication of the final, generally covariant formulation of the general theory of relativity:

In §12 of my work of last year, everything is correct (in the first three paragraphs) up to that which is printed with emphasis at the end of the third paragraph. From the fact that the two systems G(x) and G′(x), referred to the same reference system, satisfy the conditions of the grav. field, no contradiction follows with the univocalness of events. That which was apparently compelling in these reflections founders immediately, if one considers that
  1. the reference system signifies nothing real
  2. that the (simultaneous) realization of two different g-systems (or better, two different grav. fields) in the same region of the continuum is impossible according to the nature of the theory.

In place of §12, the following reflections must appear. The physically real in the universe of events (in contrast to that which is dependent upon the choice of a reference system) consists in spatiotemporal coincidences.* [Footnote *: and in nothing else!] Real are, e.g., the intersections of two different world lines, or the statement that they do not intersect. Those statements that refer to the physically real therefore do not founder on any univocal coordinate transformation. If two systems of the gµv (or in general the variables employed in the description of the world) are so created that one can obtain the second from the first through mere spacetime transformation, then they are completely equivalent. For they have all spatiotemporal point coincidences in common, i.e., everything that is observable.

These reflections show at the same time how natural the demand for general covariance is. (EA 9-363, ECP 8-173)

Einstein's new point of view, according to which the physically real consists exclusively in that which can be constructed on the basis of spacetime coincidences, spacetime points, for example, being regarded as intersections of world lines, is now known as the “point-coincidence argument.” Spacetime coincidences play this privileged ontic role because they are invariant and, thus, univocally determined. Spacetime coordinates lack such invariance, a circumstance that Einstein thereafter repeatedly formulated as the claim that space and time “thereby lose the last vestige of physical reality” (see, for example, Einstein to Ehrenfest, 5 January 1916, EA 9-372, ECP 8-180).

One telling measure of the philosophical importance of Einstein's new perspective on the ontology of spacetime is the fact that Schlick devoted his first book, Raum und Zeit in den gegenwärtigen Physik (1917), a book for which Einstein had high praise (see Howard 1984 and 1999), to an exploration of the philosophical implications of the claim that space and time have thereby lost the last vestige of physical reality. Mention has already been made of Schlick's defense of an underdetermination thesis based on his doctrine of truth as unambiguous coordination. That view is here developed at considerable length. But what most interested Einstein was Schlick's discussion of the reality concept. Schlick argued that Mach was wrong to regard only the elements of sensation as real. Spacetime events, individuated invariantly as spacetime coincidences, have as much or more right to be taken as real, precisely because of the univocal manner of their determination. Einstein wholeheartedly agreed, though he ventured the above-quoted suggestion that one should distinguish the two kinds of reality—that of the elements and that of the spacetime events—on the ground that if “two different peoples” pursued physics independently of one another they were fated to agree about the elements but would almost surely produce different theoretical constructions at the level of the spacetime event ontology. Note, again, that underdetermination is not a failure of univocalness. Different though they will be, each people's theoretical construction of an event ontology would be expected to be univocal.

Schlick, of course, went on to become the founder of the Vienna Circle, a leading figure in the development of logical empiricism, a champion of verificationism. That being so, an important question arises about Schlick's interpretation of Einstein on the univocal determination of spacetime events as spacetime coincidences. The question is this: Do such univocal coincidences play such a privileged role because of their reality or because of their observability. Clearly the former—the reality of that which is univocally determined—is important. But are univocal spacetime coincidences real because, thanks to their invariance, they are observable? Or is their observability consequent upon their invariant reality? Einstein, himself, repeatedly stressed the observable character of spacetime coincidences, as in the 26 December 1915 letter to Ehrenfest quoted above (for additional references and a fuller discussion, see Howard 1999).[3]

Schlick, still a self-described realist in 1917, was clear about the relationship between observability and reality. He distinguished macroscopic coincidences in the field of our sense experience, to which he does accord a privileged and foundational epistemic status, from the microscopic point coincidences that define an ontology of spacetime manifold points. Mapping the former onto the latter is, for Schlick, an important part of the business of confirmation, but the reality of the spacetime manifold points is in no way consequent upon their observability. Indeed, how, strictly speaking, can one even talk of the observation of infinitesimal spacetime coincidences of the kind encountered in the intersection of two world lines? In fact, the order of implication goes the other way: Spacetime events individuated as spacetime coincidences are real because they are invariant, and such observability as they might possess is consequent upon their status as invariant bits of physical reality. For Einstein, and for Schlick in 1917, understanding the latter—physical reality—is the goal of physical theory.

5. Realism and Separability

As we have seen, Schlick's Raum und Zeit in den gegenwärtigen Physik promoted a realistic interpretation of the ontology of general relativity. After reading the manuscript early in 1917, Einstein wrote to Schlick on 21 May that “the last section ‘Relations to Philosophy’ seems to me excellent” (EA 21-618, ECP 8-343), just the sort of praise one would expect from a fellow realist. Three years earlier, the Bonn mathematician, Eduard Study, had written another well-known, indeed very well-known defense of realism, Die realistische Weltansicht und die Lehre vom Raume (1914). Einstein read it in September of 1918. Much of it he liked, especially the droll style, as he said to Study in a letter of 17 September (EA 22-301, ECP 8-618). Pressed by Study to say more about the points where he disagreed, Einstein replied on 25 September in a rather surprising way:

I am supposed to explain to you my doubts? By laying stress on these it will appear that I want to pick holes in you everywhere. But things are not so bad, because I do not feel comfortable and at home in any of the “isms.” It always seems to me as though such an ism were strong only so long as it nourishes itself on the weakness of it counter-ism; but if the latter is struck dead, and it is alone on an open field, then it also turns out to be unsteady on its feet. So, away we go!

“The physical world is real.” That is supposed to be the fundamental hypothesis. What does “hypothesis” mean here? For me, a hypothesis is a statement, whose truth must be assumed for the moment, but whose meaning must be raised above all ambiguity. The above statement appears to me, however, to be, in itself, meaningless, as if one said: “The physical world is cock-a-doodle-doo.” It appears to me that the “real” is an intrinsically empty, meaningless category (pigeon hole), whose monstrous importance lies only in the fact that I can do certain things in it and not certain others. This division is, to be sure, not an arbitrary one, but instead ….

I concede that the natural sciences concern the “real,” but I am still not a realist. (EA 22-307, ECP-8-624)

Lest there be any doubt that Einstein has little sympathy for the other side, he adds:

The positivist or pragmatist is strong as long as he battles against the opinion that there [are] concepts that are anchored in the “A priori.” When, in his enthusiasm, [he] forgets that all knowledge consists [in] concepts and judgments, then that is a weakness that lies not in the nature of things but in his personal disposition just as with the senseless battle against hypotheses, cf. the clear book by Duhem. In any case, the railing against atoms rests upon this weakness. Oh, how hard things are for man in this world; the path to originality leads through unreason (in the sciences), through ugliness (in the arts)-at least the path that many find passable. (EA 22-307, ECP-8-624)

What could Einstein mean by saying that he concedes that the natural sciences concern the “real,” but that he is “still not a realist” and that the “real” in the statement, “the physical world is real,” is an “intrinsically empty, meaningless category”?

The answer might be that realism, for Einstein, is not a philosophical doctrine about the interpretation of scientific theories or the semantics of theoretical terms.[4] For Einstein, realism is a physical postulate, one of a most interesting kind, as he explained on 18 March 1948 in a long note at the end of the manuscript of Max Born's Waynflete Lectures, Natural Philosophy of Cause and Chance (1949), which Born had sent to Einstein for commentary:

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

If one adheres to this program, then one can hardly view the quantum-theoretical description as a complete representation of the physically real. If one attempts, nevertheless, so to view it, then one must assume that the physically real in B undergoes a sudden change because of a measurement in A. My physical instincts bristle at that suggestion.

However, if one renounces the assumption that what is present in different parts of space has an independent, real existence, then I do not at all see what physics is supposed to describe. For what is thought to by a ‘system’ is, after all, just conventional, and I do not see how one is supposed to divide up the world objectively so that one can make statements about the parts. (Born 1969, 223–224; my translation)

Realism is thus the thesis of spatial separability, the claim that spatial separation is a sufficient condition for the individuation of physical systems, and its assumption is here made into almost a necessary condition for the possibility of an intelligible science of physics.

The postulate of spatial separability as that which undergirds the ontic independence and, hence, individual identities of the systems that physics describes was an important part of Einstein's thinking about the foundations of physics since at least the time of his very first paper on the quantum hypothesis in 1905 (Einstein 1905a; for more detail on the early history of this idea in Einstein's thinking, see Howard 1990b). But the true significance of the separability principle emerged most clearly in 1935, when (as hinted in the just-quoted remark) Einstein made it one of the central premises of his argument for the incompleteness of quantum mechanics (see Howard 1985 and 1989). It is not so clearly deployed in the published version of the Einstein, Podolsky, Rosen paper (1935), but Einstein did not write that paper and did not like the way the argument appeared there. Separability is, however, an explicit premise in all of Einstein's later presentations of the argument for the incompleteness of quantum mechanics, both in correspondence and in print (see Howard 1985 for a detailed list of references).

In brief, the argument is this. Separability implies that spacelike separated systems have associated with them independent real states of affairs. A second postulate, locality, implies that the events in one region of spacetime cannot physically influence physical reality in a region of spacetime separated from the first by a spacelike interval. Consider now an experiment in which two systems, A and B, interact and separate, subsequent measurements on each corresponding to spacelike separated events. Separability implies that A and B have separate real physical states, and locality implies that the measurement performed on A cannot influence B's real physical state. But quantum mechanics ascribes different theoretical states, different wave functions, to B depending upon that parameter that is measured on A. Therefore, quantum mechanics ascribes different theoretical states to B, when B possesses, in fact, one real physical state. Hence quantum mechanics is incomplete.

