Relativity priority dispute

Albert Einstein presented the theories of Special Relativity and General Relativity in groundbreaking publications that either contained no formal references to previous literature, or referred only to a small number of his predecessors for fundamental results on which he based his theories, most notably to the work of Hendrik Lorentz for special relativity, and to the work of Gauss, Riemann, and Mach for general relativity. Subsequently claims have been put forward about both theories, asserting that they were formulated, either wholly or in part, by others before Einstein. At issue is the extent to which Einstein and various other individuals should be credited for the formulation of these theories, based on priority considerations.

The general history of the development of these theories, including the contributions made by many other scientists, is found at History of special relativity and History of general relativity.

The candidates for credit

Concerning special relativity, the most important names that are mentioned in discussions about the distribution of credit are Albert Einstein, Hendrik Lorentz, Henri Poincaré, and Hermann Minkowski. Consideration is also given to numerous other scientists for either anticipations of some aspects of the theory, or else for contributions to the development or elaboration of the theory. These include Woldemar Voigt, August Föppl, Joseph Larmor, Emil Cohn, Friedrich Hasenöhrl, Max Planck, Max von Laue, Gilbert Newton Lewis and Richard Chase Tolman, and others. In addition, polemics exist about alleged contributions of others such as Olinto De Pretto, and Einstein's first wife Mileva Marić, although these are not considered to have any foundation by serious scholars.[1]

Concerning general relativity, there is a controversy about the amount of credit that should go to Einstein, Marcel Grossmann, and David Hilbert. Many others (such as Gauss, Riemann, William Kingdon Clifford, Ricci, and Levi-Civita) contributed to the development of the mathematical tools and geometrical ideas underlying the theory. Also polemics exist about alleged contributions of others such as Paul Gerber.

Undisputed and well known facts

The following facts are undisputed and generally accepted as true:

Special relativity

General relativity

Disputed claims

The following things seem to be unclear, unknown or disputed:

Special relativity

General relativity

There are a large number of opinions related to these involving questions of "who should get the credit" - these are not enumerated here.

Special Relativity

Historians of special relativity

In his History of the theories of ether and electricity from 1953, E. T. Whittaker claimed that relativity is the creation of Lorentz and Poincaré and attributed to Einstein's papers only little importance.[11] However, most historians of science, like Gerald Holton, Arthur I. Miller, Abraham Pais, John Stachel, or Olivier Darrigol have other points of view. They admit that Lorentz and Poincaré developed the mathematics of special relativity, and many scientists originally spoke about the "Lorentz-Einstein theory". But they argue that it was Einstein who completely eliminated the classical ether and demonstrated the relativity of space and time. They also argue that Poincaré demonstrated the relativity of space and time only in his philosophical writings, but in his physical papers he maintained the ether as a privileged frame of reference that is perfectly undetectable, and continued (like Lorentz) to distinguish between "real" lengths and times measured by observers at rest within the aether, and "apparent" lengths and times measured by observers in motion within the aether.[B 2][B 3][B 4][B 5][B 6] Darrigol summarizes:

Most of the components of Einstein's paper appeared in others' anterior works on the electrodynamics of moving bodies. Poincaré and Alfred Bucherer had the relativity principle. Lorentz and Larmor had most of the Lorentz transformations, Poincaré had them all. Cohn and Bucherer rejected the ether. Poincaré, Cohn, and Abraham had a physical interpretation of Lorentz's local time. Larmor and Cohn alluded to the dilation of time. Lorentz and Poincaré had the relativistic dynamics of the electron. None of these authors, however, dared to reform the concepts of space and time. None of them imagined a new kinematics based on two postulates. None of them derived the Lorentz transformations on this basis. None of them fully understood the physical implications of these transformations. It all was Einstein's unique feat.[B 7]

Comments by Lorentz, Poincaré, and Einstein

Lorentz

In a paper that was written in 1914 and published in 1921,[12] Lorentz expressed appreciation for Poincaré's Palermo paper (1906)[13] on relativity. Lorentz stated:

I did not indicate the transformation which suits best. That was done by Poincaré and then by Mr. Einstein and Minkowski. [..] Because I had not thought of the direct way which led there, and because I had the idea that there is an essential difference between systems x, y, z, t and x',y',z',t'. In one we use - such was my thought - coordinate axes which have a fixed position in the aether and which we can call "true" time; in the other system, on the contrary, we would deal with simple auxiliary quantities whose introduction is only a mathematical artifice. [..] I did not establish the principle of relativity as rigorously and universally true. Poincaré, on the contrary, obtained a perfect invariance of the equations of electrodynamics, and he formulated the "postulate of relativity", terms which he was the first to employ. [..] Let us add that by correcting the imperfections of my work he never reproached me for them.

However, a 1916 reprint of his main work "The theory of electrons" contains notes (written in 1909 and 1915) in which Lorentz sketched the differences between his results and that of Einstein as follows:[14]

[p. 230]: the chief difference [is] that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. [p. 321]: The chief cause of my failure was my clinging to the idea that the variable t only can be considered as the true time and that my local time t' must be regarded as no more than an auxiliary mathematical quantity. In Einstein's theory, on the contrary, t' plays the same part as t; if we want to describe phenomena in terms of x', y', z', t' we must work with these variables exactly as we could do with x, y, z, t.

Regarding the fact, that in this book Lorentz only mentioned Einstein and not Poincaré in connection with a) the synchronisation by light signals, b) the reciprocity of the Lorentz transformation, and c) the relativistic transformation law for charge density, Janssen comments:[B 8]

[p.90]: My guess is that it has to do with the fact that Einstein made the physical interpretation of the Lorentz transformation the basis for a remarkably clear and simple discussion of the electrodynamics of moving bodies, whereas Poincaré's remarks on the physical interpretation of Lorentz transformed quantities may have struck Lorentz as inconsequential philosophical asides in expositions that otherwise closely followed his own. I also have a sense that Lorentz found Einstein's physically very intuitive approach more appealing than Poincaré's rather abstract but mathematically more elegant approach.

And at a conference on the Michelson–Morley experiment in 1927 at which Lorentz and Michelson were present, Michelson suggested that Lorentz was the initiator of the theory of relativity. Lorentz then replied:[15]

I considered my time transformation only as a heuristic working hypothesis. So the theory of relativity is really solely Einstein's work. And there can be no doubt that he would have conceived it even if the work of all his predecessors in the theory of this field had not been done at all. His work is in this respect independent of the previous theories.

