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Title: on einstein's doctoral thesis.

Abstract: Einstein's thesis ``A New Determination of Molecular Dimensions'' was the second of his five celebrated papers in 1905. Although it is -- thanks to its widespread practical applications -- the most quoted of his papers, it is less known than the other four. The main aim of the talk is to show what exactly Einstein did in his dissertation. As an important application of the theoretical results for the viscosity and diffusion of solutions, he got (after eliminating a calculational error) an excellent value for the Avogadro number from data for sugar dissolved in water. This was in agreement with the value he and Planck had obtained from the black-body radiation. Two weeks after he finished the `Doktorarbeit', Einstein submitted his paper on Brownian motion, in which the diffusion formula of his thesis plays a crucial role.

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The Flowering (1906–1913): Einstein Introduces Himself to the Scientific Community

• First Online: 18 October 2023

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• Luis Navarro Veguillas 9  

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My own interest in those years was less concerned with the detailed consequences of Planck’s results, however important these might be.

My own interest in those years was less concerned with the detailed consequences of Planck’s results, however important these might be. My major question was: What general conclusions can be drawn from the radiation-formula concerning the structure of radiation and even more generally concerning the electro-magnetic foundation of physics . Albert Einstein, 1949.

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In Schilpp (1970), 47.

Max von Laue was to publish in 1911 the first book devoted exclusively to the theory of relativity: Das Relativitätsprinzip .

Friedrich Adler would soon abandon physics to devote himself to politics. Between 1911 and 1916 he was secretary of the Austrian Social Democratic Party, of which his father, Victor Adler, had been a founder and high leader. In 1916 Friedrich Adler—not to be confused with Alfred Adler, the Austrian psychologist co-founder of psychoanalysis—was charged with and convicted of the murder of the Austrian Prime Minister, Count Stürgkh. His death sentence was not carried out, and he was released in 1919, after the end of the First World War.

Einstein was one of the one hundred and ten recipients of a honoris causa doctorate by the University of Geneva in the same ceremony, which was held at this university to commemorate the tercentenary of its foundation by Calvin. Other prestigious personalities invested at the same ceremony were Marie Curie, Wilhelm Ostwald and Ernest Solvay.

The German University of Prague —actually Karl-Ferdinand Universität — had resulted from the splitting, in 1882, of the former University of Prague (founded in 1349) into two: one in Czech-language and another in German-language.

Einstein’s starting wage in Prague, which included salary and various allowances, amounted to 9,100 Swiss francs, which was far more than the 5,500 francs he earned in Zurich. For details of Einstein’s financial retributions in Prague, see Beck (1995), 163.

Nobel Prize in Physics 1903 was awarded half a prize money for Henri Becquerel (1852–1908), “in recognition of the extraordinary services he has rendered by his discovery of spontaneous radioactivity”, and half for Curie couple, “in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel”.

Nobel Prize in Chemistry 1911 was awarded “in recognition of her services to the advancement of chemistry by the discovery of the elements radium and polonium, by the isolation of radium and the study of the nature and compounds of this remarkable element”.

Reprinted (in French) in Seelig (2005), 228–229.

For a more detailed account of the relations between Einstein and Grossman, especially as far as their collaboration in general relativity, see, for instance Pais (2005), 208–227.

Walter Nernst would be awarded the Nobel Prize in Chemistry 1920, “in recognition of his work in thermochemistry”.

Einstein, like many others in those days, sometimes referred to it as Berliner Akademie der Wissenschaften —Berlin Academy of Sciences—. The institution traces its origins back to 1700, when it was founded by the Elector of Brandenburg Frederick III—later King Frederick I of Prussia (1657–1713)— under the auspices of Gottfried Leibniz (1646–1716), who was its first president.

Stern had submitted his doctoral dissertation in physical chemistry in Breslau. He moved to Prague to work with Einstein as an assistant and would later accompany him on his move to Zurich in August 1912.

It was not until 1909 that Einstein would use the notation k (“Boltzmann constant”) for the R/N quotient.

Proposed in 1819 by the Frenchmen Pierre Louis Dulong (1785–1836) and Alexis Thérèse Petit (1791–1820).

This quantity c is now often referred to as the molar heat capacity —or, also, molar heat— at constant volume. We will abbreviate it, as Einstein also usually does, by simply calling it “specific heat”.

Petit and Dulong enunciated their phenomenological law in 1819. The first theoretical justification of the law is due to Boltzmann, who deduced it in 1876 from the principle of equipartition of energy. For more details on specific heats in the nineteenth century, see Pais (2005), 389–397.

At that time, it was accepted that the wavelengths corresponding to the ultraviolet region were assumed to be between 0.10 μ and 0.36 μ, and the range of the infrared region to be between 0.81 μ and 61.1 μ; see notes 23 and 24 in Stachel (1989), 390.

These are data published by H. F. Weber, in 1875, which Einstein claims to have obtained from the tables of H. Landolt and R. Börnstein, published in 1905. See notes 31 and 32 in Stachel (1989), 391.

In Einstein’s original paper, and in the English translation, it appears \(x = {(}TL/\beta \lambda {)}\) , instead of \(x = {(}T\lambda /\beta L{)}\) , which is correct. Given the meticulousness of the editors, it is surprising that this slip of the tongue should have escaped their notice.

For more details on this 1907 Einstein’s work, as well as on its relevance for the development of quantum physics, see Klein (1965).

Gedankenexperiment (thought experiment) is a terminology widely used to refer to an ideal experiment proposed to critique a theory or some particular aspect of a it. The experiment is not designed to be performed, but to be subjected to rigorous logical analysis. Therefore, the experiment does not need to be feasible; in general, they are not, but the possible consequences that its logical analysis may bring to light do not lose their value. This sort of “experiments”, although not very abundant, have played a relevant role at certain times in the history of physics. Some famous examples: “Galileo’s boat”, “Maxwell’s demon”, “Schrödinger’s cat", “Wigner’s friend”, etc.

In Schilpp (1970), 154. Wolfgang Pauli (1900-1958) received the Nobel Prize in Physics 1945 “for the discovery of the Exclusion Principle, also called the Pauli Principle”.

Einstein (1909b), 392. A linguistic detail: in this paper Einstein calls plate [ Platte ] what in Einstein (1909a) and in later papers he would call mirror [ Spiegel ]. For the sake of simplicity, we shall use the word mirror in both situations.

From 1907 Einstein already uses the letter c (from Latin celeritas , velocity?) to designate the speed of light in vacuum, instead of the previous L. For details of the origin of the notation c —although it is usually attributed to Drude in 1894, it is a not uncomplicated assignment—, see Mendelson (2006).

See Bergia and Navarro (1988), paragraphs 2 and 3. Pay attention to the notation when comparing works: we designate with ∆ —for convenience and because Einstein will do it later— the variation in the linear momentum of the mirror, while in 1909 he represents with ∆ the variation in the velocity of the mirror.

Einstein (1909b), 379. Incidentally: a paragraph like the above serves to dismiss outright the so-called “wave-particle duality” as the cause of Einstein’s estrangement from later quantum mechanics.

For a detailed analysis of Einstein’s thought —around this time— about the validity of the principle of equipartition energy, see Bergia; Navarro (1997), especially, 195–200.

Letters from Einstein to Laub (March 1910) and to Sommerfeld (July 1910). In Beck (1995), 148–149 and 157–158, respectively.

Letter from A. Einstein to M. Besso, 13 May 1911. In Beck (1995), 187. Pay attention to Einstein’s reflection on the convenience of introducing oscillations with different frequencies.

For those who are interested in following the calculations, see the commented English translation of this paper by Einstein and Hopf in Bergia et al. (1979).

For a detailed exposition of the origin, development and prospects of stochastic electrodynamics see De la Peña; Cetto (1996).

In Chapter III of Kuhn (1978), entitled “Planck and the electromagnetic H-theorem, 1897–1899”, it can be found some of Planck’s ideas and developments about stochastic fields, which appeared in his early work on black body radiation. In particular, on pages 73–74, there appear developments with random phases, very similar to ( 2.17 ).

Tyndall effect occurs in colloids, or colloidal suspensions, but not in dissolutions. That is why it is currently used —among many other applications— to distinguish between colloids and solutions. In a colloidal suspension, the size of the suspended particles usually ranges between one micron and one thousandth of a micron, whereas in a solution the solute particles do not reach a thousandth of a micron.

For further information on the relationship between Smoluchowski and Einstein respective investigations on critical opalescence, see the note “Einstein on critical opalescence”, in Klein et al. (1993a), 283–285.

Letter from A. Einstein to M. Smoluchowski June 11, 1908. In Beck (1995), 76.

By this time, and especially in connection with his first quantum ideas, Einstein had already resorted on several occasions to Boltzmann’s principle and had dealt critically with its analysis. For more details on these aspects, one can see Navarro; Pérez (2002b), in Spanish.

Ornstein and Zernike (1914). Ornstein had received his doctorate in 1908 under Lorentz supervision. Zernike would be awarded the Nobel Prize in Physics 1953 “for his demonstration of the phase contrast method, especially for his invention of the phase contrast microscope”.

Solvay’s industrial and economic success was largely due to his invention of the ingenious “Solvay process” for the industrial production of soda, which he had patented in 1861.