One wants to ask many questions. First, what notion of completeness is being invoked here? It is not deductive completeness. It is closer in kind to what is termed “categoricity” in formal semantics, a categorical theory being one whose models are all isomorphic to one another. It is closer still to the principle discussed above—and cited as a precursor of the concept of categoricity—namely, the principle of univocalness, which we found doing such important work in Einstein's quest for a general theory of relativity, where it was the premise forcing the adoption of an invariant and thus univocal scheme for the individuation of spacetime manifold points.

The next question is why separability is viewed by Einstein as virtually an a priori necessary condition for the possibility of a science of physics. One reason is because a field theory like general relativity, which was Einstein's model for a future unified foundation for physics, is an extreme embodiment of the principle of separability: “Field theory has carried out this principle to the extreme, in that it localizes within infinitely small (four-dimensional) space-elements the elementary things existing independently of the one another that it takes as basic, as well as the elementary laws it postulates for them” (Einstein 1948, 321–322). And a field theory like general relativity can do this because the infinitesimal metric interval—the careful way to think about separation in general relativistic spacetime—is invariant (hence univocally determined) under all continuous coordinate transformations.

Another reason why Einstein would be inclined to view separability as an a priori necessity is that, in thus invoking separability to ground individuation, Einstein places himself in a tradition of so viewing spatial separability with very strong Kantian roots (and, before Kant, Newtonian roots), a tradition in which spatial separability was known by the name that Arthur Schopenhauer famously gave to it, the principium individuationis (for a fuller discussion of this historical context, see Howard 1997).

A final question one wants to ask is: “What does any of this have to do with realism?” One might grant Einstein's point that a real ontology requires a principle of individuation without agreeing that separability provides the only conceivable such principle. Separability together with the invariance of the infinitesimal metric interval implies that, in a general relativistic spacetime, there are joints everywhere, meaning that we can carve up the universe in any way we choose and still have ontically independent parts. But quantum entanglement can be read as implying that this libertarian scheme of individuation does not work. Can quantum mechanics not be given a realistic interpretation? Many would say, “yes.” Einstein said, “no.”

6. The Principle Theories—Constructive Theories Distinction

There is much that is original in Einstein's philosophy of science as described thus far. At the very least, he rearranged the bits and pieces of doctrine that he learned from others—Kant, Mach, Duhem, Poincaré, Schlick, and others—in a strikingly novel way. But Einstein's most original contribution to twentieth-century philosophy of science lies elsewhere, in his distinction between what he termed “principle theories” and “constructive theories.”

This idea first found its way into print in a brief 1919 article in the Times of London (Einstein 1919). A constructive theory, as the name implies, provides a constructive model for the phenomena of interest. An example would be kinetic theory. A principle theory consists of a set of individually well-confirmed, high-level empirical generalizations. Examples include the first and second laws of thermodynamics. Ultimate understanding requires a constructive theory, but often, says Einstein, progress in theory is impeded by premature attempts at developing constructive theories in the absence of sufficient constraints by means of which to narrow the range of possible of constructive. It is the function of principle theories to provide such constraint, and progress is often best achieved by focusing first on the establishment of such principles. According to Einstein, that is how he achieved his breakthrough with the theory of relativity, which, he says, is a principle theory, its two principles being the relativity principle and the light principle.

While the principle theories-constructive theories distinction first made its way into print in 1919, there is considerable evidence that it played an explicit role in Einstein's thinking much earlier. Nor was it only the relativity and light principles that served Einstein as constraints in his theorizing. Thus, he explicitly mentions also the Boltzmann principle, S = k log W, as another such:

This equation connects thermodynamics with the molecular theory. It yields, as well, the statistical probabilities of the states of systems for which we are not in a position to construct a molecular-theoretical model. To that extent, Boltzmann's magnificent idea is of significance for theoretical physics … because it provides a heuristic principle whose range extends beyond the domain of validity of molecular mechanics. (Einstein 1915, p. 262).

Einstein is here alluding the famous entropic analogy whereby, in his 1905 photon hypothesis paper, he reasoned from the fact that black body radiation in the Wien regime satisfied the Boltzmann principle to the conclusion that, in that regime, radiation behaved as if it consisted of mutually independent, corpuscle-like quanta of electromagnetic energy. The quantum hypothesis is a constructive model of radiation; the Boltzmann principle is the constraint that first suggested that model.

There are anticipations of the principle theories-constructive theories distinction in the nineteenth-century electrodynamics literature, James Clerk Maxwell, in particular, being a source from which Einstein might well have drawn (see Harman 1998). At the turn of the century, the “physics of principles” was a subject under wide discussion (see, for example, Poincaré 1904; for further discussion, see Giedymin 1982). But however extensive his borrowings (no explicit debt was ever acknowledged), in Einstein's hands the distinction becomes a methodological tool of impressive scope and fertility. What is puzzling, and even a bit sad, is that this most original methodological insight of Einstein's had comparatively little impact on later philosophy of science or practice in physics.

7. Conclusion: Albert Einstein: Philosopher-Physicist

Einstein's influence on twentieth-century philosophy of science is comparable to his influence on twentieth-century physics. What made that possible? One explanation looks to the institutional and disciplinary history of theoretical physics and the philosophy of science. Each was, in its own domain, a new mode of thought in the latter nineteenth century, and each finally began to secure for itself a solid institutional basis in the early twentieth century. In a curious way, the two movements helped one another. Philosophers of science helped to legitimate theoretical physics by locating the significant cognitive content of science in its theories. Theoretical physicists helped to legitimate the philosophy of science by providing for analysis a subject matter that was radically reshaping our understanding of nature and the place of humankind within it. In some cases the help was even more direct, as with the work of Einstein and Max Planck in the mid-1920s to create in the physics department at the University of Berlin a chair in the philosophy of science for Reichenbach (see Hecht and Hartmann 1982). And we should remember the example of the physicists Mach and Ludwig Boltzmann who were the first two occupants of the new chair for the philosophy of science at the University of Vienna at the turn of the century.

Another explanation looks to the education of young physicists in Einstein's day. Not only was Einstein's own youthful reading heavily focused on philosophy, more generally, and the philosophy of science, in particular (for an overview, see Einstein 1989, xxiv–xxv; see also Howard 1994b), in which respect he was not unlike other physicists of his generation, but also his university physics curriculum included a required course on “The Theory of Scientific Thought” (see Einstein 1987, Doc. 28). An obvious question is whether or not the early cultivation of a philosophical habit of mind made a difference in the way Einstein and his contemporaries approached physics. As indicated by his November 1944 letter to Robert Thorton quoted at the beginning of this article, Einstein thought that it did.


Einstein's Work

1905a“Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt.” Annalen der Physik 17:132–148.
1905b“Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen.” Annalen der Physik 17: 549–560.
1905c“Zur Elektrodynamik bewegter Körper.” Annalen der Physik 17: 891–921.
1915“Theoretische Atomistik.” In Die Kultur der Gegenwart. Ihre Entwicklung und ihre Ziele. Paul Hinneberg, ed. Part 3, Mathematik, Naturwissenschaften, Medizin. Section 3, Anorganischen Naturwissenschaften. E. Lecher, ed. Vol. 1, Die Physik. Emil Warburg, ed. Leipzig and Berlin: B. G. Teubner, 251–263.
1916“Ernst Mach.” Physikalische Zeitschrift 17: 101–104.
1918“Motive des Forschens.” In Zu Max Plancks sechzigstem Geburtstag. Ansprachen, gehalten am 26. April 1918 in der Deutschen Physikalischen Gesellschaft. Karlsruhe: C. F. Müller, pp. 29–32. English translation: “Principles of Research.” In Einstein 1954, 224–227.
1919“Time, Space, and Gravitation.” Times (London). 28 November 1919, 13–14. Reprinted as “What is the Theory of Relativity?” In Einstein 1954, 227–232.
1921Geometrie und Erfahrung. Erweiterte Fassung des Festvortrages gehalten an der Preussischen Akademie der Wissenschaften zu Belin am 27. Januar 1921. Berlin: Julius Springer. English translation: “Geometry and Experience.” In Einstein 1954, 232–246.
1924Review of Elsbach 1924. Deutsche Literaturzeitung 45, 1688–1689.
1933On the Method of Theoretical Physics. The Herbert Spencer Lecture, delivered at Oxford, 10 June 1933. Oxford: Clarendon Press. New translation by Sonja Bargmann in Einstein 1954, 270–276.
1934“Das Raum-, Äther- und Feld-Problem der Physik.” English translation: In Einstein 1954, 276–285.
1935with Boris Podolsky and Nathan Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Physical Review 47: 777–780.
1936“Physik und Realität.” Journal of The Franklin Institute 221: 313–347. English translation: “Physics and Reality.” Jean Piccard, trans. Journal of the Franklin Institute 221: 348–382. Reprinted in Einstein 1954, 290–323.
1946“Autobiographical Notes.” In Schilpp 1949, 1–94. Quotations are taken from the corrected English translation in: Autobiographical Notes: A Centennial Edition. Paul Arthur Schilpp, trans. and ed. La Salle, Illinois: Open Court, 1979.
1948“Quanten-Mechanik und Wirklichkeit.” Dialectica 2: 320–24.
1949“Remarks Concerning the Essays Brought together in this Co-operative Volume.” In Schilpp 1949, 665-688.
1950“On the Generalized Theory of Gravitation.” Scientific American 182, April, 13–17. Reprinted in Einstein 1954, 341–356.
1954Ideas and Opinions. New York: Bonanza Books.
1987The Collected Papers of Albert Einstein. Vol. 1, The Early Years, 1879–1902. John Stachel, et al., eds. Princeton, NJ: Princeton University Press.
1989The Collected Papers of Albert Einstein. Vol. 2, The Swiss Years: Writings, 1900–1909. John Stachel, et al., eds. Princeton, NJ: Princeton University Press.