Poincaré

Poincaré attributed the development of the new mechanics almost entirely to Lorentz. He only mentioned Einstein in connection with the photoelectric effect,[16] but not in connection with special relativity. For example, in 1912 Poincaré raises the question whether "the mechanics of Lorentz" will still exist after the development of the quantum theory. He wrote:[16]

“ In all instances in which it differs from that of Newton, the mechanics of Lorentz endures. We continue to believe that no body in motion will ever be able to exceed the speed of light; that the mass of a body is not a constant, but depends on its speed and the angle formed by this speed with the force which acts upon the body; that no experiment will ever be able to determine whether a body is at rest or in absolute motion either in relation to absolute space or even in relation to the ether. ”

Einstein

It is now known that Einstein was well aware of the scientific research of his time. The well known historian of science, Jürgen Renn, Director of the Max Planck Institute for the History of Science wrote on Einstein's contributions to the Annalen der Physik:[17]

“ The Annalen also served as a source of modest additional income for Einstein, who wrote more than twenty reports for its Beiblätter - mainly on the theory of heat - thus demonstrating an impressive mastery of the contemporary literature. This activity started in 1905.[18] and probably resulted from his earlier publications in the Annalen in this field. Going by his publications between 1900 and early 1905, one would conclude that Einstein's specialty was thermodynamics. ”

Einstein wrote in 1907[19] that one needed only to realize that an auxiliary quantity that was introduced by Lorentz and that he called "local time" can simply be defined as "time." In 1909[20] and 1912[21] Einstein explained:[B 9]

...it is impossible to base a theory of the transformation laws of space and time on the principle of relativity alone. As we know, this is connected with the relativity of the concepts of "simultaneity" and "shape of moving bodies." To fill this gap, I introduced the principle of the constancy of the velocity of light, which I borrowed from H. A. Lorentz's theory of the stationary luminiferous ether, and which, like the principle of relativity, contains a physical assumption that seemed to be justified only by the relevant experiments (experiments by Fizeau, Rowland, etc.)[21]
— Albert Einstein (1912), translated by Anna Beck (1996).

But Einstein and his supporters took the position that this "light postulate" together with the principle of relativity renders the ether superfluous and leads directly to Einstein's version of relativity. It is also known[22] that Einstein had been reading and studying Poincaré's 1902-book Science and hypothesis well before 1905, which included:

Einstein refers to Poincaré in connection with the inertia of energy in 1906[23] and the non-Euclidean geometry in 1921,[24] but not in connection with the Lorentz transformation, the relativity principle or the synchronisation procedure by light signals. However, in the last years before his death Einstein acknowledged some of Poincaré's contributions (according to Darrigol, maybe because his biographer Pais in 1950 sent Einstein a copy of Poincarè's Palermo paper, which he said that he had not read before). Einstein wrote in 1953:[B 10]

“ There is no doubt, that the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905. Lorentz had already recognized that the transformations named after him are essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further. Concerning myself, I knew only Lorentz's important work of 1895 [...] but not Lorentz's later work, nor the consecutive investigations by Poincaré. In this sense my work of 1905 was independent. [..] The new feature of it was the realization of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell's equations and was concerned with the nature of space and time in general. A further new result was that the "Lorentz invariance" is a general condition for any physical theory. ”

General Relativity

Did Hilbert claim priority for parts of General Relativity?

Kip Thorne concludes, in remarks based on Hilbert's 1924 paper, that Hilbert regarded the General Theory of relativity as Einstein's: "Quite naturally, and in accord with Hilbert's view of things, the resulting law of warpage was quickly given the name the Einstein field equation rather than being named after Hilbert. Hilbert had carried out the last few mathematical steps to its discovery independently and almost simultaneously with Einstein, but Einstein was responsible for essentially everything that preceded those steps...".[B 11] However, Kip Thorne also stated, "Remarkably, Einstein was not the first to discover the correct form of the law of warpage [. . . .] Recognition for the first discovery must go to Hilbert."[B 11]

Arguments have been made that Hilbert claimed priority for the field equations themselves; the sources cited for this are:

So far, there seems to be no consensus that these statements form a clear claim by Hilbert to have published the field equations first.

Did Einstein develop the field equations independently?

For a long time, it was believed that Einstein and Hilbert found the field equations of gravity independently. While Hilbert's paper was submitted somewhat earlier than Einstein's, it only appeared in 1916, after Einstein's field equations paper had appeared in print. For this reason there was no good reason to suspect plagiarism on either side. In 1978, a November 18, 1915 letter from Einstein to Hilbert resurfaced, in which Einstein thanked Hilbert for sending an explanation of Hilbert's work. This was not unexpected to most scholars, who were well aware of the correspondence between Hilbert and Einstein that November, and who continued to hold the view expressed by Albrecht Fölsing in his Einstein biography:

In November, when Einstein was totally absorbed in his theory of gravitation, he essentially only corresponded with Hilbert, sending Hilbert his publications and, on November 18, thanking him for a draft of his article. Einstein must have received that article immediately before writing this letter. Could Einstein, casting his eye over Hilbert's paper, have discovered the term which was still lacking in his own equations, and thus 'nostrified' Hilbert? [B 15]

In the very next sentence, after asking the rhetorical question, Folsing answers it with "This is not really probable...", and then goes on to explain in detail why

"[Einstein's] eventual derivation of the equations was a logical development of his earlier arguments—in which, despite all the mathematics, physical principles invariably predominated. His approach was thus quite different from Hilbert's, and Einstein's achievements can, therefore, surely be regarded as authentic."

In their 1997 Science paper,[B 16] Corry, Renn and Stachel quote the above passage and comment that "the arguments by which Einstein is exculpated are rather weak, turning on his slowness in fully grasping Hilbert's mathematics", and so they attempted to find more definitive evidence of the relationship between the work of Hilbert and Einstein, basing their work largely on a recently discovered pre-print of Hilbert's paper. A discussion of the controversy around this paper is given below.

Those who contend that Einstein's paper was motivated by the information obtained from Hilbert have referred to the following sources:

Those who contend that Einstein's work takes priority over Hilbert's,[B 16] or that both authors did their work independently[B 17] have used the following arguments:

Attackers and defenders

This section cites notable publications where people have expressed a view on the issues outlined above.