For a comprehensive summary of the development —including attendees, papers and discussions— of the first sixteen conferences, between 1911 and 1973, see Mehra (1975).

Ernest Rutherford (1871–1937) has been already awarded the Nobel Prize in Chemistry 1908 “for his investigations into the disintegration of the elements, and the chemistry of radioactive substances”.

Lord Rayleigh sent a short communication to Nernst, to be read and discussed at the meeting. Van der Waals has been awarded the Nobel Prize in Physics 1910 “for his work on the equation of state for gases and liquids”.

The papers presented were commissioned to the respective authors by the organization of the conference, among topics previously proposed by Nernst; see Mehra (1975), 6–7. Further details on the first Solvay conference can be found in Barkan (1993). For a discussion of various aspects related to the role of the Solvay conferences in the development of modern physics, see Marage; Wallenborn (1995).

Langevin and De Broglie (1912), 12–39. In his paper Lorentz suggested ways of avoiding these difficulties, although without reaching definitive conclusions. For some clarifications, see Bergia; Navarro (1997), 201–202.

Langevin; De Broglie (1912), 53–73. In relation to Poincaré’s critique see, Bergia; Navarro (1997), 204.

Langevin; De Broglie (1912), 93–114. For a detailed exposition in context of “Planck’s second theory”, see Kuhn (1978), Chap. 10.

Langevin and De Broglie (1912), 393–404. Langevin’s theory, as we have pointed out on other occasions, is of a classical nature, without the slightest contamination of quantum ideas. See Navarro and Olivella (1997).

Langevin and De Broglie (1912), 402–404. Langevin’s remark was made in response to a question from Wien.

Einstein (1911 a and 1911d). For a discussion of the role played by specific heats in the evolution of Einstein’s thinking about quantum ideas, see Klein (1965).

Einstein (1912 a). In Beck (1993), 408. This idea had already appeared in Einstein (1911b), 365. In spite of the opposition of some scholars—Nernst among them, as Einstein recognizes in his Solvay memoir—, it would soon be adopted and refined in the face of mismatches with certain experimental data; see Debye (1912).

Let us insist that this incessant search for the necessary quantum—against the Planck’s sufficient one—is a clearly detectable characteristic in Einstein’s research in those days.

For a detailed analysis of the differences between Einstein’s and Gibbs’ conceptions, not only in relation to probability but also to statistical mechanics itself, see Navarro (1998).

Einstein (1912a). In Beck (1993), 437. Although we shall return to this topic later, a summary of the formulation and applications of the adiabatic principle by Ehrenfest—its introducer—can be found in Klein (1985), Chap. 11.

Letter from A. Einstein to E. Solvay, 22 November 1911. In Beck (1995), 227.

Letter from A. Einstein to H. Zangger, 7 November 1911. In Beck (1995), 219–220. Zangger turned out to be first a friend of Einstein, then a confidant of Albert and Mileva to the point of becoming the couple’s legal intermediary when the marriage began to break up; after their divorce he took care of children’s interests.

Letter from A. Einstein to H. Zangger, 15 November 1911. In Beck (1995), 221–222. Einstein and Poincaré had just met personally in Brussels and would not meet again, as the Frenchman died only a few months later. They never clearly manifested mutual admiration, especially as far as their respective formulations of the especial theory of relativity was concerned. For more details on the relationship between Poincaré and Einstein, see, for example, Pais (2005), 169–172.

Letter from A. Einstein to M. A. Besso, December 26, 1911. In Beck (1995), 241.

Ehrenfest also justifies the requirement of certain additional conditions—which we will not mention here—about the asymptotic behaviour of G ( q ). [Ehrenfest (1911), 197–198].

To solve the functional equation ( 2.36 ) there is no special difficulty at present. It is sufficient to derive the spectral decomposition of the function in the right-hand member, after substituting f ( σ ) by ( 2.35 ) in the case of Planck, and by ( 2.33 ) in Wien’s case.

Let us recall that the Brussels meeting took place between 30 October and 3 November. Poincaré died on 17 July 1912, in Paris.

The treatment through any possible mechanism has to lead to the same results, so that—as Poincaré indicates at the end of his article—he chooses which considers the most adequate one.

Poincaré refers to W as “ dernier multiplicateur ” of the equations of motion, according to the usual terminology he used in his reports on integral invariants. Poincaré (1912), 6–7.

Remember here that X is proportional to the absolute temperature T .

See the letter of A. Einstein to M. Besso 21 October 1911. In Beck (1995), 215.

Ehrenfest (1959). Because of several incidents, the publication did not come out until 1912, with the Ehrenfests as authors. It soon became—and still is today—a classical text on the foundations of statistical mechanics and in particular for the comparison of Boltzmann’s and Gibbs’ views. On this last topic, one can also see Navarro (1998), 166–169.

On the limited impact of Ehrenfest (1911), see Navarro; Pérez (2004), 126–130.

Bergia; Navarro (1988), especially 85–90. See also Editorial note: Einstein on the law of photochemical equivalence , in Klein et al. (1995), 109–113.

Einstein (1912 b). In Beck (1996), 89. Here Einstein still does not call N Avogadro’s number and, instead, continues referring to “the number of molecules in a gram-molecule”.

Letter from A. Einstein to M. Besso 4 February 1912. In Beck (1995), 105. Emphasis in the original. The substance referred to in this letter is possibly ammonia; see note 7 in Klein et al. (1993 b), 407.

Letter from A. Einstein to E. Warburg, 25 April 1912. In Beck (1995), 289.

In this section we follow a part of our research on the subject, as shown in Navarro and Pérez (2006).

Letter from M. Planck to H. Lorentz, 7 January 1910. Excerpt quoted in Kuhn (1978), 274.

For a more detailed account of Planck’s second theory and its vicissitudes throughout the second decade of the twentieth century, see Kuhn (1978), Chap. 10.

For a precise analysis of the role played by the measurements of the specific heat of hydrogen, together with the corresponding theoretical interpretations, see Gearhart (2010).

Niels Bohr would be awarded the Nobel Prize in Physics 1922 “for his services in the investigation of the structure of atoms and of the radiation emanating from them”.

For more details about Ehrenfest’s treatment, as well as the comparison with that of Einstein and Stern, see, for example, Navarro; Pérez (2006), especially 215–223.

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Navarro Veguillas, L. (2023). The Flowering (1906–1913): Einstein Introduces Himself to the Scientific Community. In: The Lesser-Known Albert Einstein. History of Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-35568-4_2

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Einstein’s Philosophy of Science

Albert Einstein (1879–1955) is well known as the most prominent physicist of the twentieth century. His contributions to twentieth-century philosophy of science, though of comparable importance, are less well known. Einstein’s own philosophy of science is an original synthesis of elements drawn from sources as diverse as neo-Kantianism, conventionalism, and logical empiricism, its distinctive feature being its novel blending of realism with a holist, underdeterminationist form of conventionalism. Of special note is the manner in which Einstein’s philosophical thinking was driven by and contributed to the solution of problems first encountered in his work in physics. Equally significant are Einstein’s relations with and influence on other prominent twentieth-century philosophers of science, including Moritz Schlick, Hans Reichenbach, Ernst Cassirer, Philipp Frank, Henri Bergson, Émile Meyerson.

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

2. theoretical holism: the nature and role of conventions in science, 3. simplicity and theory choice, 4. univocalness in the theoretical representation of nature, 5. realism and separability, 6. the principle theories—constructive theories distinction, 7. conclusion: albert einstein: philosopher-physicist, einstein’s work, related literature, other internet resources, related entries.

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). 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 (see Sauer 2014 for non-technical overview on Einstein’s approach to the unified field theory program). 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:

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

The emphasis on the continuity and coherence in the development of Einstein’s philosophy of science contrasts 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. However, Einstein was probably never an ardent “Machian” positivist, [ 1 ] 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). Starting from the mid-1920s till the end of the decade Einstein show some interest in the rationalistic realism of Émile Meyerson (Einstein, 1928; cf. Giovanelli 2018; on the contemporary debate between Einstein and Bergson, see Canales 2015). 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.

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 . ( Collected Papers of Albert Einstein , hereafter CPAE, Vol. 3, Doc. 11 [pp. 12–13])

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 started to prevail at the turn of the 1920s.

During the decade 1905–1915, Einstein had more or less explicitly assumed that in a good theory there are certain individual parts that can be directly coordinated with the behavior of physically-existent objects used as probes. A theory can be said to be ‘true or false’ if such objects respectively behave or do not behave as predicted. In special relativity, as in classical mechanics, the fundamental geometrical/kinematical variables, the space and time coordinates, are measured with rods and clocks separately from the other non-geometrical variables, say, charge electric field strengths, which were supposed to be defined by measuring the force on a charge test particle. In general relativity, coordinates are no longer directly measurable independently from the gravitational field. Still, the line element \(ds\) (distance between nearby spacetime points) was supposed to have a ‘natural’ distance that can be measured with rods and clocks. In the late 1910s, pressed by the epistemological objections raised by different interlocutors—in particular Hermann Weyl (Ryckman 2005) and the young Wolfgang Pauli (Stachel, 2005)—Einstein was forced to recognize that this epistemological model was at most a provisional compromise. In principle rod- and clock-like structures should emerge as solutions of a future relativistic theory of matter, possibly a field theory encompassing gravitation and electromagnetism. In this context, the sharp distinction between rods and clocks that serve to define the geometrical/kinematical structure of the theory and other material systems would become questionable. Einstein regarded such distinction as provisionally necessary, give the current state of physics. However, he recognized that in principle a physical theory should construct rods and clocks as solutions to its equations (see Ryckman 2017, ch. VII for an overview on Einstein view on the relation between geometry and experience).