Related Literature

  • Born, Max (1949). Natural Philosophy of Cause and Chance. Oxford: Oxford University Press.
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  • Carnap, Rudolf (1928). Der logische Aufbau der Welt. Berlin-Schlachtensee: Weltkreis-Verlag. English translation: The Logical Structure of the World & Psuedoproblems in Philosophy. Rolf A. George, trans. Berkeley and Los Angeles: University of California Press, 1969.
  • Duhem, Pierre (1906). La Théorie physique: son objet et sa structure. Paris: Chevalier & Rivière. English translation of the 2nd. ed. (1914): The Aim and Structure of Physical Theory. P. P. Wiener, trans. Princeton, NJ: Princeton University Press, 1954. Reprint: New York: Athaneum, 1962.
  • ––– (1908). Ziel und Struktur der physikalischen Theorien. Friedrich Adler, trans. Foreword by Ernst Mach. Leipzig: Johann Ambrosius Barth.
  • Elsbach, Alfred (1924). Kant und Einstein. Untersuchungen über das Verhältnis der modernen Erkenntnistheorie zur Relativitätstheorie. Berlin and Leipzig: Walter de Gruyter.
  • Fine, Arthur (1986). “Einstein's Realism.” In The Shaky Game: Einstein, Realism, and the Quantum Theory. Chicago: University of Chicago Press, 86–111.
  • Friedman, Michael (1983). Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science. Princeton, NJ: Princeton University Press.
  • Giedymin, Jerzy (1982). “The Physics of the Principles and Its Philosophy: Hamilton, Poincaré and Ramsey.” In Science and Convention: Essays on Henri Poincaré's Philosophy of Science and the Conventionalist Tradition. Oxford: Pergamon, 42–89.
  • Harman, P. M. (1998). The Natural Philosophy of James Clerk Maxwell. Cambridge: Cambridge University Press.
  • Hecht, Hartmut and Hoffmann, Dieter (1982). “Die Berufung Hans Reichenbachs an die Berliner Universität.” Deutsche Zeitschrift für Philosophie 30: 651–662.
  • Holton, Gerald (1968). “Mach, Einstein, and the Search for Reality.” Daedalus 97: 636–673. Reprinted in Thematic Origins of Scientific Thought: Kepler to Einstein. Cambridge, MA: Harvard University Press, 1973, 219–259.
  • Howard, Don (1984). “Realism and Conventionalism in Einstein's Philosophy of Science: The Einstein-Schlick Correspondence.” Philosophia Naturalis 21: 618–629.
  • ––– (1985). “Einstein on Locality and Separability.” Studies in History and Philosophy of Science 16: 171–201.
  • ––– (1989). “Holism, Separability, and the Metaphysical Implications of the Bell Experiments.” In Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem. James T. Cushing and Ernan McMullin, eds. Notre Dame, IN: University of Notre Dame Press, 224–253.
  • ––– (1990a). “Einstein and Duhem.” Synthese 83: 363–384.
  • ––– (1990b). “'Nicht sein kann was nicht sein darf,’ or the Prehistory of EPR, 1909–1935: Einstein's Early Worries about the Quantum Mechanics of Composite Systems.” In Sixty-Two Years of Uncertainty: Historical, Philosophical, and Physical Inquiries into the Foundations of Quantum Mechanics. Proceedings of the 1989 Conference, “Ettore Majorana” Centre for Scientific Culture, International School of History of Science, Erice, Italy, 5–14 August. Arthur Miller, ed. New York: Plenum, 61–111.
  • ––– (1992). “Einstein and Eindeutigkeit: A Neglected Theme in the Philosophical Background to General Relativity.” In Jean Eisenstaedt and A. J. Kox, eds. Studies in the History of General Relativity. Einstein Studies, vol. 3. Boston: Birkhäuser, 154–243.
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Albert Einstein (…) is a Kantian and a Greek empirical rationalist rather than a Humean British positivisic empiricist
[Northrop 1949, 390]

I. Problem-Situations

1On September 26, 1905 Albert Einstein’s paper ‘On the Electrodynamics of Moving Bodies’ appeared in the Annalen der Physik. It is generally agreed that it is one of the most important scientific papers ever written. But was it a revolutionary paper? Einstein generalizes the Galilean relativity principle to include electro-magnetic phenomena; he postulates the velocity of light in vacuum as an upper speed limit on all phenomena. He uses the Lorentz transformations for the calculation of spatial and temporal measurements in the transition from one reference frame to another. There is much to be said for the view that Einstein’s Special theory of relativity completes classical physics, especially the work of James C. Maxwell. [Holton 2000] Einstein himself did not see his theory as a ‘revolutionary act’. But Einstein’s work did introduce a philosophical revolution in our fundamental notions. This means that general notions, like mass, energy, time, space, causation, determinism, which are used in human attempts to construct coherent schemes of nature, have undergone radical changes as a result of scientific discoveries, such as those associated with the Special and General theory of relativity (STR, GTR) and Quantum Mechanics (QM). According to Max Born the revision of old concepts has to happen under the constraints of new experience. [Born 1949, 75] We can consider them as physico-philosophical notions because they are not tied to any particular physical theory and have often been the subject of philosophical reflection from the Greeks to the present day. Hans Reichenbach characterized Einstein as a philosopher by implication but also speaks of the ‘philosophical consequences’ of Einstein’s work. [Reichenbach 1949, 310] (cf. [Howard 2004]) That is, Einstein was willing to consider the status of the physico-philosophical notions in the light of his scientific discoveries. It may be more appropriate to characterize Einstein’s philosophical innovations as consequences of his scientific work. Implications can be hidden in the logic of a situation. But Einstein and many other physicists of his generation were fully aware of the philosophical dimensions of their scientific work. I prefer therefore to speak of the philosophical consequences of Einstein’s work. In order to appreciate what is meant by philosophical consequences, we should distinguish them from the deductive consequences of physical theories. A deductive consequence follows from the principles and internal logic of the theory. It is a deductive consequence of the premises of STR that reference frames do not share a universal time axis. A philosophical consequence of a physical theory concerns its conceptual features. Certain conceptual positions are compatible or incompatible with the theory but they are not directly testable and are subject to interpretations. For instance a notion of absolute time is incompatible with the theory of relativity. But physicists and philosophers have argued, alternatively, that the theory of relativity can be made compatible with a static or a dynamic view of time. The philosophical consequences of the theory of relativity extend far beyond the familiar reshaping of the notions of space and time. What made Einstein a great physicist was his ability to question unquestioned assumptions in the tradition of physical theorizing. What made him an even greater physicist was his ability to recognize the limits of his own work. This talent led him from the Special to the General theory of relativity and beyond to attempts to construct a unified field theory. What made him a decent philosopher was his willingness to pursue the philosophical consequences of his physical discoveries, e.g., regarding the physico-philosophical notions.

2Einstein followed the logic of the problem situation, which his physical discoveries had created, into the field of philosophy. A problem situation indicates that at any time, t, in the history of science there exist perceived problems, which attract a number of tentative solutions [Popper 1963, 198–200]; for instance the great puzzle of the 17th century was to know why planets stay in their orbits around the sun; some of these tentative solutions will be eliminated; for a certain period of time, t+t', usually one theory survives and is regarded in the scientific community as the most adequate theory in the light of the available evidence. If the available evidence is inconclusive with regard to competing theories, it may still be possible, as we shall see, to appeal to other constraints to achieve a distribution of credibility over the competitors. These tentative solutions include philosophical presuppositions, which may change under the impact of scientific discoveries. For instance, classical physics presupposes a unique time axis for all reference frames; a presupposition, which became questionable with the emergence of the STR. To regard Einstein as a philosopher is to consider his position on a number of philosophical issues. Einstein philosophizes within the constraints of science, in particular his science. His questions are familiar to every philosopher of science: How do theories relate to the external world? What is the nature of reality? What is the nature of time and space? What is the status of scientific theories? What does quantum mechanics tell us about reality? Given the principle of relativity, what is to be regarded as the real?

II. Facts and Concepts

3As Einstein philosophizes within the ambit of the theory of relativity, he sets these philosophical questions within a concrete scientific problem situation. His answers derive their significance from this problem situation. The problem situation is the kinematics of reference frames, given the results of classical mechanics and electromagnetism. Historically, his first concern was the notion of time. When the Special theory of relativity was generalized to the General theory, his second philosophical worry became the notion of space—or more precisely space-time, for Einstein had accepted Minkowski’s four-dimensional representation of the relativity theory. But with hindsight we can reorder his philosophical concerns into a logically more coherent picture.

4Einstein’s fundamental philosophical position arises from the age-old puzzle of how a body of concepts is related to collection of facts. More generally, how do abstract scientific theories relate to concrete empirical data? How do scientific theories represent empirical reality? Such questions of representation go beyond the immediate concern of scientists who could contend themselves with the solution of particular technical problems. However such questions lie in the nature of scientific theorizing, as the Greek astronomer Ptolemy already knew. Once a theoretical account, like geocentrism, is available the question arises: to which extent is it an accurate account of the real world? As we shall see, Einstein’s solution to this question, with respect to the theory of relativity, can be cast in terms of scientific constraints. Einstein’s philosophical worry derived from his dissatisfaction with Newtonian physics as a fundamental theory. When Einstein aired his worry, for instance in his Obituary of Ernst Mach (1916), he warned against the Kantian tendency to regard certain concepts as thought necessities. Once certain concepts have been formed, often on the basis of experience, there is a danger that they will quickly take on an independent existence. People are tempted to regard them as necessary presuppositions, without which science cannot be done. For instance, for two thousand years astronomers regarded the circle as the only permissible orbit of planets. Concepts, however, just like theories, are always subject to revisions. Einstein complained that

Concepts, which have proved useful in the ordering of things, easily acquire such a degree of authority over us that we forget their earthly origin. We take them as unchangeable givens. They come to bear the stamp of ‘thought necessities’, of the ‘a priori given’. ([Einstein 1916, 102]; translated by the author)

5What Einstein had in mind were the notions of space and time. Isaac Newton had regarded it as necessary to introduce the notions of absolute space and time into his mechanics in order to make sense of his laws of motion. Newton’s laws of motion make reference to temporal and spatial notions: state of rest, rectilinear uniform motion. A reference frame must be defined relative to which the movement of a body is ‘uniform’ or follows a ‘straight’ line. There are known rotational inaccuracies in the movement of the earth around the sun. A straight line drawn on the surface of the earth is ‘straight’ for a surveyor on earth but ‘curved’ for an observer in space. Newton mistrusted physical regularities observed on earth because they may contain systematic distortions. He required that the notions of space and time, for use in mechanics, must be freed from all reference to material motions. Newton stipulated that spatial and temporal notions must be absolute—independent of physical events and universal—all observers, whatever their location or velocity in the universe, must agree on their temporal and spatial measurements. Few classical physicists had questioned Newton’s reasoning, with the notable exception of Gottfried W. Leibniz, Ernst Mach and James Maxwell. So these notions had become part and parcel of classical physics. They had congealed to philosophical presuppositions, to thought necessities, to unquestioned assumptions. The Special theory arrived at a different result. Temporal and spatial measurements became relativized to particular reference frames. This was a necessary consequence of embracing the principle of relativity and taking the velocity of light as a fundamental postulate of the theory. Through his own work Einstein witnessed how such fundamental physico-philosophical notions as time and space required conceptual revision. This made him forever suspicious about the sway that such notions could hold over people’s minds. Einstein aims at a careful balance between concepts and facts.