Special relativity

Sir Edmund Whittaker (1954)

In 1954, Sir Edmund Taylor Whittaker, an English mathematician and historian of science, credited Poincaré with the equation E=mc^2, and he included a chapter entitled The Relativity Theory of Poincaré and Lorentz in his book A History of the Theories of Aether and Electricity.[B 20] He credited Poincaré and Lorentz, and especially alluded to Lorentz's 1904 paper (dated by Whittaker as 1903), Poincaré's St. Louis speech (The Principles of Mathematical Physics) of September 1904, and Poincaré's June 1905 paper. Whittaker attributed to Einstein's relativity paper only little importance, i.e., the formulation of the Doppler and aberration formulas.

Gerald Holton (1960)

Whittaker's claims were criticized by Gerald Holton (1960, 1973).[B 2] He argued that there are fundamental differences between the theories of Einstein on one hand, and Poincaré and Lorentz on the other hand. Einstein radically reformulated the concepts of space and time, and by that removed "absolute space" and thus the stationary luminiferous aether from physics. On the other hand, Holton argued that Poincaré and Lorentz still adhered to the stationary aether concept, and tried only to modify Newtonian dynamics, not to replace it. Holton argued, that "Poincaré's silence" (i.e., why Poincaré never mentioned Einstein's contributions to relativity) was due to their fundamentally different conceptual viewpoints. Einstein's views on space and time and the abandonment of the aether were, according to Holton, not acceptable to Poincaré, therefore the latter only referred to Lorentz as the creator of the "new mechanics". Holton also pointed out that although Poincaré's 1904 St. Louis speech was "acute and penetrating" and contained a "principle of relativity" that is confirmed by experience and needs new development, it did not "enunciate a new relativity principle". He also alluded to mistakes of Whittaker, like predating Lorentz's 1904 paper (published April 1904) to 1903.

Views similar to Holton's were later (1967, 1970) expressed by his former student, Stanley Goldberg.[B 21]

G. H. Keswani (1965)

In a 1965 series of articles tracing the history of relativity,[B 22] Keswani claimed that Poincaré and Lorentz should have the main credit for special relativity - claiming that Poincaré pointedly credited Lorentz multiple times, while Lorentz credited Poincaré and Einstein, refusing to take credit for himself. He also downplayed the theory of general relativity, saying "Einstein's general theory of relativity is only a theory of gravitation and of modifications in the laws of physics in gravitational fields".[B 22] This would leave the special theory of relativity as the unique theory of relativity. Keswani cited also Vladimir Fock for this same opinion.

This series of articles prompted responses, among others from Herbert Dingle and Karl Popper.

Dingle said, among other things, ".. the 'principle of relativity' had various meanings, and the theories associated with it were quite distinct; they were not different forms of the same theory. Each of the three protagonists.... was very well aware of the others .... but each preferred his own views"[B 23]

Karl Popper says "Though Einstein appears to have known Poincaré's Science and Hypothesis prior to 1905, there is no theory like Einstein's in this great book."[B 24]

Keswani did not accept the criticism, and replied in two letters also published in the same journal ([B 25] and [B 26] - in his reply to Dingle, he argues that the three relativity theories were at heart the same: ".. they meant much that was common. And that much mattered the most."[B 25]

Dingle commented the year after on the history of crediting: "Until the first World War, Lorentz's and Einstein's theories were regarded as different forms of the same idea, but Lorentz, having priority and being a more established figure speaking a more familiar language, was credited with it." (Dingle 1967, Nature 216 p. 119-122).

Arthur I. Miller (1973)

Miller (1973, 1981)[B 3] agreed with the analysis of Holton and Goldberg, and further argued that although the terminology (like the principle of relativity) used by Poincaré and Einstein were very similar, their content differs sharply. According to Miller, Poincaré used this principle to complete the aether based "electromagnetic world-view" of Lorentz and Abraham. He also argued that Poincaré distinguished (in his July 1905 paper) between "ideal" and "real" systems and electrons. That is, Lorentz's and Poincaré's usage of reference frames lacks an unambiguous physical interpretation, because in many cases they are only mathematical tools, while in Einstein's theory the processes in inertial frames are not only mathematically, but also physically equivalent. Miller wrote in 1981:

p. 172: "Although Poincaré's principle of relativity is stated in a manner similar to Einstein's, the difference in content is sharp. The critical difference is that Poincaré's principle admits the existence of the ether, and so considers the velocity of light to be exactly c only when it is measured in coordinate systems at rest in the ether. In inertial reference systems, the velocity of light is c and is independent of the emitter's motion as a result of certain compensatory effects such as the mathematical local time and the hypothesis of an unobservable contraction. Consequently, Poincaré's extension of the relativity principle of relative motion into the dynamics of the electron resided in electromagnetic theory, and not in mechanics...Poincaré came closest to rendering electrodynamics consistent, but not to a relativity theory." p. 217: "Poincaré related the imaginary system Σ' to the ether fixed system S'".

Miller (1996)[B 3] argues that Poincaré was guided by empiricism, and was willing to admit that experiments might prove relativity wrong, and so Einstein is more deserving of credit, even though he might have been substantially influenced by Poincaré's papers. Miller also argues that "Emphasis on conventionalism ... led Poincaré and Lorentz to continue to believe in the mathematical and observational equivalence of special relativity and Lorentz's electron theory. This is incorrect." [p. 96] Instead, Miller claims that the theories are mathematically equivalent but not physically equivalent. [p. 91-92]

Abraham Pais (1982)

In his Einstein biography Subtle is the Lord (1982),[B 4] Abraham Pais argued that Poincaré "comes near" to discovering special relativity (in his St. Louis lecture of September 1904, and the June 1905 paper), but eventually he failed, because in 1904 and also later in 1909, Poincaré treated length contraction as a third independent hypothesis besides the relativity principle and the constancy of the speed of light. According to Pais, Poincaré thus never understood (or at least he never accepted) special relativity, in which the whole theory including length contraction can simply be derived from two postulates. Consequently, he sharply criticized Whittaker's chapter on the "Relativity theory of Poincaré and Lorentz", saying "how well the author's lack of physical insight matches his ignorance of the literature", although Pais admitted that the first book of Whittaker's History of Aether and Electricity is a masterpiece.