Einstein addressed this issue in several popular writings during the 1920s, in particular, the famous lecture Geometrie und Erfahrung (Einstein 1921, see also Einstein, 1923, Einstein, 1924, Einstein 1926; Einstein 1926; see Giovanelli 2014 for an overview). Sub specie temporis , he argued, it was useful to compare the geometrical/kinematical structures of the theory with experience separately from the rest of physics. Sub specie aeterni , however, only geometry and physics taken together can be said to be ‘true or false.’ This epistemological model became more appropriate, while Einstein was moving beyond general relativity in the direction of theory unifying the gravitational and the electromagnetic field. Einstein had to rely on progressively more abstract geometrical structures which could not be defined in terms of the behavior of some physical probes. Thus, the use of such structures was justified because of their role in the theory as a whole. In the second half of the 1920s, in correspondence with Reichenbach (Giovanelli 2017) and Meyerson (Giovanelli 2018), Einstein even denied that the very distinction between geometrical and non-geometrical is meaningful (Lehmkuhl 2014).

A different, but especially interesting example of Einstein’s reliance on a form of theoretical holism 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 Kant’s philosophy. 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. The classic logical empiricist view that the moment of convention was restricted to conventional coordinating definitions that endow individual primitive terms, worked well, but did not comport well with the holism about theories

It was this argument over the nature and place of conventions in science that underlies 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 (on the relations between Einstein’s realism and constructism see Ryckman 2017, ch. 8 and 9). 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; Howard’s 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, CPAE, Vol. 8, Doc. 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.

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, van Dongen 2002, 2010, Giovanelli 2018). 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.

Einstein’s celebration of simplicity as a guide to theory choice comes clearly to the fore in the early 1930s, when he was immersed his project of a unified field theory (see, van Dongen 2010 for a reconstruction of the philosophical underpinning of Einstein’s search of a unified field theory). 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; Howard’s translation)

Einstein’s conviction that the theoretical physicist must trust simplicity is that his work was moving steadily into domains ever further removed from direct contact with observation and experiment. Einstein started to routinely claim that this was the lesson he had drawn from the way in which he had found general relativity (Norton 2000). There are, however, good reasons to think that Einstein’s selective recollections (Jannsen and Renn 2007) were instrumental to his defense of relying on a purely mathematical strategy in the search for a unified field theory (van Dongen 2010):

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; Howard’s 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). The success of previous physical theories justifies our trusting that nature is the realization of the simplest that is mathematically conceivable

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.

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 the reference system signifies nothing real 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 \(g_{\mu v}\) (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. (CPAE, Vol. 8, Doc. 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.” Einstein might have been inspired by a paper by the young mathematician Erich Kretschmann (Howard and Norton 1993; cf. Giovanelli 2013) or possibly by a conversation with Schlick (Engler and Renn, 2017). 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, CPAE, Vol. 8, Doc. 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). 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). [ 2 ]

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.

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” (CPAE, Vol. 8, Doc. 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 (CPAE, Vol. 8, Doc. 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. (CPAE, Vol. 8, Doc. 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. (CPAE, Vol. 8, Doc. 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. [ 3 ] 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; Howard’s 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.”

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, “which permit of precise formulation” (Einstein 1914, 749). 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 constructive theories. 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 (Einstein 1907, Einstein to Sommerfeld 14 January 1908, CPAE, vol. 5, Doc. 73, Einstein 1914). 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. At the turn of 1900, Hendrik A. Lorentz (Lorentz 1900, 1905; see Frisch 2005) and Henri Poincaré (for example, Poincaré 1904; see, Giedymin 1982, Darrigol 1995) presented the opposition between the “physics of principles“ and the “physics of models“ as commonplace. In a similar vein, Arnold Sommerfeld opposed a “physics of problems“, a style of doing physics based on concrete puzzle solving, to the “practice of principles“ defended by Max Planck (Seth 2010). Philipp Frank (1908, relying on Rey 1909) defined relativity theory as a “ conceptual theory“ based on abstract, but empirically well confirmed principles rather than on intuitive models. Probably many other examples could be find. . 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. Only in recent decades, Einstein constructive-principle distinction has attracted interest in the philosophical literature, originating a still living philosophical debate on the foundation of spacetime theories (Brown 2005, Janssen 2009, Lange 2014). [ 4 ]

Einstein’s influence on twentieth-century philosophy of science is comparable to his influence on twentieth-century physics (Howard 2014). 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 letters and manuscripts, if unpublished, are cited by their numbers in the Einstein Archive (EA) control index and, if published, by volume, document number, and, if necessary, page number in:

Works by year

• Born, Max, 1949. Natural Philosophy of Cause and Chance , Oxford: Oxford University Press.
• Brown, Harvey R., 2005. Physical Relativity. Space-time Structure from a Dynamical Perspective , Oxford: Clarendon Press.
• ––– (ed.), 1969. Albert Einstein-Hedwig und Max Born: Friefwechsel, 1916–1955 , Munich: Nymphenburger.
• Canales, Jimena, 2015. Einstein, Bergson and the Debate That Changed Our Understanding of Time , Princeton: Princeton University Press.
• 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.
• Darrigol, Olivier, 1995. “Henri Poincaré’s Criticism of fin de siécle Electrodynamics”, Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 26 (1): 1–44.
• 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; reprinted, 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.
• Engler, Fynn Ole and Jürgen Renn, 2013. “Hume, Einstein und Schlick über die Objektivität der Wissenschaft”, in Moritz Schlick–Die Rostocker Jahre und ihr Einfluss auf die Wiener Zeit , Fynn Ole Engler and Mathias Iven (eds.), Leipzig: Leipziger Universitätsverlag, 123–156.
• Fine, Arthur, 1986. “Einstein’s Realism”, in The Shaky Game: Einstein, Realism, and the Quantum Theory , Chicago: University of Chicago Press, 86–111.
• Frank, Philipp, 1909. “Die Stellung Des Relativitätsprinzips Im System Der Mechanik Und Der Elektrodynamik” Sitzungsberichte der Akademie der Wissenschaften 118 (IIa), 373–446.
• Friedman, Michael, 1983. Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science , Princeton, NJ: Princeton University Press.
• Frisch, Mathias, 2005. “Mechanisms, Principles, and Lorentz’s Cautious Realism”, Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 36: 659–679.
• 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.
• Giovanelli, Marco, 2013. “Erich Kretschmann as a Proto-Logical-Empiricist. Adventures and Misadventures of the Point-Coincidence Argument”, Studies in History and Philosophy of Science. Part B: Studies in History and Philosophy of Modern Physics , 44 (2), 115–134.
• –––, 2013. “Talking at Cross-Purposes. How Einstein and the Logical Empiricists never Agreed on what they were Disagreeing About”, Synthese 190 (17): 3819–3863.
• –––, 2014. “‘But One Must Not Legalize the Mentioned Sin’. Phenomenological vs. Dynamical Treatments of Rods and Clocks in Einstein’s Thought”, Studies in History and Philosophy of Science (Part B: Studies in History and Philosophy of Modern Physics), 48: 20–44.
• –––, 2016. “‘…But I StillCan’t Get Rid of a Sense of Artificiality’: The Einstein-Reichenbach Debate on the Geometrization of the Electromagnetic Field”, Studies in History and Philosophy of Science. Part B: Studies in History and Philosophy of Modern Physics , 54, 35–51.
• –––, 2018. “Physics Is a Kind of Metaphysics”, Émile Meyerson and Einstein’s late Rationalistic Realism”, European Journal for Philosophy of Science , 8: 783–829
• 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: Volume 3), Boston: Birkhäuser, 154–243.
• –––, 1993. “Was Einstein Really a Realist?” Perspectives on Science: Historical, Philosophical, Social 1: 204–251.
• –––, 1994a. “Einstein, Kant, and the Origins of Logical Empiricism”, in Language, Logic, and the Structure of Scientific Theories (Proceedings of the Carnap-Reichenbach Centennial, University of Konstanz, 21–24 May 1991), Wesley Salmon and Gereon Wolters (eds.), Pittsburgh: University of Pittsburgh Press; Konstanz: Universitätsverlag, 45–105.
• –––, 1994b. “’A kind of vessel in which the struggle for eternal truth is played out’-Albert Einstein and the Role of Personality in Science”, in The Natural History of Paradigms: Science and the Process of Intellectual Evolution , John H. Langdon and Mary E. McGann (eds.), Indianapolis: University of Indianapolis Press, 1994, 111–138.
• –––, 1996. “Relativity, Eindeutigkeit, and Monomorphism: Rudolf Carnap and the Development of the Categoricity Concept in Formal Semantics”, in Origins of Logical Empiricism (Minnesota Studies in the Philosophy of Science, Volume 16), Ronald N. Giere and Alan Richardson (eds.), Minneapolis and London: University of Minnesota Press, 115–164.
• –––, 1997. “A Peek behind the Veil of Maya: Einstein, Schopenhauer, and the Historical Background of the Conception of Space as a Ground for the Individuation of Physical Systems”, in The Cosmos of Science: Essays of Exploration (Pittsburgh-Konstanz Series in the Philosophy and History of Science, Volume 6), John Earman and John D. Norton, (eds.), Pittsburgh: University of Pittsburgh Press; Konstanz: Universitätsverlag, 87–150.
• –––, 1998. “Astride the Divided Line: Platonism, Empiricism, and Einstein’s Epistemological Opportunism”, in Idealization in Contemporary Physics (Poznan Studies in the Philosophy of the Sciences and the Humanities: Volume 63), Niall Shanks (ed.), Amsterdam and Atlanta: Rodopi, 143–163.
• –––, 1999. “Point Coincidences and Pointer Coincidences: Einstein on Invariant Structure in Spacetime Theories”, in History of General Relativity IV: The Expanding Worlds of General Relativity (Based upon the Fourth International Conference, Berlin, Germany 31 July-3 August 1995), Hubert Goenner, Jürgen Renn, Jim Ritter, and Tilman Sauer (eds.), Boston: Birkhäuser, 463–500.
• –––, 2014. “Einstein and the Development of Twentieth-century Philosophy of Science”, in The Cambridge Companion to Einstein , Michel Janssen and Christoph Lehner (eds.), Cambridge: Cambridge University Press, 354–376.
• Howard, Don and Norton, John, 1993. “Out of the Labyrinth? Einstein, Hertz, and the Göttingen Answer to the Hole Argument”, in The Attraction of Gravitation. New Studies in the History of General Relativity (Einstein Studies: Volume 5), John Earman, Michel Jannsen, and John Norton (eds.),Boston: Birkhäuser, 30–62.
• Howard, Don and Stachel, John (eds.), 1989. Einstein and the History of General Relativity (Einstein Studies: Volume 1), Boston: Birkhäuser.
• Janssen, Michel, 2009. “Drawing the Line between Kinematics and Dynamics in Special Relativity”, Studies in History and Philosophy of Science. Part B: Studies in History and Philosophy of Modern Physics , 40 (1), 26–52.
• Janssen, Michel and Jürgen Renn, 2007. “Untying the Knot. How Einstein Found His Way Back to Field Equations Discarded in the Zurich Notebook”, in: The Genesis of General Relativity Jürgen Renn et al. (eds.), 4 volumes, Dordrecht: Springer 839–925.
• Lange, Marc, 2014. “Did Einstein Really Believe That Principle Theories Are Explanatorily Powerless?”, Perspectives on Science 22 (4), 449–63.
• Lehmkuhl, Dennis, 2014. “Why Einstein Did Not Believe That General Relativity Geometrizes Gravity”, Studies in History and Philosophy of Science. Part B: Studies in History and Philosophy of Modern Physics ,, 46: 316–326.
• Le Roy, Édouard, 1901. “Un positivisme nouveau”, Revue de Métaphysique et de Morale 9: 138–153.
• Lorentz, Hendrik Antoon, 1900. “Electromagnetische theorieën van natuurkundige verschijnselen” Jaarboek der Rijksuniversiteit te Leiden , Bijlagen; repr. in Leiden: Brill 1900; German translation in Physikalische Zeitschrift , 1 (1900): 498–501, 514–519.
• –––, 1905. “La thermodynamique et les théories cinétiques.“ Bulletin des séances de la Société française de physique , 35–63.
• Mach, Ernst, 1886. Beiträge zur Analyse der Empfindungen , Jena: Gustav Fischer.
• –––, 1897. Die Mechanik in ihrer Entwickelung historisch-kritisch dargestellt , 3rd impr. and enl. ed. Leipzig: Brockhaus.
• –––, 1900. Die Analyse der Empfindungen und das Verhältniss des Physischen zum Psychischen , 2nd edition of Mach 1886, Jena: Gustav Fischer; English translation of the 5th edition of 1906, The Analysis of Sensations and the Relation of the Physical to the Psychical , Cora May Williams and Sydney Waterlow, trans. Chicago and London: Open Court, 1914. Reprint: New York: Dover, 1959.
• –––, 1906. Erkenntnis und Irrtum. Skizzen zur Psychologie der Forschung , 2nd ed. Leipzig: Johann Ambrosius Barth; English translation, Knowledge and Error: Sketches on the Psychology of Enquiry , Thomas J. McCormack and Paul Foulkes, (trans.), Dordrecht and Boston: D. Reidel, 1976.
• Meyerson, Émile, Meyerson, 1925. La déduction relativiste , Paris: Payot; Eng. tr. Meyerson 1985.
• –––, 1985. The Relativistic Deduction.Epistemological Implications of the Theory of Relativity , Eng. tr. by David A. and Mary-Alice Sipfle, Dordrecht: Reidel.
• Norton, John, 1984. “How Einstein Found His Field Equations”, Historical Studies in the Physical Sciences 14: 253–316. Reprinted in Howard and Stachel 1989, 101–159.
• –––, 2000. “’Nature is the Realisation of the Simplest Conceivable Mathematical Ideas’: Einstein and the Canon of Mathematical Simplicity”, Studies in History and Philosophy of Modern Physics 31B: 135–170.
• Petzoldt, Joseph, 1895. “Das Gesetz der Eindeutigkeit”, Vierteljahrsschrift für wissenschaftliche Philosophie und Soziologie 19: 146–203.
• Poincaré, Henri, 1901. “Sur les Principes de la Mecanique”, Bibliotheque du Congrès Internationale de Philosophie , Sec. 3, Logique et Histoire des Sciences , Paris: A. Colin. Reprinted as: “La Mécanique classique”, in La Science et l’Hypothese , Paris: Flammarion, 1902, 110–134; English translation: “The Classical Mechanics”, n Science and Hypothesis , W. J. Greenstreet (trans.), London and New York: Walter Scott, 1905, 89–110. Reprint: New York: Dover, 1952.
• –––, 1904. “The Principles of Mathematical Physics”, in Congress of Arts and Science, Universal Exposition, St. Louis, 1904 ( Philosophy and Mathematics : Volume 1), Howard J. Rogers, (ed.), Boston and New York: Houghton, Mifflin and Company, 1905, 604–622.
• Quine, Willard van Orman, 1951. “Two Dogmas of Empiricism”, Philosophical Review , 60: 20–43; reprinted in From a Logical Point of View , Cambridge, MA: Harvard University Press, 1953, 20–46.
• Reichenbach, Hans, 1920. Relativitätstheorie und Erkenntnis Apriori , Berlin: Julius Springer; English translation: The Theory of Relativity and A Priori Knowledge , Maria Reichenbach (trans. and ed.), Berkeley and Los Angeles: University of California Press, 1965.
• –––, 1924. Axiomatik der relativistischen Raum-Zeit-Lehre ( Die Wissenschaft : Volume 72), Braunschweig: Friedrich Vieweg und Sohn; English translation: Axiomatization of the Theory of Relativity , Maria Reichenbach (trans.), Berkeley and Los Angeles: University of California Press, 1969.
• –––, 1928. Philosophie der Raum-Zeit-Lehre , Berlin: Julius Springer; English translation, The Philosophy of Space & Time , Maria Reichenbach and John Freund (trans.), New York: Dover, 1957.
• –––, 1949. “The Philosophical Significance of the Theory of Relativity”, in Schilpp 1949, 289–311.
• Rey, Abel, 1907. La théorie de la physique chez les physiciens contemporains , Paris: Alcan.
• –––, 1908. Die Theorie der Physik bei den modernen Physikern , Ger. tr. of Rey 1907, by Rudolf Eisler. Leipzig: Klinkhardt.
• Ryckman, Thomas, 2005. The Reign of Relativity. Philosophy in Physics 1915–1925 , Oxford and New York: Oxford University Press.
• –––, 2017. Einstein , New York: Routledge.
• Sauer,Tilman, 2014. “Einstein’s Unified field Theory Program” in The Cambridge Companion to Einstein , Michel Janssen and Christoph Lehner (eds.), Cambridge: Cambridge University Press, 2014 281;–305.
• Schilpp, Paul Arthur (ed.), 1949. Albert Einstein: Philosopher-Scientist (The Library of Living Philosophers: Volume 7), Evanston, IL: The Library of Living Philosophers.
• Schlick, Moritz, 1910. “Das Wesen der Wahrheit nach der modernen Logik”, Vierteljahrsschrift für wissenschaftliche Philosophie und Soziologie 34: 386–477; English translation, “The Nature of Truth in Modern Logic”, in Schlick 1979, vol. 1, 41–103.
• –––, 1915. “Die philosophische Bedeutung des Relativitätsprinzips”, Zeitschrift für Philosophie und philosophische Kritik 159: 129–175. English translation: “The Philosophical Significance of the Principle of Relativity”, in Schlick 1979, vol. 1, 153–189.
• –––, 1917. Raum und Zeit in den gegenwärtigen Physik. Zur Einführung in das Verständnis der allgemeinen Relativitätstheorie , Berlin: Julius Springer; English translation of the 3rd edition, Space and Time in Contemporary Physics: An Introduction to the Theory of Relativity and Gravitation , Henry L. Brose (trans.), London and New York: Oxford University Press, 1920; reprinted in Schlick 1979, vol. 1, 207–269.
• –––, 1921. “Kritizistische oder empiristische Deutung der neuen Physik”, Kant-Studien 26: 96–111. English translation: “Critical or Empiricist Interpretation of Modern Physics”, in Schlick 1979, vol. 1, 322–334.
• –––, 1979. Philosophical Papers , 2 volumes, Henk L. Mulder and Barbara F. B. van de Velde-Schlick (eds.), Peter Heath (trans.), Dordrecht and Boston: D. Reidel.
• Seth, Suman, 2010. Crafting the Quantum , Cambridge, Mass.: MIT Press.
• Stachel, John, 1980. “Einstein’s Search for General Covariance, 1912–1915” (paper delivered at the Ninth International Conference on General Relativity and Gravitation, Jena, Germany (DDR), 17 July 1980), in Howard and Stachel 1989, 63–100.
• Study, Eduard, 1914. Die realistische Weltansicht und die Lehre vom Raume. Geometrie, Anschauung und Erfahrung ( Die Wissenschaft : Volume 54), Braunschweig: Friedrich Vieweg & Sohn.
• van Dongen, Jeroen, 2002. Einstein’s Unification: General Relativity and the Quest for Mathematical Naturalness , Ph.D. Dissertation, University of Amsterdam.
• –––, 2010. Einstein’s Unification , Cambridge and New York: Cambridge University Press