6Although the fundamental notions—energy, event, mass, space, time—are logically speaking free inventions of the human mind, they must strike empirical roots. [Einstein 1920, 141] As Einstein’s scientific theories unfolded, several philosophical consequences suggested themselves. This process can clearly be observed in the notion of time.

III. Philosophy of Being or Becoming?

7The Special theory of relativity leads to a relativization of time to particular reference frames. Observers, attached to different reference frames, which are in relative uniform motion with respect to each other, will measure the flow of time differently. In the present context the ancient philosophical question ‘What is time?’—which famously puzzled Saint Augustine—reduces to the question ‘What is physical time?’ Physical time is simply what clocks in motion tell us. Einstein time is clock time. Clock time is to be understood in a broad sense. We use mechanical clocks to measure time intervals. Other regular processes—sound pulses, atomic oscillations—could be used for the same purpose. The problem is that such processes, too, are subject to relativization. Atomic oscillations yield to gravitational forces. The wavelengths of light and sound depend on the movement of the source, as evidenced in the Doppler Effect. In the world of special relativity there is only one signal, which escapes this restriction. Light retains the same velocity, c, in all directions and irrespective of whether it is emitted from a moving or stationary source. These well-established facts led to a questioning of the traditional notion of absolute and universal time. Well-known physicists like A. Eddington [1920], K. Gödel [1949] and H. Weyl [1921] have claimed that the Special theory of relativity leads to a static view of time. The argument runs as follows: the Special theory shows that simultaneity cannot be absolute, as Newton assumed, since this presupposes a propagation of all causal influence at infinite speeds. But Einstein’s light postulate shows that light propagates at finite velocity. It is a limit velocity so that no material process can travel as fast as light. This has drastic consequences. Observers in different reference frames, which travel at relative constant speed with respect to each other, will not agree on the simultaneous happening of some event, E. Einstein presented a well-known thought experiment: Let bolts of lightning strike the front and rear end of a moving train. Do they hit the ends of the train simultaneously or not? It is the motion of the observer, which determines the answer. For stationary observers on the platform of a station, the events are simultaneous. For observers on the train they do not hit the opposite ends of the train simultaneously. The reason resides in the finite propagation of light. The train passengers rush toward the light signal from the front and run away from the rear signal. The same is true of the reading of clock times in different reference frames, which move with constant velocity with respect to each other. The observers will not agree on their respective clock times. Their clocks tick differently, depending on the state of motion. If there is no cosmic notion of time (as Newton assumed), to which all observers can appeal, time must pass at different rates for each observer, depending on the speed of the reference frame. Time cannot be an objective property of the universe. It depends on the perception of observers. The passage of time seems to be an illusion, as Eddington, Gödel and Weyl concluded. By contrast, the physical universe is static, a block universe. Einstein did at times adopt such a philosophy of being.

For us believing physicists, the distinction between past, pres­ent, and future is only an illusion, even if a stubborn one. (Quoted in [Hoffmann 1972, 257–8]) From a “happening” in three-dimensional space, physics becomes, as it were, an “existence” in the four-dimensional “world”. [Einstein 1920, Appendix II, 122; Appendix V, 150]

8The argument infers the unreality of time from the results of the relativity theory: numerous reference frames are seen in constant motion with respect to each other; each reference frame carries clocks, rigid rods and perhaps an observer; the motion of the reference frames determines different clock times, which any resident observers will record; therefore the observers cannot agree on the simultaneity of two events and there is no absolute simultaneity as in Newton’s mechanics; as observers cannot agree on the simultaneity of events across different reference frames, it seems that there are as many times as there are reference frames; the passage of time seems to be a human illusion in the sense that there is no objective, observer-independent Now. But there are also numerous passages in Einstein’s work, which express a more dynamic view of time. Rather than speaking of space-time, as Minkowski did, Einstein often prefers the expression, ‘time-space’. [Einstein & Infeld 1938, 199–208] [Einstein 1922a, 29] And he points out that time and space do not have the same status in Minkowski’s four-dimensional world.

The non-divisibility of the four-dimensional continuum of events does not at all (…) involve the equivalence of the space co-ordinates with the time co-ordinate. [Einstein 1922a, 30]

9In his theory of space-time, Einstein aligns his thinking to the relationist position, espoused by Leibniz and Mach. According to the relational view, time and space are nothing but the order of actual and possible events. Space is the coexistence of such events and time is the order of succession of such coexisting events. In his deliberations of the General theory of relativity, Einstein leaves the reader in no doubt that he regards the total mass-energy distribution in the universe as the source of the space-time metric. ‘The gravitational field determines the metrical laws of the space-time continuum.’ [Einstein 1922a, 59; 1922b, 20–4] What could be said in favour of such a dynamic view? Consider first what would happen, if all references to observers were dropped. All observers can be replaced by clocks and rods. The clocks in different reference systems will be affected by the respective relative motions of the systems. No observer will conclude that there must be a mysterious transience of time—a moving Now, signalling the march of time from past to future. Without conscious observers, there is no need for the introduction of a tensed view of time, according to which objects change their temporal properties—their dates—by moving from past to present to future. The tensed view falls foul of McTaggart’s objections and is incompatible with the findings of the Special theory of relativity. [Savitt 2000] In particular the tensed view of time requires a privileged Now, which cannot be squared with the principle of relativity. Does this leave us with a tenseless view of time, as McTaggart claimed, according to which there is only a static ‘before-after’ relation between events? Events are juxtaposed like beads on a string (B-series). The physical world just is, it is a block universe. The passing of time is a human illusion. There is an alternative between these extreme positions (of the tensed view versus the block universe). The tenseless view is mistaken in equating tenselessness with changelessness. [Grünbaum 1973, 325] [Smart 1963, 138-40] The physical occurrence of events does not exclude change. Change occurs in the transition between events, even if these events are ordered in four-dimensional Minkowski space-time. Consider, for instance, the famous twin paradox. One of the two twins is a space traveller who returns to earth after a visit to a distant star only to find that his twin brother, who remained on earth, has aged more than he has. This can be explained within the STR by a consideration of the effect of motion on the world lines of the two twins: the world line of the earth-bound twin turns out to be longer than the world line of the travelling twin [Lockwood 2005, 46–51] because the traveller’s clock, including his biological clock, is subject to time dilation effects. If we were to take the heart beats of the twins as our clocks, these electromagnetic signals, which the twins exchange during the journey, will be subject to the relativistic Doppler Effect with the result that the number of signals the twins receive respectively will not be equal. A physical change occurs. The relational view already emphasized that time was the order of succession of events. In the STR the relational notion of the ‘order of successive events’ becomes restricted to the light cone structure of Minkowski spacetime. The crucial notion of the finite propagation of light in STR limits the connectibility of reference frames to time-like connected events. It is interesting to note that several early commentators on the Special theory already proposed a dynamic interpretations of space-time, according to which worldliness propagate through space-time and acquire a history. [Cunningham 1915, § 60] [Schlick 1917, 181] [Reichenbach 1958, 183] The crucial point is that traditionally the STR only considers purely kinematic aspects of the propagation of worldlines and the relations between reference frames. But these kinematic relations have entropic aspects, as revealed in the asymmetric behaviour of electromagnetic radiation. It is these entropic aspects of worldliness, which give the relationist the purchase to consider a dynamic view of spacetime. This fits in well with a specific argument from entropy, which Einstein employed against Kurt Gödel’s idealistic interpretation of the Special theory of relativity [Gödel 1949]. Einstein considers the question of the temporal direction of events. Imagine we send a signal from B to A through P. This is an irreversible process. On thermodynamic grounds he asserts that a time-like world line from B to A through P in a light cone takes the form of an arrow making B happen beforeP and AafterP (see Figure I).

Figure I: Einstein's consideration of the (local) direction of time in response to Gödel's idealistic interpretation of the Special theory of relativity. A time-like world line exists between A and B, which lies within, not outside the light cone.