He also argued that Lorentz never abandoned the stationary aether concept, either before or after 1905:

p. 118: "Throughout the paper of 1895, the Fresnel aether is postulated explicitly"; p. 125: "Like Voigt before him, Lorentz regarded the transformation ... only as a convenient mathematical tool for proving a physical theorem ... he proposed to call t the general time and t' the local time. Although he didn't say it explicitly, it is evident that to him there was, so to speak, only one true time t."; p. 166: "8.3. Lorentz and the Aether... For example, Lorentz still opines that the contraction of the rods has a dynamic origin. There is no doubt that he had read and understood Einstein's papers by then. However, neither then nor later was he prepared to accept their conclusions as the definitive answer to the problems of the aether."

Elie Zahar (1983)

In several papers, Elie Zahar (1983, 2000)[B 27] argued that both Einstein (in his June paper) and Poincaré (in his July paper) independently discovered special relativity. He said that "though Whittaker was unjust towards Einstein, his positive account of Poincaré's actual achievement contains much more than a simple grain of truth". According to him, it was Poincaré's unsystematic and sometimes erroneous statements regarding his philosophical papers (often connected with conventionalism), which hindered many to give him due credit. In his opinion, Poincaré was rather a "structural realist" and from that he concludes, that Poincaré actually adhered to the relativity of time and space, while his allusions to the aether are of secondary importance. He continues, that due to his treatment of gravitation and four-dimensional space, Poincaré's 1905/6-paper was superior to Einstein's 1905-paper. Yet Zahar gives also credit to Einstein, who introduced Mass–Energy equivalence, and also transcended special relativity by taking a path leading to the development of general relativity.

John Stachel (1995)

John Stachel (1995)[B 28] argued that there is a debate over the respective contributions of Lorentz, Poincaré and Einstein to relativity. These questions depend on the definition of relativity, and Stachel argued that kinematics and the new view of space and time is the core of special relativity, and dynamical theories must be formulated in accordance with this scheme. Based on this definition, Einstein is the main originator of the modern understanding of special relativity. In his opinion, Lorentz interpreted the Lorentz transformation only as a mathematical device, while Poincaré's thinking was much nearer to the modern understanding of relativity. Yet Poincaré still believed in the dynamical effects of the aether and distinguished between observers being at rest or in motion with respect to it. Stachel wrote: "He never organized his many brilliant insights into a coherent theory that resolutely discarded the aether and the absolute time or transcended its electrodynamic origins to derive a new kinematics of space and time on a formulation of the relativity principle that makes no reference to the ether".

Peter Galison (2002)

In his book Einstein's clocks, Poincaré's maps (2002),[B 6][B 29] Peter Galison compared the approaches of both Poincaré and Einstein to reformulate the concepts of space and time. He wrote: "Did Einstein really discover relativity? Did Poincaré already have it? These old questions have grown as tedious as they are fruitless." This is because it depends on the question, which parts of relativity one considers as essential: the rejection of the aether, the Lorentz transformation, the connection with the nature of space and time, predictions of experimental results, or other parts. For Galison, it is more important to acknowledge that both thinkers were concerned with clock synchronization problems, and thus both developed the new operational meaning of simultaneity. However, while Poincaré followed a constructive approach and still adhered to the concepts of Lorentz's stationary aether and the distinction between "apparent" and "true" times, Einstein abandoned the aether and therefore all times in different inertial frames are equally valid. Galison argued that this does not mean that Poincaré was conservative, since Poincaré often alluded to the revolutionary character of the "new mechanics" of Lorentz.

Olivier Darrigol (2004)

In his 2004 article, "The Mystery of the Einstein-Poincaré Connection", Darrigol wrote:[B 7]

Anatoly Alexeevich Logunov on special relativity (2004)

In Anatoly Logunov's book[B 18] about Poincaré's relativity theory, there is an English translation (on p. 113, using modern notations) of the part of Poincaré's 1900 article containing E=mc2. Logunov states that Poincaré's two 1905 papers are superior to Einstein's 1905 paper. According to Logunov, Poincaré was the first scientist to recognize the importance of invariance under the Poincaré group as a guideline for developing new theories in physics. In chapter 9 of this book, Logunov points out that Poincaré's second paper was the first one to formulate a complete theory of relativistic dynamics, containing the correct relativistic analogue of Newton's F=ma.

On p. 142, Logunov points out that Einstein wrote reviews for the Beiblätter Annalen der Physik, writing 21 reviews in 1905. In his view, this contradicts the claims that Einstein worked in relative isolation and with limited access to the scientific literature. Among the papers reviewed in the Beiblätter in the fourth (of 24) issue of 1905, there is a review of Lorentz' 1904-paper by Richard Gans, which contains the Lorentz transformations. In Logunov's view, this supports the view that Einstein was familiar with the Lorentz' paper containing the correct relativistic transformation in early 1905, while his June 1905 paper does not mention Lorentz in connection with this result.

Harvey R. Brown (2005)

Harvey R. Brown (2005)[B 30] (who favors a dynamical view of relativistic effects similar to Lorentz, but "without a hidden aether frame") wrote about the road to special relativity from Michelson to Einstein in section 4:

p. 40: "The cradle of special theory of relativity was the combination of Maxwellian electromagnetism and the electron theory of Lorentz (and to a lesser extent of Larmor) based on Fresnel's notion of the stationary aether....It is well known that Einstein's special relativity was partially motivated by this failure [to find the aether wind], but in order to understand the originality of Einstein's 1905 work it is incumbent on us to review the work of the trailblazers, and in particular Michelson, FitzGerald, Lorentz, Larmor, and Poincaré. After all they were jointly responsible for the discovery of relativistic kinematics, in form if not in content, as well as a significant portion of relativistic dynamics as well."

Regarding Lorentz's work before 1905, Brown wrote about the development of Lorentz's "theorem of corresponding states" and then continued:

p. 54: "Lorentz's interpretation of these transformations is not the one Einstein would given them and which is standardly embraced today. Indeed, until Lorentz came to terms with Einstein's 1905 work, and somehow despite Poincaré's warning, he continued to believe that the true coordinate transformations were the Galilean ones, and that the 'Lorentz' transformations ... were merely a useful formal device..." p. 56. "Lorentz consistently failed to understand the operational significance of his notions of 'local' time...He did however have an intimation of time dilation in 1899, but inevitably there are caveats...The hypotheses of Lorentz's system were starting to pile up, and the spectre of ad hocness was increasingly hard to ignore."