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The document handed over to Albert Einstein at his PhD conferral 116 years ago, long neglected in an attic before embarking on an adventurous journey through several countries, has now returned to its place of creation. Thanks to a donation to the UZH Foundation enabling UZH to purchase the diploma, it is now on display in the entrance hall of the main building.

The display was officially unveiled yesterday by UZH President Michael Schaepman and the executive director of the Nobel Foundation Vidar Helgesen, as part of an event at UZH celebrating 100 years since Einstein was awarded the Nobel Prize. The anniversary event, organized by the Swedish Embassy and the Swiss and Swedish innovation councils Innosuisse and Vinnova, provided an opportunity for Swedish and Swiss delegates from academia, industry and politics to get together at UZH to discuss innovation and cooperation between the two countries.

Annus mirabilis for physics

Albert Einstein’s career is closely linked with the city of Zurich: from 1896 to 1900 he studied physics at the Eidgenössische Polytechnikum (ETH), and in 1905 submitted his doctoral thesis to the University of Zurich. His doctorate and corresponding certificate were conferred in January 1906.  He went on to work as a professor of theoretical physics, first at the University of Zurich (1909 to 1911), then at ETH Zurich (1912 to 1914).

The year of his doctoral thesis, 1905, was an incredibly productive one for Einstein. It has gone down in the history of physics as an annus mirabilis, a miracle year. Within the space of just a few months, in addition to his dissertation, Einstein published four more groundbreaking papers, all of which would be worthy of a Nobel Prize from today’s perspective. The 26-year-old Einstein completed his 17-page dissertation, entitled "A New Determination of Molecular Dimensions", on 30 April 1905 and submitted it to the University of Zurich almost two months later.

The Zurich dissertation has been frequently cited ever since. Using data on sugar solutions with a known concentration together with a new formula for diffusion, he showed how the molecular size and number of molecules in a mole (Avogadro number) could be calculated from a solution’s viscosity. His paper also lent weight to the hypothesis – a source of controversy at the time – on the existence of atoms. The findings from Einstein’s study have led to all kinds of practical applications, including in the construction and petrochemical industries. The paper has also been cited in ecological studies on the dispersion of tiny liquid droplets (aerosols) in the atmosphere. 

Four further strokes of genius

Besides his doctoral thesis, in 1905 Einstein published four other papers in the scientific journal Annalen der Physik that were to revolutionize physics. In March of that year, and therefore prior to his dissertation, he completed his study on the photoelectric effect, the work that would go on to earn him the Nobel Prize. In it, Einstein formulated his light quantum hypothesis. This states that light consists of tiny packets (quanta) of energy. If the energy of light shining on a metallic surface is sufficient, the surface will emit electrons. This releases an electrical charge that can be measured – a phenomenon known as the photoelectric effect. Although this effect had long been known in physics, Einstein was the first to explain it correctly. Only some 20 years later was the light quantum hypothesis confirmed experimentally.

Delayed Nobel Prize

Albert Einstein was awarded the Nobel Prize in 1921 “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.” Because the Nobel Committee for Physics decided in 1921 that none of the nominations met the criteria for a prize, Einstein did not receive his Nobel Prize until November 1922, when it was awarded to him retroactively. The physicist was unable to attend the official award ceremony held in Stockholm in December, as he was on a lecture tour in Japan. The envoy of Germany, Rudolf Nadolny, therefore stepped in to accept the prize on Einstein’s behalf and delivered a speech of thanks at the subsequent banquet.

"Revolutionizing Physics"

On the occasion of the 100th anniversary of Albert Einstein’s Nobel Prize, UZH and ETH have jointly issued a publication called Revolutionizing Physics . It includes facsimiles of the five original papers from Einstein’s “miracle year”, as well as a fascinating contribution by contemporary physicists at UZH and ETH, Daniel Wyler and Jürg Fröhlich, explaining and honoring Einstein’s achievements and their historical significance. 

Roger Nickl; translated by Caitlin Stephens

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• 25 April 2024
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‘Shut up and calculate’: how Einstein lost the battle to explain quantum reality

• Jim Baggott 0

Jim Baggott is a science writer based in Cape Town, South Africa. He is co-author with John Heilbron of Quantum Drama .

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For entangled particles, a change in one instantly affects the other, no matter how far apart they are. Credit: Volker Steger/SPL

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Quantum mechanics is an extraordinarily successful scientific theory, on which much of our technology-obsessed lifestyles depend. It is also bewildering. Although the theory works, it leaves physicists chasing probabilities instead of certainties and breaks the link between cause and effect. It gives us particles that are waves and waves that are particles , cats that seem to be both alive and dead, and lots of spooky quantum weirdness around hard-to-explain phenomena, such as quantum entanglement.

Myths are also rife. For instance, in the early twentieth century, when the theory’s founders were arguing among themselves about what it all meant, the views of Danish physicist Niels Bohr came to dominate. Albert Einstein famously disagreed with him and, in the 1920s and 1930s, the two locked horns in debate . A persistent myth was created that suggests Bohr won the argument by browbeating the stubborn and increasingly isolated Einstein into submission. Acting like some fanatical priesthood, physicists of Bohr’s ‘church’ sought to shut down further debate. They established the ‘Copenhagen interpretation’, named after the location of Bohr’s institute, as a dogmatic orthodoxy.

My latest book Quantum Drama , co-written with science historian John Heilbron, explores the origins of this myth and its role in motivating the singular personalities that would go on to challenge it. Their persistence in the face of widespread indifference paid off, because they helped to lay the foundations for a quantum-computing industry expected to be worth tens of billions by 2040.

John died on 5 November 2023 , so sadly did not see his last work through to publication. This essay is dedicated to his memory.

Foundational myth

A scientific myth is not produced by accident or error. It requires effort. “To qualify as a myth, a false claim should be persistent and widespread,” Heilbron said in a 2014 conference talk. “It should have a plausible and assignable reason for its endurance, and immediate cultural relevance,” he noted. “Although erroneous or fabulous, such myths are not entirely wrong, and their exaggerations bring out aspects of a situation, relationship or project that might otherwise be ignored.”

Does quantum theory imply the entire Universe is preordained?

To see how these observations apply to the historical development of quantum mechanics, let’s look more closely at the Bohr–Einstein debate. The only way to make sense of the theory, Bohr argued in 1927, was to accept his principle of complementarity. Physicists have no choice but to describe quantum experiments and their results using wholly incompatible, yet complementary, concepts borrowed from classical physics.

In one kind of experiment, an electron, for example, behaves like a classical wave. In another, it behaves like a classical particle. Physicists can observe only one type of behaviour at a time, because there is no experiment that can be devised that could show both behaviours at once.

Bohr insisted that there is no contradiction in complementarity, because the use of these classical concepts is purely symbolic. This was not about whether electrons are really waves or particles. It was about accepting that physicists can never know what an electron really is and that they must reach for symbolic descriptions of waves and particles as appropriate. With these restrictions, Bohr regarded the theory to be complete — no further elaboration was necessary.

Such a pronouncement prompts an important question. What is the purpose of physics? Is its main goal to gain ever-more-detailed descriptions and control of phenomena, regardless of whether physicists can understand these descriptions? Or, rather, is it a continuing search for deeper and deeper insights into the nature of physical reality?

Einstein preferred the second answer, and refused to accept that complementarity could be the last word on the subject. In his debate with Bohr, he devised a series of elaborate thought experiments, in which he sought to demonstrate the theory’s inconsistencies and ambiguities, and its incompleteness. These were intended to highlight matters of principle; they were not meant to be taken literally.

Entangled probabilities

In 1935, Einstein’s criticisms found their focus in a paper 1 published with his colleagues Boris Podolsky and Nathan Rosen at the Institute for Advanced Study in Princeton, New Jersey. In their thought experiment (known as EPR, the authors’ initials), a pair of particles (A and B) interact and move apart. Suppose each particle can possess, with equal probability, one of two quantum properties, which for simplicity I will call ‘up’ and ‘down’, measured in relation to some instrument setting. Assuming their properties are correlated by a physical law, if A is measured to be ‘up’, B must be ‘down’, and vice versa. The Austrian physicist Erwin Schrödinger invented the term entangled to describe this kind of situation.