10This secures the ‘one-sided (asymmetrical) character of time (…), i.e., there exists no free choice for the direction of the arrow.’ [Einstein 1949a, 687] This is true at least if points A,B and P are sufficiently close in cosmological terms. But the asymmetrical character of time is here based on a fundamental earlier-later or before-after relation between physical events without reference to an observer. There is an event, B, at which the signal is emitted. And there is a later event, A, at which the signal is received. This whole event is irreversible. There is an entropy gradient between the state of events at B and A. The assessment of this differential entropy between the two locations does not depend on a particular reference frame. According to a fundamental result of the Special theory of relativity the entropy of a system is frame-independent. [Einstein 1907, § 15] Thus all time-like connected frames will agree on the order of the succession of events, even if there is disagreement about the simultaneity of these events. It may be objected that this entropic theory of time could not form the basis for a general dynamic theory of time. As is well known the second law of thermodynamics is a statistical principle; there is an extremely low probability of a reversal of events in our observable space-time regions. Although it is unlikely in the life-time of the universe, the second law permits a spontaneous reheating of a glass of cold water by a rearrangement of the molecules. But the arrow of time is supposed to be one-directional. This objection need not worry the relationist in the present context, because the concern here is to establish the possibility of a dynamic interpretation of space-time not on a global but local scale. Locally, the entropy gradient points in the direction from B to A. All time-like connected observers agree. For the relationist this establishes, within local space-time regions, an order of the succession of events and thereby physical time for time-like related frames. Reichenbach expressed such a view in his hypothesis of the branch structure:

The paradox of the statistical direction (of time) was solved, in a continuation of Boltzmann’s ideas, by the recognition of the sectional nature of time direction: a large isolated system can indeed define a time direction in a section of its whole temporal development, if this section is rich in branch systems governed by the laws of statistical isotropy. [Reichenbach 1956, 207] (cf. [Davies 1974, § 3.4])

11Although Einstein endorsed, from time to time, the unreality of time, his whole theory of time-space is relational. It points towards a philosophy of becoming since physical time is constituted by the asymmetric, invariant order of physical events in space-time. There are several statements in Einstein’s work which suggest this relational reading of his space-time concept:

I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. [Einstein 1920, vi]
There can be no space nor any part of space without gravitational potentials; for these confer upon space its metrical qualities, without which it cannot be imagined at all. The existence of the gravitational field is inseparably bound up with the existence of space. [Einstein 1922b, 21]

12It is not the job of the philosopher to put Einstein’s philosophical thinking into a straight-jacket. The philosopher must evaluate whether the philosophical consequences, which the physicist claims to follow from the physical discoveries, do indeed follow. (As we have seen prominent physicists like Eddington, Gödel and Weyl explicitly claimed that the block universe was a philosophical consequence of the STR, whilst Einstein wavered in his support for a static universe.) This is a question of conceptual evaluation, not empirical testing. We have indicated that a dynamic interpretation of space-time is possible and compatible with the STR. It is possible if we consider the entropic aspects of space-time events and align the STR to relationist thinking. There are similar philosophical presuppositions and consequences at work in Einstein’s views on quantum mechanics.

IV. Quantum Mechanics

13Above we characterized the philosophical consequences of scientific theories—they do not follow deductively but are nevertheless conceptual consequences of these theories. As such they are not ‘justifiable by scientific methods.’ [Frank 1949b, 355] Einstein revolutionized our philosophical notion of time by relativizing both time and simultaneity to particular inertial reference frames. He thereby uprooted a prior philosophical commitment to absolute time. Scientific revolutions or innovations often upset earlier philosophical presuppositions. Such presuppositions seem to be unavoidable in science. But in his discussions of quantum mechanics, for example, Einstein was guided by a traditional notion of causality. In his lifelong opposition to the Copenhagen interpretation of quantum mechanics he disregarded the lesson about thought necessities, which the theory of relativity had taught him. According to Einstein, quantum mechanics was incomplete because it only permitted statistical statements about ensembles of atoms. Quantum mechanics was unable to make precise spatio-temporal predictions about the trajectories of individual atoms. Heisenberg’s indeterminacy principle, whose validity Einstein fully endorses, prevents deterministic spatio-temporal determinations of atomic trajectories. The ability to make such predictions was for Einstein one of the fundamental requirements of science. Only differential equations, he said, would satisfy the demand of the physicist for causality. [Einstein 1927, 255] Note that Einstein associates the notion of causality with the availability of differential equations and therefore predictive determinism. It is a functional view of causality, because it reduces the causal relation between two parameters to a functional relation between the rate of change with respect to time of one parameter, say velocity, ν, and the application of a force, F. (See [Frank 1932] [Weinert 2004, ch. 5.1]) This demand for deterministic causality is a reflection of Laplacean determinism, which the quantum theory was hoping to overcome. When Einstein warns that a probabilistic view of quantum mechanics will lead to its incompleteness, on the grounds that it does not allow for precise space-time trajectories of atomic particles, he clings to one of the most venerable presuppositions of classical physics. In his criticism of Newtonian mechanics, Einstein bemoans the inability to jettison fundamental notions like absolute space and time. But in his view of quantum mechanics he himself relies on a presupposition inherited from classical physics, e.g. the belief in strict determinism.

14It has often been debated whether Einstein’s fundamental worry about quantum mechanics derived from fear of ‘action-at-a-distance’, rather than his belief in strict causality. (See [Howard 1993] [Fine, 1986] [Cushing & McMullin, 1989]) In quantum mechanics two particles, issued from a common source with particular spin alignments, may be so far separated in space-time that no known causal interaction can take place between them. Yet a measurement of the spin property of one particle will instantly change the spin direction of the other particle even over cosmic distances. Einstein found such ‘action-at-a-distance’ unpalatable. The Born interpretation offered him a way out of the dilemma. According to the Born rule, which Einstein embraced [Einstein 1940, 923-4], the square of the wave function, |Ψ|2, only delivers statistical statements about the probability of events, not the determination of actual events in space and time.

15Einstein accepted the quantum theory as a heuristic device because the Born rule told him that it only delivered an incomplete description of reality. An incomplete description may not satisfy the ‘causal’ demand for differential equations. This incompleteness charge gave him the freedom to believe that a complete description of atomic reality could be found. Einstein yearned for a complete and direct description of reality. [Einstein 1940, 924] By this he means a direct representation of the actual space-time events, rather than a probability distribution of possible outcomes of measurements. Such a complete description of actual events in space-time will avoid non-local effects. For it will be subject to the ‘strict laws for temporal dependence.’ [Einstein 1940, 923] [Einstein 1948, 323] In physics the ‘strict laws for temporal dependence’ are typically expressed in differential equations. The incompleteness charge against QM gave him the freedom to believe that a complete description of reality would recover the differential equations, which described the temporal evolution of real physical systems in space-time. The Schrödinger equation is of course a differential equation, which spells out the time evolution of a quantum system. However, this does not satisfy Einstein, because the Schrödinger equation describes time evolution in an abstract Hilbert space.

16Einstein’s insistence on a complete description of real events and his functional view of causality leads me to agree with Fine [Fine 1986, 97–103] that Einstein’s concern with nonlocality was not primary. It was a consequence of a deeper concern with strict causality. Einstein actually maintains that a renunciation of the principle of locality would render empirically testable laws impossible. And locality is expressed in differential equations in real space-time. [Einstein 1927, 261] Since the discovery of Bell’s inequalities in the 1960s much effort has gone into distinguishing various senses of ‘locality.’ If we speak, with Einstein, of the ‘mutually independent existence of spatially distant things’, we formulate a principle of spatial separability. (See [Einstein 1948] transl. in [Howard 1993, 238]) In view of the results of quantum mechanics, we must distinguish this principle of separability from the principle of locality. This principle has been formulated in a number of ways. Einstein locality means that no ‘faster-than-light-signals’ should be permitted to propagate between spatially separated quantum systems. But locality can also mean that a spin measurement performed on one system, which is spatially separated from another system in the sense of satisfying Einstein locality, cannot influence the spin state of the other system. This type of locality Einstein calls the ‘principle of local action’.

17However various types of entanglement have been observed between quantum systems, which display degrees of correlations of their spin properties even though they are spatially separated in the sense of Einstein locality. Einstein’s principle of local action is violated in quantum mechanics. [Cushing & McMullin 1989] [Howard 2004, §5] Schrödinger dubbed this now familiar type of correlation ‘entanglement of our predictions or of our knowledge’ concerning the quantum states of a photon pair. [Schrödinger 1935, 827] Recently, the programme of decoherence has identified environmental entanglement, i.e. the irreversible loss of interference terms to the environment in the creation of classical states. Quantum mechanics was Einstein’s bête noire. His opposition never faltered. Today it is generally regarded as untenable. Quantum systems manifest degrees of entanglement over large distances. Einstein’s ‘spooky action-at-a distance’ is a laboratory reality.

18We see in Einstein’s work both the role of presuppositions (causality in QM) and the effect of scientific discoveries on fundamental notions (time, space, mass). Less well-known is that Einstein makes some significant contributions to our understanding of scientific theories. In particular his views harbour a possible solution to the vexing question of the representational power of scientific theories.

V. The Representational Nature of Scientific Theories

19To Einstein, scientific constructs (laws, models, and theories) are free inventions of the human mind. No amount of inductive generalizations can lead from empirical phenomena to the complicated equations of the theory of relativity. But science is not fiction. Science assumes the existence of an external world. Scientific theories are statements about the external world. ‘Physics is the attempt at the conceptual construction of a model of the real world, as well as its lawful structure.’ (Quoted in [Fine 1986, 97], italics in original) Einstein therefore depicts scientific knowledge as a synthesis of reason and experience, which raises the question of the representational nature of scientific constructs.

20Einstein makes a famous distinction between constructive theories and principle theories. [Einstein 1919; Miller, 1998, 125] The role of a constructive theory is to propose models, which assign an underlying structure to the observable phenomena. The kinetic theory of gases models gas molecules as if they were billiard balls. Early atom models modelled atoms as if they were tiny planetary systems. The role of a principle theory is to propose fundamental principles: the laws of thermodynamics, the principles of relativity, of covariance and invariance, and the constancy of light. These principles constitute constraints on the construction of models and theories. They forbid the occurrence of physical events, like superluminary velocities or perpetual motion machines.