Then the contribution of Poincaré's to relativity:

p. 62: "Indeed, the claim that this giant of pure and applied mathematics co-discovered special relativity is not uncommon, and it is not hard to see why. Poincaré was the first to extend the relativity principle to optics and electrodynamics exactly. Whereas Lorentz, in his theorem of corresponding states, had from 1899 effectively assumed this extension of the relativity principle up to second-order effects, Poincaré took it to hold for all orders. Poincaré was the first to show that Maxwell's equations with source terms are strictly Lorentz covariant. … Poincaré was the first to use the generalized relativity principle as a constraint on the form of the coordinate transformations. He recognized that the relativity principle implies that the transformations form a group, and in further appealing to spatial isotropy. … Poincaré was the first to see the connection between Lorentz's ‘local time’, and the issue of clock synchrony. … It is fair to say that Poincaré was the first to understand the relativity of simultaneity, and the conventionality of distant simultaneity. Poincaré anticipated Minkowski's interpretation of the Lorentz transformations as a passive, rigid rotation within a four-dimensional pseudo-Euclidean space-time. He was also aware that the the [sic] electromagnetic potentials transform in the manner of what is now called a Minkowski 4-vector. He anticipated the major results of relativistic dynamics (and in particular the relativistic relations between force, momentum and velocity), but not E=mc² in its full generality."

However, Brown continued with the reasons which speak against Poincaré's co-discovery:

p. 63-64: "What are the grounds for denying Poincaré the title of co-discoverer of special relativity? ... Although Poincaré understood independently of Einstein how the Lorentz transformations give rise to non-Galilean transformation rules for velocities (indeed Poincaré derived the correct relativistic rules), it is not clear that he had a full appreciation of the modern operational significance attached to coordinate transformations.... he did not seem to understand the role played by the second-order terms in the transformation. Compared with the cases of Lorentz and Larmor, it is even less clear that Poincaré understood either length contraction or time dilation to be a consequence of the coordinate transformation.... What Poincaré was holding out for was no less than a new theory of ether and matter - something far more ambitions than what appeared in Einstein's 1905 relativity paper...p. 65. Like Einstein half a decade later, Poincaré wanted new physics, not a reinterpretations or reorganization of existing notions."

Brown denies the idea of other authors and historians, that the major difference between Einstein and his predecessors is Einstein's rejection of the aether, because, it is always possible to add for whatever reason the notion of a privileged frame to special relativity, as long as one accepts that it will remain unobservable, and also Poincaré argued that "some day, no doubt, the aether will thrown aside as useless". However, Brown gave some examples, what in his opinion were the new features in Einstein's work:

p. 66: "The full meaning of relativistic kinematics was simply not properly understood before Einstein. Nor was the 'theory of relativity' as Einstein articulated it in 1905 anticipated even in its programmatic form." p. 69. "How did Albert Einstein...arrive at his special theory of relativity?...I want only to stress that it is impossible to understand Einstein's discovery (if that is the right word) of special relativity without taking on board the impacts of the quantum in physics." p. 81. "In this respect [Brown refers to the conventional nature of distant simultaneity] Einstein was doing little more than expanding on a theme that Poincaré had already introduced. Where Einstein goes well beyond the great mathematician is in his treatment of the coordinate transformations... In particular, the extraction of the phenomena of length contraction and time dilation directly from the Lorentz transformations in section 4 of the 1905 paper is completely original."

After that, Brown develops his own dynamical interpretation of special relativity as opposed to the kinematical approach of Einstein's 1905 paper (although he says that this dynamical view is already contained in Einstein's 1905-paper, "masqueraded in the language of kinematics", p. 82), and the modern understanding of space-time.

Roger Cerf (2006)

Roger Cerf (2006)[B 31] gave priority to Einstein for developing special relativity, and criticized the assertions of Leveugle and others concerning the priority of Poincaré. While Cerf agreed that Poincaré made important contributions to relativity, he argued (following Pais) that Poincaré "stopped short before the crucial step" because he handled length contraction as a "third hypothesis", therefore Poincaré lacked a complete understanding of the basic principles of relativity. "Einstein's crucial step was that he abandoned the mechanistic ether in favor of a new kinematics." He also denies the idea, that Poincaré invented E=mc² in its modern relativistic sense, because he did not realize the implications of this relationship. Cerf considers Leveugle's Hilbert-Planck-Einstein connection an implausible conspiracy theory.

Shaul Katzir (2005)

Katzir (2005)[B 32] argued that "Poincaré's work should not be seen as an attempt to formulate special relativity, but as an independent attempt to resolve questions in electrodynamics." Contrary to Miller and others, Katzir thinks that Poincaré's development of electrodynamics led him to the rejection of the pure electromagnetic world-view (due to the non-electromagnetic Poincaré-Stresses introduced in 1905), and Poincaré's theory represents a "relativistic physics" which is guided by the relativity principle. In this physics, however, "Lorentz's theory and Newton's theory remained as the fundamental bases of electrodynamics and gravitation."

Scott Walter (2005, 2007)

Walter (2005) argues that both Poincaré and Einstein put forward the theory of relativity in 1905. And in 2007 he wrote, that although Poincaré formally introduced four-dimensional spacetime in 1905/6, he was still clinging to the idea of "Galilei spacetime". That is, Poincaré preferred Lorentz covariance over Galilei covariance when it is about phenomena accessible to experimental tests; yet in terms of space and time, Poincaré preferred Galilei spacetime over Minkowski spacetime, and length contraction and time dilation "are merely apparent phenomena due to motion with respect to the ether". This is the fundamental difference in the two principal approaches to relativity theory, namely that of "Lorentz and Poincaré" on one side, and "Einstein and Minkowski" on the other side.[B 33]

General relativity

E.T. Whittaker

Whittaker (1954)[B 20] stated that David Hilbert had derived the theory of General Relativity from an elegant variational principle almost simultaneously with Einstein's discovery of the theory.

Albrecht Fölsing on the Hilbert-Einstein interaction (1993)

From Fölsing's 1993 (English translation 1998)[B 15] Einstein biography " Hilbert, like all his other colleagues, acknowledged Einstein as the sole creator of relativity theory."