How Einstein built on the past to make his breakthroughs

If the entangled particles are allowed to move so far apart that they can no longer affect one another, physicists might say that they are no longer in ‘causal contact’. Quantum mechanics predicts that scientists should still be able to measure A and thereby — with certainty — infer the correlated property of B.

But the theory gives us only probabilities. We have no way of knowing in advance what result we will get for A. If A is found to be ‘down’, how does the distant, causally disconnected B ‘know’ how to correlate with its entangled partner and give the result ‘up’? The particles cannot break the correlation, because this would break the physical law that created it.

Physicists could simply assume that, when far enough apart, the particles are separate and distinct, or ‘locally real’, each possessing properties that were fixed at the moment of their interaction. Suppose A sets off towards a measuring instrument carrying the property ‘up’. A devious experimenter is perfectly at liberty to change the instrument setting so that when A arrives, it is now measured to be ‘down’. How, then, is the correlation established? Do the particles somehow remain in contact, sending messages to each other or exerting influences on each other over vast distances at speeds faster than light, in conflict with Einstein’s special theory of relativity?

The alternative possibility, equally discomforting to contemplate, is that the entangled particles do not actually exist independently of each other. They are ‘non-local’, implying that their properties are not fixed until a measurement is made on one of them.

Both these alternatives were unacceptable to Einstein, leading him to conclude that quantum mechanics cannot be complete.

Niels Bohr (left) and Albert Einstein. Credit: Universal History Archive/Universal Images Group via Getty

The EPR thought experiment delivered a shock to Bohr’s camp, but it was quickly (if unconvincingly) rebuffed by Bohr. Einstein’s challenge was not enough; he was content to criticize the theory but there was no consensus on an alternative to Bohr’s complementarity. Bohr was judged by the wider scientific community to have won the debate and, by the early 1950s, Einstein’s star was waning.

Unlike Bohr, Einstein had established no school of his own. He had rather retreated into his own mind, in vain pursuit of a theory that would unify electromagnetism and gravity, and so eliminate the need for quantum mechanics altogether. He referred to himself as a “lone traveler”. In 1948, US theoretical physicist J. Robert Oppenheimer remarked to a reporter at Time magazine that the older Einstein had become “a landmark, but not a beacon”.

Prevailing view

Subsequent readings of this period in quantum history promoted a persistent and widespread suggestion that the Copenhagen interpretation had been established as the orthodox view. I offer two anecdotes as illustration. When learning quantum mechanics as a graduate student at Harvard University in the 1950s, US physicist N. David Mermin recalled vivid memories of the responses that his conceptual enquiries elicited from his professors, whom he viewed as ‘agents of Copenhagen’. “You’ll never get a PhD if you allow yourself to be distracted by such frivolities,” they advised him, “so get back to serious business and produce some results. Shut up, in other words, and calculate.”

The spy who flunked it: Kurt Gödel’s forgotten part in the atom-bomb story

It seemed that dissidents faced serious repercussions. When US physicist John Clauser — a pioneer of experimental tests of quantum mechanics in the early 1970s — struggled to find an academic position, he was clear in his own mind about the reasons. He thought he had fallen foul of the ‘religion’ fostered by Bohr and the Copenhagen church: “Any physicist who openly criticized or even seriously questioned these foundations ... was immediately branded as a ‘quack’. Quacks naturally found it difficult to find decent jobs within the profession.”

But pulling on the historical threads suggests a different explanation for both Mermin’s and Clauser’s struggles. Because there was no viable alternative to complementarity, those writing the first post-war student textbooks on quantum mechanics in the late 1940s had little choice but to present (often garbled) versions of Bohr’s theory. Bohr was notoriously vague and more than occasionally incomprehensible. Awkward questions about the theory’s foundations were typically given short shrift. It was more important for students to learn how to apply the theory than to fret about what it meant.

One important exception is US physicist David Bohm’s 1951 book Quantum Theory , which contains an extensive discussion of the theory’s interpretation, including EPR’s challenge. But, at the time, Bohm stuck to Bohr’s mantra.

The Americanization of post-war physics meant that no value was placed on ‘philosophical’ debates that did not yield practical results. The task of ‘getting to the numbers’ meant that there was no time or inclination for the kind of pointless discussion in which Bohr and Einstein had indulged. Pragmatism prevailed. Physicists encouraged their students to choose research topics that were likely to provide them with a suitable grounding for an academic career, or ones that appealed to prospective employers. These did not include research on quantum foundations.

These developments conspired to produce a subtly different kind of orthodoxy. In The Structure of Scientific Revolutions (1962), US philosopher Thomas Kuhn describes ‘normal’ science as the everyday puzzle-solving activities of scientists in the context of a prevailing ‘paradigm’. This can be interpreted as the foundational framework on which scientific understanding is based. Kuhn argued that researchers pursuing normal science tend to accept foundational theories without question and seek to solve problems within the bounds of these concepts. Only when intractable problems accumulate and the situation becomes intolerable might the paradigm ‘shift’, in a process that Kuhn likened to a political revolution.

Do black holes explode? The 50-year-old puzzle that challenges quantum physics

The prevailing view also defines what kinds of problem the community will accept as scientific and which problems researchers are encouraged (and funded) to investigate. As Kuhn acknowledged in his book: “Other problems, including many that had previously been standard, are rejected as metaphysical, as the concern of another discipline, or sometimes as just too problematic to be worth the time.”

What Kuhn says about normal science can be applied to ‘mainstream’ physics. By the 1950s, the physics community had become broadly indifferent to foundational questions that lay outside the mainstream. Such questions were judged to belong in a philosophy class, and there was no place for philosophy in physics. Mermin’s professors were not, as he had first thought, ‘agents of Copenhagen’. As he later told me, his professors “had no interest in understanding Bohr, and thought that Einstein’s distaste for [quantum mechanics] was just silly”. Instead, they were “just indifferent to philosophy. Full stop. Quantum mechanics worked. Why worry about what it meant?”

It is more likely that Clauser fell foul of the orthodoxy of mainstream physics. His experimental tests of quantum mechanics 2 in 1972 were met with indifference or, more actively, dismissal as junk or fringe science. After all, as expected, quantum mechanics passed Clauser’s tests and arguably nothing new was discovered. Clauser failed to get an academic position not because he had had the audacity to challenge the Copenhagen interpretation; his audacity was in challenging the mainstream. As a colleague told Clauser later, physics faculty members at one university to which he had applied “thought that the whole field was controversial”.

Aspect, Clauser and Zeilinger won the 2022 physics Nobel for work on entangled photons. Credit: Claudio Bresciani/TT News Agency/AFP via Getty

However, it’s important to acknowledge that the enduring myth of the Copenhagen interpretation contains grains of truth, too. Bohr had a strong and domineering personality. He wanted to be associated with quantum theory in much the same way that Einstein is associated with theories of relativity. Complementarity was accepted as the last word on the subject by the physicists of Bohr’s school. Most vociferous were Bohr’s ‘bulldog’ Léon Rosenfeld, Wolfgang Pauli and Werner Heisenberg, although all came to hold distinct views about what the interpretation actually meant.

They did seek to shut down rivals. French physicist Louis de Broglie’s ‘pilot wave’ interpretation, which restores causality and determinism in a theory in which real particles are guided by a real wave, was shot down by Pauli in 1927. Some 30 years later, US physicist Hugh Everett’s relative state or many-worlds interpretation was dismissed, as Rosenfeld later described, as “hopelessly wrong ideas”. Rosenfeld added that Everett “was undescribably stupid and could not understand the simplest things in quantum mechanics”.

Unorthodox interpretations

But the myth of the Copenhagen interpretation served an important purpose. It motivated a project that might otherwise have been ignored. Einstein liked Bohm’s Quantum Theory and asked to see him in Princeton in the spring of 1951. Their discussion prompted Bohm to abandon Bohr’s views, and he went on to reinvent de Broglie’s pilot wave theory. He also developed an alternative to the EPR challenge that held the promise of translation into a real experiment.

Befuddled by Bohrian vagueness, finding no solace in student textbooks and inspired by Bohm, Irish physicist John Bell pushed back against the Copenhagen interpretation and, in 1964, built on Bohm’s version of EPR to develop a now-famous theorem 3 . The assumption that the entangled particles A and B are locally real leads to predictions that are incompatible with those of quantum mechanics. This was no longer a matter for philosophers alone: this was about real physics.

It took Clauser three attempts to pass his graduate course on advanced quantum mechanics at Columbia University because his brain “kind of refused to do it”. He blamed Bohr and Copenhagen, found Bohm and Bell, and in 1972 became the first to perform experimental tests of Bell’s theorem with entangled photons 2 .

How to introduce quantum computers without slowing economic growth

French physicist Alain Aspect similarly struggled to discern a “physical world behind the mathematics”, was perplexed by complementarity (“Bohr is impossible to understand”) and found Bell. In 1982, he performed what would become an iconic test of Bell’s theorem 4 , changing the settings of the instruments used to measure the properties of pairs of entangled photons while the particles were mid-flight. This prevented the photons from somehow conspiring to correlate themselves through messages or influences passed between them, because the nature of the measurements to be made on them was not set until they were already too far apart. All these tests settled in favour of quantum mechanics and non-locality.