21All scientific theories give rise to a philosophical question: how do scientific theories relate to the external world? Ernst Mach’s answer is cast in terms of phenomenalism; Duhem’s answer in terms of holism; Poincaré’s answer in terms of conventionalism. Einstein’s answer was influenced by these authors but it was also particularly pragmatic, e.g., it was shaped by his work on relativity. Firstly, Einstein was primarily concerned with what he called principle theories, like the theory of relativity. Here the role of constraints comes to the fore. Einstein often declares the world of experience as the final arbiter of the validity of scientific theories. In Popperian fashion he regarded all scientific theories as falsifiable. But empirical evidence, in the theory of relativity, is only one form of constraint. Scientific theories present hypothetical ‘pictures’ of the external world. But Einstein was no naïve realist. A scientific theory constructs a coherent and logically rigid account of the available empirical data. Logical consistency was Einstein’s second constraint on theories since he believed in the mathematical simplicity of nature. [Einstein 1933, 274] The coherence of a theory may always come under threat with new empirical discoveries. There is nothing final about the representation of a scientific theory of the external world. Theories are free inventions, yet they must retain roots in the empirical world. Does this mean that there is always a plethora of competing theoretical accounts, which nevertheless are compatible with the available evidence? If this were the case scientific theories would face the serious problem of underdetermination. That is, there would always be a number of theories, which are able to explain the empirical evidence, although they fundamentally disagree about their theoretical structure. For instance the Copernican model of the solar system (1543) explains the same observational evidence as the Ptolemaic account although the Copernican model is based on the principle of heliocentrism, while the Ptolemaic account embraces the principle of geocentrism. In this situation Einstein recommends pragmatically to distinguish a logical from a practical point of view. From the logical point of view, Einstein grants that there are always numerous theoretical accounts, which could in principle account for the available evidence. For there seems to be no limit to the number of competing constructions, which, at least in principle, could claim to give a coherent and simple account of the available phenomena. This is due to the fact that theories are the result of human ingenuity. Yet in practice, the number of available theories is always limited. Einstein did not believe that many competing representations of the empirical world could be sustained. He goes even further: he believes that there is one correct theory. The structure of the external world has the power to eliminate many rival accounts. The surviving theory displays such a degree of rigidity that any modification in it will lead to its falsehood. ‘Rigidity here means that the theory is either true or false but not modifiable.’ [Einstein 1950b, 350; 1936] (cf. [Hentschel 1992], [Scheibe 1992] and [Weinberg 1993]) Einstein illustrates the lack of underdetermination, from the practical perspective of the working physicist, by the analogy of solving a crossword puzzle. Although we are free to insert any word into the columns and rows of a word puzzle, this freedom is very restricted. Only one word will ‘fit’, only one word will solve ‘the puzzle in all its forms.’ [Einstein 1936, § 1] The structure of the external world practically determines the form of the theoretical system. [Einstein 1918b; 1933]

22Going beyond Einstein it will also be useful to split the space of possible theories or models into alternative and rival accounts. Alternative accounts, like the Schrödinger and Heisenberg pictures in quantum mechanics are mathematically equivalent; covariant formulations of physical laws in the General theory of relativity are form-invariant. They pose no problem in terms of underdetermination. Rival accounts like Lorentz’s and Einstein’s models of the kinematics of reference systems are based on incompatible theoretical principles. Lorentz’s account of time dilation and length contraction postulates an absolute rest frame, whilst Einstein’s motivation was to abandon all need for absolute reference frames. Rival accounts therefore pose a problem from the point of view of underdetermination. In the practice of science, however, there is little underdetermination. How can this be explained? If we look at Einstein’s philosophical writings about physics, we notice his insistence on constraints such as unification and the logical simplicity of a theory; he also holds that evidence is the final arbiter of a theory’s fate. Einstein locality, logical simplicity and unification are methodological constraints, since they are principles of the methods of science. Compatibility with available and new evidence is an empirical constraint. In the present context the methodological constraints are of lesser importance than some of the other constraints, which are associated with the theory of relativity. Looking at Einstein’s way of doing physics, we notice his employment of a number of theoretical constraints, since they derive more particularly from the theories of relativity. In particular, as we shall see, the light postulate, relativity principles, covariance and invariance principles. We can characterize constraints as restrictive conditions of an empirical or theoretical kind, which descriptive and explanatory accounts must satisfy to count as viable candidates for the scientific description and explanation of the natural world. With respect to the theory of relativity, Einstein holds that the interplay of specific constraints—like covariance, invariance, relativity—creates a fit of the theory or model with the evidence extracted from the external world. Any modification, he holds, would destroy the coherence of the theory of relativity. [Einstein 1918b; 1919; 1933] This provides a clue to a solution of the puzzle of how theories manage to represent the world. A theory ‘represents’ a section of the empirical world, if it satisfies a certain number of constraints. The representation is illustrated in terms of fit, as in the analogy of the crossword puzzle. But ‘fit’ should be understood in terms of satisfaction of constraints. [Weinert 2006] The representation is not an image, nor need it be perfect or absolute.

In order that thinking might not degenerate into ‘metaphysics’, or into empty talk it is only necessary that enough propositions of the conceptual system be firmly enough connected with sensory experiences and that the conceptual system, in view of its task of ordering and surveying sense-experience, should show as much unity and parsimony as possible. [Einstein 1944, 289]

23We have thus assigned to pure reason and experience their places in a theoretical system of physics. The structure of the systems is the work of reason; the empirical contents and their mutual relations must find their representation in the conclusions of the theory. In the possibility of such a representation lies the sole value and justification of the whole system, and especially of the concepts and fundamental principles which underlie it. [Einstein 1933, 272]

24As it changes with the changing nature of constraints, fit comes in degrees. In the simplest case, a model represents the topologic structure of a system; e.g. a heliocentric scale model of the solar system represents the spatial arrangement of the planets around the sun. The models used in the theory of relativity are more sophisticated structural models, which combine a topologic with an algebraic structure. The algebraic structure of the model expresses the mathematical relations between the components of the model. Consider, for instance, Einstein’s thought experiment, which involves two discs whose circumference and diameter are to be measured. [Einstein 1920, 80; 1922a, 58–9] Let the discs be arranged in such a manner that disc B rotates uniformly about a common axis with disc A. This is its topologic aspect. But the main interest lies in the algebraic structure, e.g., how the parameters on the two discs will be measured. To carry out the measurements, measuring rods are placed along the radius and tangentially to the edge of the disc. A does not rotate so that the ratio of circumference to diameter is equal to π. From the point of view of A the ratio C/D on B will be greater than π. Due to length contraction of the tangential rods the circumference will appear greater on B than on A. Now place two similar clocks on B, one at the centre, C1 and one at the periphery, C2. Judged from A, C2 will go slower than C1. We may assume that no faulty instruments are involved. These respective measurements are objective. Observers on the respective discs will regard their respective measurements as accurate. Mathematically, the thought experiment stresses the effect of motion on the measurement of the parameters. Note that the algebraic structure implied by Euclidean geometry fails and must be replaced by a structure provided by Riemannian geometry.

25Let the empirical facts, methodological principles and theoretical postulates constitute a constraint space. The theory of relativity satisfies a number of empirical and theoretical constraints, which improve its fit to the external world. The empirical facts comprise Einstein famous predictions: the red shift of light as a function of gravitational field strengths and the bending of light rays in the vicinity of strong gravitational fields. He also explains the perihelion advance of Mercury and other planets. In the theory of relativity the most important theoretical constraints are the following:

1) The postulation of the constancy of the speed of light

26It had been known since Roemer’s first determination of the speed of light in 1675 that light propagates at a finite velocity of approximately 300 000 km/s. Einstein turned this value into a theoretical postulate such that the speed of light becomes the limit velocity, which no material particle can reach. In the language of the Minkowski representation of space-time this means that from any event, E, light signals converge from the past and diverge into the future at a constant speed, forming past and future cones. All inertial observers will see the angle of convergence and divergence inclined at 45° to the vertical. The light cones do not tilt. And all observers measure the same velocity for c, irrespective of the direction and their state of motion with respect to the light source.

2) Principles of Relativity

27Einstein began his 1905 paper on the Special theory of relativity by a consideration of standard attempts to explain Faraday’s induction current. He complained that according to the then current view an asymmetry of explanation for an observationally indistinguishable phenomenon occurred. If the coil is in motion with respect to the magnet at rest (in the ether), the charges in the coil experience a magnetic force, which pushes the electrons around the coil, inducing a current. If the magnet is in motion with respect to a coil at rest, the magnetic force is no longer the cause of the current, for no magnetic force applies to charges at rest. The magnet now produces an electric field in the coil, resulting in the current. To avoid this asymmetry of explanation—an asymmetry not present in the phenomena—Einstein postulated the physical equivalence of reference frames. In its general form the principle of relativity states that all coordinate systems, which represent physical systems in (uniform or non-uniform) motion with respect to each other, must be equivalent from the physical point of view. [Einstein 1920, 59, 97–8] In other words, the laws which govern the changes that happen to physical systems in motion with respect to each other are independent of the particular coordinate system, to which these changes are referred. So it is not admissible that an induced current is explained differently, depending on whether the magnet or the coil is in motion.

3) Invariance and Symmetries

28We can understand reference frames (in the STR) as idealized physical systems whose space-time coordinates are given by rigid rods and idealized clocks. They are subject to various symmetry operations, like rotation or translation in space and time. The Special theory obeys the Lorentz-transformations, because the Galilean transformations fail as we approach the speed of light. The Galilean transformations, for instance, result in different values for the speed of light, if we change from a stationary to a moving reference frame. The Lorentz-transformations deal with space-time transformations of a global kind; that is, they are constant throughout the space-time region. They form a symmetry group. (The General theory requires a larger symmetry group.) Symmetry constraints emphasize physical aspects: the symmetry operations return some values of parameters as invariant (like the space-time interval) and leave others as variant (like the clock readings in different reference frames, in constant motion with respect to each other). Symmetries result from transformations that leave all relevant structure intact. We are familiar with such symmetry transformations in daily life. We easily change the clock as we travel between different time zones. But the tennis games we play at home and abroad are the same as far as the physical parameters are concerned.

4) Covariance

29Covariance is prima facie a mathematical constraint. The modern use is quite different from the way Einstein uses the notion of covariance. Einstein associates covariance with the transformation rules of the theory of relativity.