Cory/Renn/Stachel and Friedwardt Winterberg (1997/2003)

In 1997, Cory, Renn and Stachel published a 3-page article in Science entitled "Belated Decision in the Hilbert-Einstein Priority Dispute" , concluding that Hilbert had not anticipated Einstein's equations.[B 16][B 34]

Friedwardt Winterberg,[B 35] a professor of physics at the University of Nevada, Reno, disputed these conclusions, observing that the galley proofs of Hilbert's articles had been tampered with - part of one page had been cut off. He goes on to argue that the removed part of the article contained the equations that Einstein later published, and he wrote that the cut off part of the proofs suggests a crude attempt by someone to falsify the historical record. "Science" declined to publish this; it was printed in revised form in "Zeitschrift für Naturforschung", with a dateline of June 5, 2003. Winterberg criticized Corry Renn and Statchel for having omitted the fact that part of Hilbert's proofs were cut off. Winterberg wrote that the correct field equations are still present on the existing pages of the proofs in various equivalent forms. In this paper Winterberg asserted that Einstein sought the help of Hilbert and Klein to help him find the correct field equation, without mentioning the research of Fölsing (1997) and Sauer (1999) according to which Hilbert invited Einstein to Göttingen to give a week of lectures on general relativity in June 1915, which however does not necessarily contradict Winterberg. Hilbert at the time was looking for physics problems to solve.

A short reply to Winterberg's article could be found at ; the original long reply can be accessed via the Internet Archive at . In this reply, Winterberg's hypothesis is called "paranoid" and "speculative". Cory et al. offer the following alternative speculation: "it is possible that Hilbert himself cropped off the top of p. 7 to include it with the three sheets he sent Klein, in order that they not end in mid-sentence."[B 36]

As of September 2006, the Max Planck Institute of Berlin has replaced the short reply with a note saying that the Max Planck Society "distances itself from statements published on this website [...] concerning Prof. Friedwart Winterberg" and stating that "the Max Planck Society will not take a position in [this] scientific dispute".

Ivan Todorov, in a paper published on ArXiv,[B 17] says of the debate:

Their [CRS's] attempt to support on this ground Einstein's accusation of "nostrification" goes much too far. A calm, non-confrontational reaction was soon provided by a thorough study[B 14] of Hilbert's route to the "Foundations of Physics" (see also the relatively even handed survey (Viz 01)).

In the paper recommended by Todorov as calm and non-confrontational, Tilman Sauer[B 14] concludes that the printer's proofs show conclusively that Einstein did not plagiarize Hilbert, stating

any possibility that Einstein took the clue for the final step toward his field equations from Hilbert's note [Nov 20, 1915] is now definitely precluded.

Max Born's letters to David Hilbert, quoted in Wuensch, is quoted by Todorov as evidence that Einstein's thinking towards general covariance was influenced by the competition with Hilbert.

Todorov ends his paper by stating:

Einstein and Hilbert had the moral strength and wisdom - after a month of intense competition, from which, in a final account, everybody (including science itself) profited - to avoid a lifelong priority dispute (something in which Leibniz and Newton failed). It would be a shame to subsequent generations of scientists and historians of science to try to undo their achievement.

Anatoly Alexeevich Logunov on general relativity (2004)

Anatoly Logunov (a former vice president of the Soviet Academy of Sciences[26] and currently the scientific advisor of the Institute for High Energy Physics[27]), is author of a book about Poincaré's relativity theory and coauthor, with Mestvirishvili and Petrov, of an article rejecting the conclusions of the Corry/Renn/Stachel paper. They discuss both Einstein's and Hilbert's papers, claiming that Einstein and Hilbert arrived at the correct field equations independently. Specifically, they conclude that:

Their pathways were different but they led exactly to the same result. Nobody "nostrified" the other. So no "belated decision in the Einstein–Hilbert priority dispute", about which [Corry, Renn, and Stachel] wrote, can be taken. Moreover, the very Einstein–Hilbert dispute never took place.
All is absolutely clear: both authors made everything to immortalize their names in the title of the gravitational field equations. But general relativity is Einstein's theory.[B 37]

Wuensch and Sommer (2005)

Daniela Wuensch,[B 1] a historian of science and a Hilbert and Kaluza expert, responded to Bjerknes, Winterberg and Logunov's criticisms of the Corry/Renn/Stachel paper in a book which appeared in 2005, wherein she defends the view that the cut to Hilbert's printer proofs was made in recent times. Moreover, she presents a theory about what might have been on the missing part of the proofs, based upon her knowledge of Hilbert's papers and lectures.

She defends the view that knowledge of Hilbert's November 16, 1915 letter was crucial to Einstein's development of the field equations: Einstein arrived at the correct field equations only with Hilbert's help ("nach großer Anstrengung mit Hilfe Hilberts"), but nevertheless calls Einstein's reaction (his negative comments on Hilbert in the November 26 letter to Zangger) "understandable" ("Einsteins Reaktion ist verständlich") because Einstein had worked on the problem for a long time.

According to her publisher, Klaus Sommer, Wuensch concludes though that:

This comprehensive study concludes with a historical interpretation. It shows that while it is true that Hilbert must be seen as the one who first discovered the field equations, the general theory of relativity is indeed Einstein's achievement, whereas Hilbert developed a unified theory of gravitation and electromagnetism.

In 2006, Wuensch was invited to give a talk at the annual meeting of the German Physics Society (Deutsche Physikalische Gesellschaft) about her views about the priority issue for the field equations.

Wuensch's publisher, Klaus Sommer, in an article in "Physik in unserer Zeit",[B 38] supported Wuensch's view that Einstein obtained some results not independently but from the information obtained from Hilbert's November 16 letter and from the notes of Hilbert's talk. While he does not call Einstein a plagiarist, Sommer speculates that Einstein's conciliatory December 20 letter was motivated by the fear that Hilbert might comment on Einstein's behaviour in the final version of his paper. Sommer claimed that a scandal caused by Hilbert could have done more damage to Einstein than any scandal before ("Ein Skandal Hilberts hätte ihm mehr geschadet als jeder andere zuvor").

David E. Rowe (2006)

The contentions of Wuensch and Sommer have been strongly contested by the historian of mathematics and natural sciences David E. Rowe in a detailed review of Wuensch's book published in Historia Mathematica in 2006.[28] Rowe argues that Wuensch's book offers nothing but tendentious, unsubstantiated, and in many cases highly implausible, speculations.