Although the wider physics community still considered testing quantum mechanics to be a fringe science and mostly a waste of time, exposing a hitherto unsuspected phenomenon — quantum entanglement and non-locality — was not. Aspect’s cause was aided by US physicist Richard Feynman, who in 1981 had published his own version of Bell’s theorem 5 and had speculated on the possibility of building a quantum computer. In 1984, Charles Bennett at IBM and Giles Brassard at the University of Montreal in Canada proposed entanglement as the basis for an innovative system of quantum cryptography 6 .

It is tempting to think that these developments finally helped to bring work on quantum foundations into mainstream physics, making it respectable. Not so. According to Austrian physicist Anton Zeilinger, who has helped to found the science of quantum information and its promise of a quantum technology, even those working in quantum information consider foundations to be “not the right thing”. “We don’t understand the reason why. Must be psychological reasons, something like that, something very deep,” Zeilinger says. The lack of any kind of physical mechanism to explain how entanglement works does not prevent the pragmatic physicist from getting to the numbers.

Similarly, by awarding the 2022 Nobel Prize in Physics to Clauser, Aspect and Zeilinger , the Nobels as an institution have not necessarily become friendly to foundational research. Commenting on the award, the chair of the Nobel Committee for Physics, Anders Irbäck, said: “It has become increasingly clear that a new kind of quantum technology is emerging. We can see that the laureates’ work with entangled states is of great importance, even beyond the fundamental questions about the interpretation of quantum mechanics.” Or, rather, their work is of great importance because of the efforts of those few dissidents, such as Bohm and Bell, who were prepared to resist the orthodoxy of mainstream physics, which they interpreted as the enduring myth of the Copenhagen interpretation.

The lesson from Bohr–Einstein and the riddle of entanglement is this. Even if we are prepared to acknowledge the myth, we still need to exercise care. Heilbron warned against wanton slaying: “The myth you slay today may contain a truth you need tomorrow.”

Nature 629 , 29-32 (2024)

doi: https://doi.org/10.1038/d41586-024-01216-z

Updates & Corrections

Correction 25 April 2024 : An earlier version of this Essay misnamed the Institute for Advanced Study.

Einstein, A., Podolsky, B. & Rosen, N. Phys. Rev. 47 , 777–780 (1935).

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Freedman, S. J. & Clauser, J. F. Phys. Rev. Lett. 28 , 938–941 (1972).

Bell, J. S. Phys. Phys. Fiz. 1 , 195–200 (1964).

Aspect, A., Dalibard, J. & Roger, G. Phys. Rev. Lett. 49 , 1804–1807 (1982).

Feynman, R. P. Int . J. Theor. Phys. 21 , 467–488 (1982).

Bennett, C. H. & Brassard, G. in Proc. IEEE Int. Conf. on Computers, Systems and Signal Processing 175–179 (IEEE, 1984).

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Two Books on Einstein and the World He Made

A lbert Einstein is one of the most written-about figures of the 20th century, and for good reason. His theories upended the system that physicists had used to describe the world since Newton. Along the way, he became a figure of public fascination—a true celebrity. Now two books further scrutinize different aspects of the man.

Samuel Graydon’s “Einstein in Time and Space” is not an exhaustive biography. Instead it presents 99 vignettes, most of them one to three pages long, that highlight key qualities of this complex person: the curious child, the rebellious student, the serial adulterer, the wily prankster, the loyal friend, the civil-rights defender, the intellect unsurpassed in his time. Mr. Graydon, the science editor at the Times Literary Supplement, has chosen his number of chapters in a playful homage to the atomic number of the element einsteinium.

Even if readers are familiar with these stories, Mr. Graydon’s approach often delivers a fresh take on episodes not strongly emphasized in other biographies. Here is Einstein the engineer patenting a unique refrigerator design and a hearing aid. There he is building a miniature cable car out of matchboxes for his young son Hans. “That was one of the nicest toys I had,” Hans later recalled.

As a correspondent, Einstein could be quite impish: “So, what are you up to, you frozen whale, you smoked, dried, canned piece of soul, or whatever else I would like to hurl at your head?” he once wrote to a friend. While starting his career in Bern, Switzerland, the young physicist formed a little club called the Olympia Academy with two friends to discuss science and philosophy. “Einstein, despite being the youngest,” writes Mr. Graydon, “was elected president, earning him the title ‘Albert Ritter von Steissbein’ (roughly, ‘Sir Albert, Knight of Backside’). A certificate was made up, featuring a drawing of a bust of Einstein beneath a string of sausages.”

Mr. Graydon’s stated goal is to point out “the inconsistencies inherent in a life, the inexplicable, incompatible, insane motivations that punctuate days and years.” The author notes how Einstein, a devoted pacifist, maintained a close friendship with the German chemist Fritz Haber, who pioneered the use of both chlorine and mustard gas during World War I. He observes that the deep thinker didn’t pass up the chance to party with the movie stars Charlie Chaplin, Mary Pickford and Douglas Fairbanks when out in California.

The book also includes moments of quiet dignity, such as the story of the black contralto Marian Anderson, who had been invited in 1937 to give a concert at Princeton University but was denied a room at the local hotel due to her race. Einstein simply prepared a room for her at his home, an invitation that was extended from that day forward whenever she visited the town.

Mr. Graydon has woven from these separate strands a compelling and beautifully written narrative, though I have one caveat. In his acknowledgments, the author admits that he “lightly fictionalized” a few chapters about representative days at Einstein’s office. Given the wealth of material on hand, a summary of Einstein’s life hardly needs any false embellishments.

While “Einstein in Time and Space” primarily concentrates on Einstein’s personal experiences, Hanoch Gutfreund and Jürgen Renn’s “The Einsteinian Revolution” delves deeply into his science. Mr. Gutfreund, the academic director of the Albert Einstein Archives at the Hebrew University of Jerusalem, and Mr. Renn, the director of the Max Planck Institute for the History of Science in Berlin, have written extensively on Einstein and with this book take on a particular challenge: “to dispel the popular myth that Albert Einstein, the unconventional scientific genius, instigated an overwhelming scientific revolution through pure thought alone.” They succeed in that goal, along the way providing an excellent overview of Einstein’s major discoveries, from his early work on quantum theory to general relativity, the new law of gravity that overturned Newton. It is a welcome addition to any collection of books on modern physics.

A true understanding of Einstein’s accomplishments, they write, demands a revision of the legendary concept of the “paradigm shift.” The notion was introduced in 1962 by the historian of science Thomas Kuhn, who argued that a scientific revolution suddenly replaces a previous system of knowledge with a new one unconnected to the past. But Messrs. Gutfreund and Renn prefer to view Einstein’s work as an evolutionary process, where the new system is built upon the scientific scaffolding already in place.

In the late 19th century, that scaffolding was constructed around three dominant areas of physics: mechanics, thermodynamics and electromagnetism. Troubling puzzles were beginning to arise at the intersections between these fields, and many scientists attempted to find solutions within their own isolated specialties. But Einstein—with his deep reading of the scientific literature and the philosophy of science, his constant dialogues with scientific friends, and his careful attention to new experimental discoveries—stood above those boundaries, enabling him to perceive an entirely new vista.

The authors provide a detailed examination of Einstein’s annus mirabilis in 1905, when he recognized that light can act like a particle as well as a wave; proved that atoms exist; linked matter with energy in that celebrated equation E=mc2; and, with the special theory of relativity, swept away the idea that we live in a fixed space governed by a universal clock.

Before these discoveries, the authors note, the Dutch physicist Hendrik Lorentz had developed a mathematical scheme to explain the behavior of charged particles moving through the ether—the medium that supposedly permeates physical space to allow light to travel. Lorentz’s equations foresaw many of the phenomena later explained by special relativity. But his physical interpretation, complicated and full of assumptions, was still rooted in classical physics. Einstein jettisoned this kludge by doing away with the ether, recognizing that space and time are not absolute and declaring that the speed of light is a constant whether a body is stationary or in motion.

Einstein didn’t arrive at this solution in a single eureka moment. It was the result of deep reflection over the years, influenced by such philosophers as David Hume, who questioned the causal relations between events; Ernst Mach, who objected to Newton’s idea of absolute space; and Henri Poincaré, who early on noted the possible relativity of time. Einstein stood upon the shoulders of giants to gain his new perspective.

While “The Einsteinian Revolution” is written for a general audience, a background in physics helps make certain sections more accessible. Yet the authors’ overall thesis is clear and convincing. “The substance of Einstein’s work was not new,” they stress, “but rather was the result of an accumulation of knowledge over centuries; it was his conceptual organization that was new.” Their book, along with Mr. Graydon’s “Einstein in Time and Space,” enhances our understanding of both a great scientist and an exemplary humanist.

Ms. Bartusiak is a professor emeritus at MIT and the author of “Einstein’s Unfinished Symphony.”

Stephen Hawking: Everything you need to know about the thesis that 'broke the Internet'

Your cheat sheet into the mind of one of the world’s greatest physicists.