30He imposes on the laws of physics the condition that they must be covariant a) with respect to the Lorentz transformations (in the Special theory of relativity) [Einstein 1949c, 8; 1950, 346] and b) to general transformations of the coordinate systems (in the General theory). [Einstein 1920, 54–63; 1950, 347] The theory of relativity will only permit laws of physics, which will remain covariant with respect to these coordinate transformations. [Einstein 1930, 145–6] This means that the laws must retain their form (‘Gestalt’) ‘for coordinate systems of any kind of states of motion.’ [Einstein 1940, 922] They must be formulated in such a manner that their expressions are equivalent in coordinate systems of any state of motion. [Einstein 1916; 1920, 42–3, 153; 1922a, 8–9; 1940, 922; 1949a, 69] A change from coordinate system, K, to coordinate system, K', by permissible transformations, must not change the form of the physical laws. This leads to the characterization of covariance as form invariance. [Weinert 2007a] Einstein often illustrates covariance with respect to the space-time interval ds2. [Einstein 1922a, 28] In Minkowski space-time, the space-time interval ds2 is expressed as an invariant expression in what remains essentially a quasi-Euclidean space:

312.6 If the expression satisfies covariance it must remain form-invariant under the substitution of a different coordinate system, i.e.,

ds= 0 = ds'2:

32The equation for the space-time interval, ds, remains form-invariant if K is substituted by another quasi-Euclidean inertial frame, K', as indicated by the coordinates Δx'ν. For Einstein a fit must exist between the theory of relativity and the material world. We explicated fit in terms of the satisfaction of constraints, associated with the theory of relativity. If their amount and their interconnections can be increased, then many scientific theories will fail to satisfy the constraints. It will usually leave us with only one plausible survivor. For instance, after the development of the Special theory, Einstein increased the constraints on an admissible relativity theory. Inertial reference frames should not be privileged over non-inertial frames. This extension of the relativity principle and the demand of covariance lead to the General theory of relativity. This theory was able to explain the perihelion advance of Mercury, where Newtonian mechanics had failed. It would be exaggerated to claim that there is such a tight fit between the theory and the world, that there is a one-to-one mapping of the theoretical with the empirical elements. Einstein, in fact, rejected naïve realism. [Einstein 1944, 280–1] Due to the need for approximations and idealizations there will always be theoretical structure, for which there is no direct empirical evidence. For instance, the evidence does not tell us whether space-time exists, devoid of all matter. But Einstein holds that one theory always satisfies the constraints better than its rivals. It does not follow from this argument that the survivor—let us say the theory of relativity—will be true. It does follow that the process of elimination will leave us with the most adequate theoretical account presently available. New experimental or observational evidence may force us to abandon this survivor. The desire for unification and logical simplicity may persuade us to develop alternative theoretical accounts. Einstein’s attempt to extend the principle of relativity from its restriction in the Special theory to inertial reference frames to non-inertial reference frame in the General theory is a case in point. Although Einstein does claim that there is one correct theory, he cannot mean this in an absolute sense. His insistence on the eternal revisability of scientific theories, including constraints, speaks against this interpretation. What he must mean is that there is always one theory, at any one point, which best fits the available evidence. This one theory copes best with all the constraints, which logic and evidence erect; but there is nothing final about such a theory; it will always remain falsifiable.

VI. What is Einstein’s philosophical allegiance?

33He has been appropriated by neo-Kantians, realists, positivists and holists alike. Each camp can claim textual evidence for its preferred interpretation [Frank 1949] [Holton 1965; 1973] [Howard, 1990; 1993; 2004]. In a number of papers, Don Howard has promoted the view that Einstein agreed with Duhem’s underdetermination thesis, and generally adopted a holist view of theory confirmation, e.g. only a theory as a whole body of statements faces the verdict of experimental evidence. [Howard 1990; 1993] This view implies the denial of crucial experiments, and a certain latitude of choice of conceptual elements with respect to the empirical evidence. It is akin to conventionalist ideas associated with Poincaré. According to this interpretation there exist logically incompatible theories, which nevertheless are equally compatible with the evidence. The question is whether Einstein’s way of doing physics is compatible with this strong holist interpretation.

34If we look at the development of the theory of relativity, we notice that there are several problems with this holist interpretation. Einstein’s insistence that at any one point in the history of science only one rival theory is the most adequate theory (alone capable of satisfying all the constraints) suggests that confirmation holism does not necessarily imply the existence of equally good competitors, e.g. observationally indistinguishable but ontologically divergent theories. In particular, Einstein’s work on relativity shows that other than empirical constraints are at hand to distribute credibility unevenly over the space of possible theories. Einstein actually employs these constraints, as we have seen, to argue in favour of the relativity theory. In his discussion of the rotating disc thought experiment, Einstein explicitly avoids saving Euclidean geometry ‘come what may’, although this is a conventionalist stratagem.

35We should also note that neither Duhem nor Quine were the complete holists they are made out to be. Discussions of holism usually highlight the radical underdetermination of an entire theory by empirical evidence. [Howard 1993] It is often overlooked that both Duhem and Quine accepted the coherence of scientific theories as a constraint, as much as Einstein did. According to this aspect, theories are structured conceptual systems, which entertain many mathematical and conceptual interrelations between them. This aspect makes the deducibility of empirical laws from more fundamental laws possible. Duhem, for instance, appeals to an analogy of science with an organism,

in which one part cannot be made to function except when the parts that are most remote from it are called into play, some more than others, but all to some degree. [Duhem 1954, 187–8] [Weinert 1995]

36The coherence aspect corresponds to Einstein’s insistence on the rigidity of scientific theories, for which he uses the analogy of the crossword puzzle (Section V). This rigidity shows that changes in one part of the theory will affect other parts of the theory, so that the ‘latitude of choice’ is more restricted than holism is ready to admit. The presence of constraints and the concern for ‘fit’ point in the direction of a stronger form of realism. Einstein is fond of the view that theoretical constructions are not inductive generalizations from experience but free inventions of the human mind. Nevertheless there must be a ‘fit’ between the theoretical expressions and the external world. This fit is achieved in the theory of relativity, we suggested, through the introduction of constraints. The increase in constraints—extension of the relativity principle to non-inertial motion, the introduction of the principle of equivalence and the form-invariance of laws (covariance principle)—takes Einstein from the STR to the GTR. If there is indeed a ‘fit’ between what the theory says and what the material world presents, the question of realism returns.

37Consider, for instance, Einstein’s view of Poincaré’s conventionalism about geometry. Einstein reflected on the status of geometry in the light of the GTR. [Einstein 1921; 1922b] He distinguishes an axiomatic and a practical geometry. He agrees with Poincaré that the laws of axiomatic geometry are based on conventional choices, say in favour of Euclidean geometry and its axioms. But Einstein sees an important difference between an axiomatic and a practical geometry: the former makes no reference to the world of experience, whilst the latter does.

The question whether the practical geometry of the universe is Euclidean or not, has a clear meaning, and its answer can only be furnished by experience. [Einstein 1922b, 23]

38According to Einstein this view of geometry was an essential prerequisite for the development of the GTR.

The question whether the structure of [the four-dimensional] continuum [of space-time] is Euclidian, or in accordance with Riemann’s general scheme, or otherwise, is, according to the view which is here being advocated, properly speaking a physical question which must be answered by experience, and not a question of mere convention to be selected on practical grounds. [Einstein 1922b, 39]

39What counterbalances the strong holist interpretation of Einstein’s views is Einstein’s repeated insistence that out of many rival theories there is one with the most adequate fit and that practical geometry allows fewer conventional elements than Poincaré is ready to concede. From the point of view of Einstein’s problem situation, his philosophical attitude was characterized during his lifetime as a form of critical realism. Einstein certainly approved of this way, in which Lenzen and Northrop characterized his epistemological position (See [Lenzen 1949] [Northrop 1949] [Einstein 1949b, 683]). It simply regards scientific theories as hypothetical constructs, free inventions of the human mind. But there is also an external world, irrespective of human awareness. To be scientific, theories are required to represent reality. They represent reality by satisfying both empirical and theoretical constraints. A theory is not a mirror image of the world. It is a mathematical representation, which provides coherence of the empirical data and shows their interconnections. Theories are hypothetical, approximate constructions, which in a process of fitting and refitting, deliver a coherent picture of the external world. In human efforts to understand the world, experience and reason go hand in hand. In modern terms, Einstein’s relativity theory may be characterized as leading to a form of structural realism. [Weinert 2007b] The relativity theories are principle theories, which employ general coordinate systems to explain the behaviour of physical systems in uniform or accelerated motion with respect to each other. Such coordinate systems are well-suited to represent physical systems, since they can be regarded as structural models of the target systems. Physical systems typically display structures, consisting of relata and relations. As the models of the relativity theories are able to represent both the topologic and algebraic aspects inherent in physical systems, they can be said to represent the structure of physical systems. Einstein declares that ‘the concepts of physics refer to a real external world, i.e., ideas are posited of things that claim a ‘real existence’ independent of the perceiving subject (bodies, fields etc.)’ [Einstein 1948, 321, transl. Howard, 1993, 238] These representational claims cover both the relata (fields, material particles, reference frames) and the relations (the mathematical relations between the relata). Given that scientific theories manage to represent aspects of the external world, what picture of reality does the relativity theory espouse?

VII. What is Reality?

40The structural realist makes the assumption that there is a structured external material world. Theories which ‘fit’ a domain of this external world present us with a view of physical reality. Such views have changed with the progression of physical theories. There was a time when physicists liked to think of the world as a massive clockwork. Particles populated the universe. Only their primary qualities mattered. They were at rest or in constant regular motion. Einstein suspected that this classical picture was mistaken. It required Newton’s absolute space and time and action at a distance. For Einstein, physicists like Heinrich Hertz, Michael Faraday and James Maxwell made significant steps in the revision of the physical worldview when they introduced fields as fundamental physical entities. Einstein regarded the theory of relativity as a field theory, which dispenses with action at a distance. But Einstein was never able to overcome the fundamental dualism in the physical worldview between particles and fields. This may be the reason why we find in Einstein’s work two concepts of physical reality. In his relativistic thinking about the nature of reality, Einstein became one of the first physicists to realize the significance of symmetries and invariance in science as a new criterion of what the physicist should regard as objective and physically real.