See also

Footnotes

  1. 1 2 On Mileva Marić's alleged contributions, see The Einstein Controversy, Physics Central, 17 December 2008.
  2. ↑ [Poi02]
  3. ↑ [Sta89], p. 893, footnote 10
  4. ↑ [Ein05d], last section
  5. ↑ Einstein, Albert: "Ether and the Theory of Relativity" (1920), republished in Sidelights on Relativity (Methuen, London, 1922)
  6. ↑ Isaacson, Walter (2007). Einstein: His Life and Universe. Simon and Schuster. p. 318. ISBN 0-7432-6473-8. Extract of page 318
  7. ↑ M. Grossmann, Entwurf einer verallgemeinerten REltivitatstheroie und einer Theorie der Gravitation: II. Mathematischer Teil (I. Physikalischer Teil von A. Einstein), B. G Teubner, Leipzig and Berlin 1913, p. 36.
  8. ↑ D. Hilbert, Nac. Ges. Wiss. Goettingen 1916, 395, cited in [Cor97].
  9. ↑ [Hil24] page 2
  10. ↑ F. Winterberg, Z.f. Naturforschung 59a, 715 (2004)
  11. ↑ Whittaker (1953), pp. 27-77
  12. ↑ [Lor14]
  13. ↑ [Poi06]
  14. ↑ Lorentz, H.A (1916), The theory of electrons, Leipzig & Berlin: B.G. Teubner
  15. ↑ Lorentz, H.A.; Lorentz, H. A.; Miller, D. C.; Kennedy, R. J.; Hedrick, E. R.; Epstein, P. S. (1928), "Conference on the Michelson-Morley Experiment", The Astrophysical Journal 68: 345–351, Bibcode:1928ApJ....68..341M, doi:10.1086/143148
  16. 1 2 [Poi13]
  17. ↑ Renn, J.,: Albert Einstein in den Annalen der Physik, 2005
  18. ↑ The titles of 21 reviews written in 1905 can be found in "The Collected Papers of Albert Einstein, Volume 2". See online.
  19. ↑ Einstein, A. (1907), "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen" (PDF), Jahrbuch der Radioaktivität und Elektronik 4: 411–462
  20. ↑ Einstein, A. (1909), "Über die Entwicklungen unserer Anschauungen über das Wesen und die Konstitution der Strahlung" (PDF), Physikalische Zeitschrift 10 (22): 817–825. See also English translation
  21. 1 2 Einstein, A. (1912), "Relativität und Gravitation. Erwiderung auf eine Bemerkung von M. Abraham" (PDF), Annalen der Physik 38 (10): 1059–1064, Bibcode:1912AnP...343.1059E, doi:10.1002/andp.19123431014. English translation: Einstein, Albert (1996). The Collected Papers of Albert Einstein, Volume 4: The Swiss Years: Writings, 1912–1914 (English translation supplement; translated by Anna Beck, with Don Howard, consultant ed.). Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-02610-7.
  22. ↑ Darrigol, O. (2004), "The Mystery of the Einstein-Poincaré Connection", Isis 95 (4): 614–626, doi:10.1086/430652, PMID 16011297
  23. ↑ Einstein, A. (1906), "Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie" (PDF), Annalen der Physik 20 (8): 627–633, Bibcode:1906AnP...325..627E, doi:10.1002/andp.19063250814
  24. ↑ Einstein, A. (1922), Geometry and Experience, London: Methuen & Co..
  25. ↑ [Hil24] English translation from Bje03a, p. 17;
  26. ↑ "Luganov, Anatoly". 1999. Archived from the original on 2007-10-22. Retrieved 2015-04-12.
  27. ↑ "Institute of High Energy Physics contact information". 2015. Archived from the original on 2015-02-15. Retrieved 2015-04-12.
  28. ↑ David E. Rowe, Review of Daniela Wuensch's Zwei Wirkliche Kerle, Historia Mathematica, vol. 33, Issue 4, November 2006, pp. 500-508. http://www.sciencedirect.com/science/article/pii/S0315086005000509

References

Works of physics (primary sources)