Scribbled in pencil on one of its early pages is "no copying without the author's consent". In October 2017, Stephen Hawking allowed his PhD thesis — Properties of Expanding Universes — to be made available online through the University of Cambridge's Apollo portal. The website crashed almost immediately under the sheer weight of traffic. It was downloaded almost 60,000 times in the first 24 hours alone.

Hawking was 24 years old when he received his PhD in 1966 and, despite being diagnosed with motor neurone disease at just 21, could still handwrite that "this dissertation is my original work." In a statement to accompany its release, the late physicist said: "By making my PhD thesis Open Access, I hope to inspire people around the world to look up at the stars and not down at their feet; to wonder about our place in the universe and to try and make sense of the cosmos." 

Here, we break it down, guiding you through the physics until we reach the conclusion that made Hawking a household name.

Step 1: What’s it about?

Hawking's PhD thesis relates to Albert Einstein's General Theory of Relativity — the more accurate theory of gravity that replaced Isaac Newton 's original ideas. Newton said gravity was a pull between two objects. Einstein said that gravity is the result of massive objects warping the fabric of space and time (space-time) around them. According to Einstein, Earth orbits the sun because we're caught in the depression our star makes in space-time.

Hawking applies the mathematics of general relativity to models of the birth of our universe ( cosmologies ). The earliest cosmologies had our universe as a static entity that had existed forever. This idea was so ingrained that when Einstein's original calculations suggested a static universe was unlikely, he added a "cosmological constant" to the math in order to keep the universe static. He would later reportedly call it his "greatest blunder".

Things began to change when Edwin Hubble made an important discovery. Hawking writes: "the discovery of the recession of the nebulae [galaxies] by Hubble led to the abandonment of static models in favor of ones in which we're expanding."

Step 2: Our expanding universe

Some astronomers seized the idea of an expanding universe to argue that the universe must have had a beginning — a moment of creation called the Big Bang . The name was coined by Fred Hoyle, an advocate of the alternative Steady State Model. This theory states that the universe has been around forever, and that new stars form in the gaps created as the universe expands. There was no initial creation event.

Hawking spends chapter one of his thesis taking down the premise, formally encapsulated in a model called Hoyle-Narlikar theory. Hawking laments that although the General Theory of Relativity is powerful, it allows for many different solutions to its equations. That means many different models can be consistent with it. He says that's "one of the weaknesses of the Einstein theory."

The famous physicist then shows that a requirement of Hoyle-Narlikar theory appears to "exclude those models that seem to correspond to the actual universe." In short, the Steady State Model fails to match observation.

Step 3: Space: It looks the same everywhere

Hawking says that the assumptions of the Hoyle-Narlikar theory are in direct contradiction of the Robertson-Walker metric, named after American physicist Howard P. Robertson and British mathematician Arthur Walker. Today it is more widely called the Friedmann–Lemaître–Robertson–Walker (FLRW) metric. A metric is an exact solution to the equations of Einstein's General Theory of Relativity. Devised in the 1920s and 1930s, FLRW forms the basis of our modern model of the universe. Its key feature is that it assumes matter is evenly distributed in an expanding (or contracting) universe — a premise backed up by astronomical observations. 

Interestingly, Hawking offers Hoyle and Narlikar a ray of hope. "A possible way to save the Hoyle-Narlikar theory would be to allow masses of both positive and negative sign," he writes, before adding: "There does not seem to be any matter having these properties in our region of space." Today, we know that the expansion of the universe is accelerating, perhaps due to dark energy — a shadowy entity with an anti-gravitational property perhaps akin to particles with a negative mass.

Step 4: The problem with galaxies

Even geniuses get it wrong sometimes. Hawking's second chapter covers perturbations — small variations in the local curvature of space-time — and how they evolve as the universe expands. He says that a small perturbation “will not contract to form a galaxy." Later in the chapter he goes on to say: "We see that galaxies cannot form as the result of the growth of small perturbations."

That couldn't be further from our modern-day picture of how galaxies form. The key ingredient Hawking was missing is dark matter , an invisible substance thought to be spread throughout the universe, which provides a gravitational glue that holds galaxies together. Dark matter gathered around small space-time perturbations, eventually drawing in more and more material until early galaxies formed.

Our modern working cosmological picture is known as the ΛCDM model (pronounced Lambda CDM). Lambda is the Greek letter cosmologists use to denote the cosmological constant that Einstein originally introduced (albeit for the wrong reasons). CDM stands for cold dark matter. These two factors have been added to the FLRW model since Hawking wrote his thesis.

Step 5: Gravitational waves don’t disappear

Where Hawking was wrong on galaxies, he was very right on gravitational waves —ripples in the fabric of space-time that move outwards through the universe. They were predicted by Einstein when he first devised his Theory of General Relativity back in 1915, and in Hawking's time were also known as gravitational radiation.

Hawking uses Einstein's equations to show that gravitational waves aren't absorbed by matter in the universe as they travel through it, assuming the universe is largely made of dust. In fact, Hawking says that "gravitational radiation behaves in much the same way as other radiation fields [such as light]."

The physicist does note how esoteric the topic is in the 1960s. "This is slightly academic since gravitational radiation has not yet been detected, let alone investigated."

It would take physicists until September 2015 to detect gravitational waves for the first time using the Laser Interferometer Gravitational-Wave Observatory (LIGO). They were produced by the collision of two black holes — one 36- and the other 29-times the mass of the sun — about 1.3-billion-light-years away.

Related: Lab-grown black hole analog behaves just like Stephen Hawking said it would

Step 6: Are we living in an open, closed, or flat cosmos?

Hawking is heading for a groundbreaking conclusion, but first he sets himself up by introducing the idea of the overall shape of space. There are three general forms the curvature of space can take: open, closed, or flat.

A closed universe resembles Earth's surface — it has no boundary. You can keep traveling around the planet without coming to an edge. An open universe is shaped more like a saddle. A flat universe, as the name suggests, is like a sheet of paper. 

Imagine a triangle drawn onto the surface. We all learn at school that the angles inside a triangle sum to 180 degrees. However, that's only the case for triangles on flat surfaces, not open or closed ones. Draw a line from the Earth's North Pole down to the equator, before taking a 90-degree turn to travel along it. Then make another 90-degree turn back towards the North Pole. The angle between your path away from and towards the North Pole cannot be zero, so the angles inside that triangle must add up to more than 180 degrees.

Step 7: The universe is flat!

Hawking then links the idea of open and closed universes to Cauchy surfaces, named after the French mathematician and physicist Augustin-Louis Cauchy (1789—1857). A Cauchy surface is a slice through space-time, the equivalent of an instant of time. All points on the surface are connected in time. A path along a Cauchy surface cannot see you revisit a previous moment. In Hawking's own words: “A Cauchy surface will be taken to mean a complete, connected space-like surface that intersects every time-like and null line once and once only.”

He then says that closed universes are known as "compact" Cauchy surfaces, and open universes as “non-compact” ones. The former example is said to have "positive" curvature, the latter "negative" curvature. 

A flat universe has zero curvature. He moves on to set up the landmark assertions he's about to make about singularities by saying they are “applicable to models... with surfaces... which have negative or zero curvature.” Modern astronomers believe the universe is flat, meaning its zero curvature satisfies Hawking's conditions. 

Step 8: Hawking drops a bombshell

Most of the early chapters of Hawking's thesis are unremarkable — they don't offer anything particularly revolutionary, and he even gets a few things wrong. However, in his final chapter the physicist drops a bombshell that will make his name and ignite a stellar career, during which he will become one of the most famous scientists on the planet.

He says that space-time can begin and end at a singularity , and what's more he can prove it. A singularity is an infinitely small and infinitely dense point. It literally has zero size, and space and time both end (or begin) at a singularity. They had been predicted for decades, particularly when physicists started to apply Einstein's General Theory of Relativity to the picture of an expanding universe. 

If the universe is expanding today then it was smaller yesterday. Keep working back, and you find all matter in the universe condensed into a tiny, hot point — the moment of creation, a Big Bang. But just how do you prove that you can indeed get singularities in space-time?

Step 9: Hawking’s proof that the Big Bang happened

Hawking's proof leans on a very old method for proving a mathematical theory: Proof by contradiction. First you assume the thing you are trying to prove isn't true, then show that the resulting conclusions are demonstrably false. In fact, Hawking's most important section begins with the words "assume that space-time is singularity-free." There then follows some very complicated maths to show that such a universe would be simultaneously both open and closed — compact and non-compact at the same time. "This is a contradiction," Hawking said. "Thus the assumption that space-time is non-singular must be false." 

In one swoop, Hawking had proven that it is possible for space-time to begin as a singularity — that space and time in our universe could have had an origin. The Big Bang theory had just received a significant shot in the arm. Hawking started to write his PhD in October 1965, just 17 months after the discovery of the Cosmic Microwave Background — the leftover energy from the Big Bang. Together, these discoveries buried the Steady State Model for good.

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Colin Stuart is an award-winning astronomy author, speaker and tutor based in the UK. His popular science books have sold over 400,000 copies worldwide and have been translated into 21 languages. The asteroid (15347) Colinstuart is named after him and he runs an online Astrophysics for Beginners course and a science writing course .

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Analyzing Albert Einstein's Theory of Relativity Thesis Defense

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