41The starting point is the principle of relativity. In the STR it states that all reference systems, which represent physical systems in motion with respect to each other, must be equivalent from the physical point of view. But we have already observed that in the transition from one reference system to another some properties change. The classic examples are temporal and spatial measurements, as well as mass determinations. From the phenomenon of time dilation and the relativity of simultaneity some physicists concluded that time cannot be a physical property of the universe. Some transitions to other reference systems do not, however, affect the physical properties. The classic example is the velocity of light in vacuum. The Special theory of relativity postulates that the value of ‘c’ will be the same in all time-like connected reference systems, which move at constant speed with respect to each other. Some physical properties are immune to changes in reference systems, while others are not. The velocity of light is the same in all directions and irrespective of whether it is emitted from a moving or stationary source. But the wavelengths of light depend on the movement of the source (Doppler Effect). Symmetry principles, like the geometric symmetries of the STR, show the invariant aspects of the equations, which apply to Minkowski space-time. While in classical physics, many properties, like time, mass, space, energy were regarded as ‘absolute’, in the Special theory of relativity, many properties became relational. Relational means that they cannot be considered in abstraction from the coordinate values in particular reference frames. So the question arises, ‘What is real?’ For it seems that if two observers disagree about the length of an object or the simultaneous occurrence of an event, they cannot both be right. An object, so it appears to us, cannot have two different lengths at the same time.

42But we need to take into consideration the lessons of relativity.

43The answer to the question of reality is embedded in the mathematics of the Special theory of relativity. Minkowski’s four-dimensional interpretation of space-time provided Einstein with a new criterion for the physically real. Physics, he says, deals with ‘events’ in space and time. [Einstein 1949c] Temporal and spatial measurements varied from reference frame to reference frame. They could not be physically real. But the space-time interval, ds, remained invariant for every observer. It was therefore to be regarded as real. [Einstein 1920 App. II, 1922a, 23–31; 1936, 34-41] [Scheibe 1981] In general, what a scientific theory tells us to regard as ‘real’ is what remains invariant in transitions between different reference frames. These transitions are governed by transformation groups. In the STR the Lorentz transformations take us from one reference system to another. They state how the spatial and temporal coordinates of one reference systems translate into another. As we change between various reference systems, say, from stationary to constantly moving systems, the laws of physics express invariant properties of physical systems, like the space-time interval of equation (1). Einstein at first considered inertial systems and later accelerated systems. The laws of physics must retain their form (remain covariant) under the substitution of coordinate systems through all transformations. [Norton 1989; 1993] What remains invariant is to be regarded as the physically real.

44More specifically Einstein advanced his ‘point-coincidence argument’. Einstein explicitly claims that the laws of physics are statements about space-time coincidences. In fact only such statements can ‘claim physical existence’. [Einstein 1918a, 241; 1920, 95] [Norton 1992, 298] As a material point moves through space-time its reference frame is marked by a large number of co-ordinate values x1, x2, x3, x4. This is true of any material point in motion. It is only where the space-time coordinates of the frames intersect that they ‘have a particular system of coordinate values x1, x2, x3, x4 in common’. [Einstein 1916a, 86; 1920, 95] In terms of observers, attached to different reference systems, it is at such points of encounters that they can agree on the temporal and spatial measurements. Many physicists concluded as a philosophical consequence of the relativity theory that only the invariant can be the physically real. [Eddington 1920] [Weyl 1921] [Born 1953] [Dirac 1958] [Wigner 1967, Part I] [Planck 1975]

45However, as Born pointed out frame-dependent properties may also lay claim to reality. [Born 1953] [Weinert 2004, ch. 2.8] Clock and meter readings in particular reference frames are not perceptual illusions of observers. These measurements have perspectival reality since they are relational. They are relational in the sense that they must be derived from the coordinate values of particular reference frames. Born compared the perspectival realities to projections, which are defined in a number of ‘equivalent systems of reference’.

In every physical theory there is a rule which connects projections of the same object on different systems of reference, called a law of transformation, and all these transformations have the property of forming a group, i.e. the sequence of two consecutive transformations is a transformation of the same kind. Invariants are quantities having the same value for any system of reference, hence they are independent of the transformations. [Born 1953, 144]

46The Lorentz transformations show, Born adds, that quantities

like distances in rigid systems, time intervals shown by clocks in different positions, masses of bodies, are now found to be projections, components of invariant quantities not directly accessible. [Born 1953, 144]

47This leads to a modified view of physical reality, which is still compatible with the Minkowski presentation of the theory of relativity. It admits both frame-dependent and frame-independent realities. The invariant is not the only reality but it is the focus of physics. What now becomes of the criterion that only the invariant is to be regarded as real? It derives from the fact that physics is not interested in perspectival realities. Physics is interested in the underlying structures, which relate the different perspectives. Relativistic physics is interested in the structure of space-time. This structure can be described mathematically, as Minkowski has done. It will tell us that the space-time interval, ds, is invariant across the reference systems. The particular perspectives then result from attaching clocks and rods to the world lines, which crisscross space-time. Once the symmetries tell us what remains invariant across reference frames, it is not difficult to derive the perspectival aspects, which attach to different reference frames, as a function of velocity. The theory of relativity led Einstein to an invariance view of reality. But his opposition to the Copenhagen interpretation of QM led him to a more classical separability view of reality: spatially separated system, A and B, which obey Einstein locality, possess physical properties, which are not immediately affected by external influences on either of the systems. [Einstein 1948]

VIII. Philosophy and Science

48Philosophical consequences do not flow from scientific theories with logical compulsion. Nevertheless, certain kinds of philosophical positions are more akin to scientific findings than others. For instance, a belief in Newton’s absolute space and time and the invariance of mass has become incompatible with the findings of STR. An adherence to Euclidean geometry has become incompatible with the GTR. Einstein’s belief in deterministic causality and the principle of local action has become questionable in the light of QM. He once accused philosophers of dragging concepts into the den of the a priori.

Philosophers had a harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism, where they are under our control, to the intangible heights of the a priori. [Einstein 1922a, 2, italics in original]

49Sometimes, however, the very foundations of science become shaky. This happened twice in Einstein’s lifetime: relativity and quantum theory. Then the physicist himself is forced to become a philosopher through a ‘critical contemplation of the theoretical foundations’. The philosopher-scientist is a familiar figure in the history of science (Newton, Leibniz, Darwin, Bohr, Born, Duhem, Planck, Poincaré). Max Born gave expression to the role of the philosopher-scientist when he wrote that

History has shown that science has played a leading part in the development of human thought. [Born 1949, 75]

50This philosophical turn of scientists is due to a basic epistemological situation in the sciences, of which Einstein was very aware: the need to map symbolic systems (theories, models, equations) onto an independently existing reality. This mapping has to satisfy criteria of ‘fit’. If the scientific discoveries are sufficiently profound, conceptual consequences become unavoidable because they touch on our most profound physico-philosophical notions (determinism, nature, time etc.). A need arises to rethink these fundamental notions; Einstein and other philosopher-scientists did not shirk from this task. A philosopher-scientist is someone who in Einstein’s words considers the career of ‘certain fundamental concepts’ within the problem situation, in which they arise. The problem situation may be the kinematics of reference systems or the evolutionary theory. The physico-philosophical concepts need to be reassessed in the light of scientific discoveries, because they acted as unquestioned assumptions prior to the new discovery. In Einstein’s case these were concepts like mass, space and time, the nature of physical reality and of scientific theories. In such reassessments the scientist turns to more conceptual issues, which are no longer deductive consequences of the theory. As Einstein realized, when the foundations of science become problematic, the man of science becomes a philosopher. [Einstein 1936, § 1] The philosophical legacy of Einstein’s scientific work is immense. It ranges from metaphysics to the philosophy of physics. The theory of relativity demonstrates clearly how difficult the relationship between facts and concepts has become. We cannot simply cling to the concepts, irrespective of what experiment and observation tell us. This was Einstein’s charge against Newton and Lorentz. Ironically it also reflects his own difficulties with quantum mechanics, since he relies on notions like determinism and separability. Nor can we simply inductively generalize from the facts, neglecting the concepts. Therefore Einstein believed in the importance of theoretical thinking and the power of constraints. As Einstein realized himself, science makes philosophical presuppositions. The scientist needs philosophical ideas, simply because amongst the experimental and mathematical tools in the toolbox of the scientist there are conceptual tools, like the fundamental notions. Philosophical presuppositions can both guide and misguide the scientist. When the philosophical presuppositions change as a result of scientific discoveries, science does not dictate to philosophy the answers. But it constrains the philosophical consequences, which follow.

51The philosophical consequences include such questions as to which extent the Special theory is compatible with objective becoming or static being. Then there was the question of determinism in the interpretations of quantum mechanics, and the question of causal relations between entangled quantum systems. There is the issue of the representational nature of theories, more precisely the question of fit, which we interpreted as the requirement for the satisfaction of certain constraints. Finally, the philosophical notion of physical reality must be in harmony with the scientific findings. The ‘point-coincidence argument’ therefore led physicists to the invariance criterion of physical reality but Einstein’s notion of ‘local action’ (no-action-at-a-distance) has not found the approval of quantum physicists. Einstein’s work has shown that there is a genuine interaction between science and philosophy. Every true theorist is a ‘tamed metaphysicist’. [Einstein 1936 17; 1950b, 342] We have seen how Einstein’s physical problem situation lead to philosophical consequences. A consideration of Einstein’s career as a physicist-philosopher illustrates Reichenbach’s observation that the ‘evolution of philosophical ideas is guided by the evolution of physical theories’. [Reichenbach 1949, 301]

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