Citations

  1. 1 2 3 4 Daniela Wuensch, "zwei wirkliche Kerle", Neues zur Entdeckung der Gravitationsgleichungen der Allgemeinen Relativitätstheorie durch Einstein und Hilbert. Termessos, 2005, ISBN 3-938016-04-3
  2. 1 2 Holton, G. (1960), "On the Origins of the Special Theory of Relativity", American Journal of Physics 28 (7): 627–636, Bibcode:1960AmJPh..28..627H, doi:10.1119/1.1935922
    • Holton, Gerald (1973/88), Thematic Origins of Scientific Thought: Kepler to Einstein, Harvard University Press, ISBN 0-674-87748-9 Check date values in: |date= (help)
  3. 1 2 3 Miller, A.I. (1973), "A study of Henri Poincaré's "Sur la Dynamique de l'Electron", Arch. Hist. Exact Sci. 10 (3–5): 207–328, doi:10.1007/BF00412332
    • Miller, Arthur I. (1981), Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, ISBN 0-201-04679-2
    • Miller, A.I. (1996), "Why did Poincaré not formulate special relativity in 1905?", in Jean-Louis Greffe, Gerhard Heinzmann, Kuno Lorenz, Henri Poincaré : science et philosophie, Berlin, pp. 69–100
  4. 1 2 Pais, Abraham (1982), Subtle is the Lord: The Science and the Life of Albert Einstein, New York: Oxford University Press, ISBN 0-19-280672-6
  5. ↑ Torretti, Roberto (1983), Relativity and Geometry, Elsevier, ISBN 0-08-026773-4
  6. 1 2 Galison, Peter (2003), Einstein's Clocks, Poincaré's Maps: Empires of Time, New York: W.W. Norton, ISBN 0-393-32604-7
  7. 1 2 Darrigol, O. (2000), Electrodynamics from Ampére to Einstein, Oxford: Clarendon Press, ISBN 0-19-850594-9
  8. ↑ Janssen, M. (1995), A Comparison between Lorentz's Ether Theory and Special Relativity in the Light of the Experiments of Trouton and Noble(thesis)
  9. ↑ Alberto A. Mart́ínez (2009), Kinematics: the lost origins of Einstein's relativity, Johns Hopkins University Press, ISBN 0-8018-9135-3
  10. ↑ Born, M. (1956), Physics im my generation, London & New York: Pergamon Press
  11. 1 2 Kip Thorne (1994): Black Holes and Time Warps: Einstein's Outrageous Legacy, W. W. Norton & Company; Reprint edition (January 1995). ISBN 0-393-31276-3
  12. ↑ Mehra, J. (1974) "Einstein, Hilbert, and the Theory of Gravitation" Reidel, Dordrecht, Netherlands.
  13. ↑
    Bjerknes, Christopher Jon (2003), Anticipations of Einstein in the General Theory of Relativity, Downers Grove, Illinois: XTX Inc., ISBN 0-9719629-6-0 Author's site
  14. 1 2 3 4 5 Tilman Sauer, "The relativity of discovery: Hilbert's first note on the foundations of physics", Arch. Hist. Exact Sci., v53, 529-575 (1999)
  15. 1 2 Fölsing, Albrecht: Einstein - a biography; Penguin (Non-Classics); New Ed edition (June 1, 1998). ISBN 0-14-023719-4.
  16. 1 2 3 Leo Corry, Jürgen Renn, John Stachel: "Belated Decision in the Hilbert-Einstein Priority Dispute", SCIENCE, Vol. 278, 14 November 1997 - article text
  17. 1 2 Todorov, Ivan T., Einstein and Hilbert: The Creation of General Relativity, Institut fuer Theoretische Physik Universitaet Goettingen, arXiv:physics/0504179v1, 25 April 2005.
  18. 1 2 Logunov, A. A (2004): "Henri Poincaré and Relativity Theory" - Phys. Usp. 47 (2004) 607-621; Usp. Fiz. Nauk 174 (2004) 663-678 - PraXis 2004 abstract - PDF
  19. ↑ Jürgen Renn und Tilman Sauer (1996), "Einsteins Züricher Notizbuch: Die Entdeckung der Feldgleichungen der Gravitation im Jahre 1912", preprint 28 from Max Planck Institute - Web link. Publication date implied from web directory.
  20. 1 2 Whittaker, E. T (1953) A History of the Theories of Aether and Electricity: Vol 2 The Modern Theories 1900-1926. Chapter II: The Relativity Theory of Poincaré and Lorentz, Nelson, London.
  21. ↑ Goldberg, S. (1967), "Henri Poincaré and Einstein's Theory of Relativity", American Journal of Physics 35 (10): 934–944, Bibcode:1967AmJPh..35..934G, doi:10.1119/1.1973643
    • Goldberg, S. (1970), "Poincaré's silence and Einstein's relativity", British journal for the history of science 5: 73–84, doi:10.1017/S0007087400010633
  22. 1 2 Keswani, G. H. (1965-6) "Origin and Concept of Relativity, Parts I, II, III", Brit. J. Phil. Sci., v15-17. British Journal for the Philosophy of Science, ISSN 0007-0882.
  23. ↑ Herbert Dingle, "Note on Mr Keswani's articles, Origin and Concept of Relativity", Brit. J. Phil. Sci., vol 16, No 63 (Nov 1965), 242-246 (a response to [Kes65])
  24. ↑ Karl R. Popper, "A Note on the Difference Between the Lorentz-Fitzgerald Contraction and the Einstein Contraction", Br. J. Phil. Sci. 16:64 (Feb 1966): 332-333 (a response to [Kes65])
  25. 1 2 Keswani, G. H. (1966), "Reply to Professor Dingle and Mr Levinson", Brit. J. Phil. Sci., Vol. 17, No. 2 (Aug 1966), 149-152 (a response to [Din65])
  26. ↑ Keswani, G. H. (1966), "Origin and Concept of Relativity: Reply to Professor Popper", Brit. J. Phil. Sci, Vol 17 no 3 (Nov 1966), 234-236 (a response to [Pop65]
  27. ↑ Zahar, Elie (1983), "Poincaré's Independent Discovery of the relativity principle", Fundamenta Scientiae 4: 147–175
    • Zahar, Elie (1989), Einstein's Revolution: A Study in Heuristic, Chicago: Open Court Publishing Company, ISBN 0-8126-9067-2
    • Zahar, E. (2001), Poincare's Philosophy: From Conventionalism to Phenomenology, Chicago: Open Court Pub Co, ISBN 0-8126-9435-X
  28. ↑ Stachel, John (1995), "History of relativity", in Laurie M. Brown, Sir Brian Pippard, Abraham Pais, Twentieth Century Physics, Philadelphia: Institute of Physics, pp. 249–356, doi:10.1201/9781420050776.ch4, ISBN 0-7503-0310-7
  29. ↑ http://www.aip.org/history/einstein/essay-einsteins-time.htm
  30. ↑ Harvey R. Brown, Physical relativity: space-time structure from a dynamical perspective. Oxford University Press, 2005.
  31. ↑ Cerf, Roger (2006), "Dismissing renewed attempts to deny Einstein the discovery of special relativity", American Journal of Physics 74 (9): 818–824, Bibcode:2006AmJPh..74..818C, doi:10.1119/1.2221341
  32. ↑ Katzir, Shaul (2005), "Poincaré's Relativistic Physics: Its Origins and Nature", Phys. Perspect. 7 (3): 268–292, Bibcode:2005PhP.....7..268K, doi:10.1007/s00016-004-0234-y
  33. ↑ Walter, S. (2005), Renn, J., ed., Albert Einstein, Chief Engineer of the Universe: 100 Authors for Einstein (Berlin: Wiley-VCH): 162–165 Missing or empty |title= (help); |contribution= ignored (help)
  34. ↑ Jürgen Renn and John Stachel, Hilbert's Foundation of Physics: From a Theory of Everything to a Constituent of General Relativity - can be downloaded from link 118 in the preprint list at Max Planck Institute for the History of Science.
  35. ↑ Friedwart Winterberg: a critique of [Cor97] as printed in "Z.f. Naturforschung 59a" 59a, 715-719 (2004).
  36. ↑ Corry, Renn Stachel: Short response to [Win02] - note: the original response was later replaced with a shorter one, and on September 14, 2006, this was replaced with a statement stating that the Max Planck Institute distances itself from Corry et al.'s statements about Winterberg. The original two versions are no longer available at this URL or at the Wayback Machine.
  37. ↑ A.A. Logunov, M.A.Mestvirishvili, V.A. Petrov (2004): How Were the Hilbert-Einstein Equations Discovered? Phys.Usp. 47 (2004) 607-621; Usp.Fiz.Nauk 174 (2004) 663-678, arXiv:physics/0405075
  38. ↑ Sommer, Klaus: "Wer entdeckte die Allgemeine Relativitätstheorie? Prioritätsstreit zwischen Hilbert und Einstein", Physik in unserer Zeit Volume 36, Issue 5, Pages 230–235. Published Online: 29 Aug 2005. Available online from Wiley InterScience (expect some problems; paid access to text only)

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