Relativity priority dispute

From Wikipedia, the free encyclopedia

This article or section may be inaccurate or unbalanced in favor of certain viewpoints. Please improve the article by adding information on neglected viewpoints, or discuss the issue on the talk page.

Albert Einstein presented the theories of Special Relativity and General Relativity in groundbreaking publications that did not include references to the work of others.

Claims have been put forward about both theories that they have been formulated by others before Einstein, and that these people should get the credit. Consequently, Albert Einstein would deserve less credit for these theories, and according to some, even no credit at all for special relativity. At issue is whether Einstein can be considered the true creator of these theories, based on priority issues.

Contents 1 The candidates for credit 2 Undisputed and well known facts 2.1 Special relativity 2.2 General relativity 3 Disputed claims 3.1 Special relativity 3.2 General relativity 4 Special Relativity 4.1 Comments by Lorentz, Poincaré, and Einstein 4.2 Historians of special relativity 5 General Relativity 5.1 Did Hilbert claim priority for parts of General Relativity? 5.2 Did Einstein develop the field equations independently? 6 Attackers and defenders 6.1 Sir Edmund Whittaker (1954) 6.2 G. H. Keswani (1965) 6.3 Kip Thorne and general relativity (1994) 6.4 Albrecht Folsing on the Hilbert-Einstein interaction (1998) 6.5 Cory/Renn/Stachel and Friedwardt Winterberg (1997/2003) 6.6 Richard Moody (2003) 6.7 Olivier Darrigol on Special Relativity (2004) 6.8 Anatoly Alexeevich Logunov (2004) 6.9 Jules Leveugle and Christian Marchal (2004/2005) 6.10 Daniela Wuensch (2005) 6.11 Klaus Sommer (2005) 7 See also 8 Footnotes 9 References 9.1 Works of physics (primary sources) 9.2 Secondary sources

[edit] The candidates for credit

The most important names that are mentioned in discussions about the distribution of credit for the development and/or priority of special relativity are Albert Einstein, Hendrik Lorentz and Henri Poincaré.

Polemics also exist about the contributions of others such as the Italian Olinto De Pretto and Einstein's wife Mileva Maric.

Concerning general relativity, it is generally accepted that Einstein should be credited for it, but there is a dispute about the amount of credit that should go to David Hilbert.

[edit] Undisputed and well known facts

The following facts are undisputed and generally known:

[edit] Special relativity

Main articles: History of special relativity and Lorentz ether theory

• In 1900 Henri Poincaré published a paper in which he said that radiation could be considered as a fictitious fluid with an equivalent mass of m_r = E / c². He derived this interpretation from Lorentz's 'theory of electrons' which incorporated Maxwell's radiation pressure.^{[citation needed]}
• In 1905 Albert Einstein was the first to suggest that when a material body lost energy (either radiation or heat) of amount E, its mass decreased by the amount E / c².^[1]
• Poincaré had described a synchronization procedure for clocks at rest relative to each other in [Poi00] and again in [Poi04a-c]. It is very similar to the one proposed by Einstein.^[2]
• Einstein's Elektrodynamik paper [Ein05c] contains no references to other literature. It does mention Lorentz, but only in §9, part II, in connection with the treatment of the electromagnetic field. Poincaré is not mentioned.

[edit] General relativity

Main article: History of general relativity

• Before 1997, "the commonly accepted view was that David Hilbert completed the general theory of relativity at least 5 days before Albert Einstein submitted his conclusive paper on this theory on 25 November 1915. Hilbert's article, bearing the date of submission 20 November 1915 but published only on 31 March 1916, presents a generally covariant theory of gravitation, including field equations essentially equivalent to those in Einstein's paper" (Corry, Renn and Stachel, 1997). Since the discovery of printer's proofs of Hilbert's paper of Nov 20, dated 6 Dec 1915, which show a number of differences from the finally published paper, this 'commonly accepted view' has been challenged.^{[citation needed]}
• The proposal to describe gravity by means of a pseudo-Riemannian metric was first made by Einstein and Grossmann in the so called Entwurf theory published 1913^{[citation needed]}. This was followed by several attempts of Einstein to find valid field equations for this theory of gravity.
• David Hilbert invited Einstein to Göttingen for a week to give six 2-hour lectures on general relativity, which he did in June-July 1915. Einstein stayed at Hilbert's house during this visit. Hilbert started working on a combined theory of gravity and electromagnetism, and Einstein and Hilbert exchanged correspondence until November 1915. Einstein gave four lectures on his theory on Nov 4, Nov 11, Nov 18 and Nov 25 in Berlin, published as Einstein (1915a, 1915b, 1915c, 1915d)^{[citation needed]}
• November 4, Einstein published non-covariant field equations and on November 11 returned to the field equations of the "Entwurf" papers, which he now made covariant by the assumption that the trace of the energy-momentum tensor was zero, as it was for electromagnetism.
• Einstein sent Hilbert proofs of his papers of Nov 4 and Nov 11. (Sauer 99, notes 63, 66)
• Nov 15 Invitation issued for Nov 20 meeting at the Academy in Göttingen. "Hilber legt vor in die Nachrichten: Grundgleichungen der Physik". (Sauer 99, note 73)
• Nov 16 Hilbert spoke at the Göttingen Mathematical Society "Grundgleichungen der Physik" (Sauer 99, note 68). Talk not published.
• Nov 16 or Nov 17 Hilbert sent Einstein some information about his talk of Nov 16 (letter lost)
• Nov 18 Einstein replies to Hilbert's letter (received by Hilbert Nov 19) saying as far as he (Einstein) could tell Hilbert's system was equivalent to the one he (Einstein) had found in the preceding weeks. (Sauer 99, note 72). Einstein also told Hilbert in this letter that he (Einstein) had "considered the only possible generally covariant field equations three years earlier", adding that "The difficulty was not to find generally covariant equations for the g^μν;this is easy with the help of the Riemann tensor. What was difficult instead was to recognize that these equations form a generalization, and that is, a simple and natural generalization of Newton's law" (A. Einstein to D. Hilbert, 18 Nov, Einstein Archives Call No. 13-093). Einstein also told Hilbert in that letter that he (Einstein) had calculated the correct perihelion advance for Mercury, using covariant field equations based on the assumption that the trace of the energy momentum tensor vanished as it did for electromagnetism.
• Nov 18 Einstein presents the calculation of the perihelion advance to Prussian Academy.
• Nov 20 Hilbert lectured to the Göttingen Academy. The proofs of his paper show that Hilbert proposed a non-covariant set of equations as the fundamental equations of physics. Thus he wrote "in order to keep the deterministic characteristic of the fundamental equations of physics [...] four further non-covariant equations ... [are] unavoidable." (proofs, pages 3 and 4. quoted by Corry et al). Hilbert then derives these four extra equations and continues "these four differential equations [...] supplement the gravitational equations [...] to yield a system of 14 equations for the 14 potentials g^μν: q_s the system of fundamental equations of physics". (proofs, page 7, quoted by Corry et al).
• In his last lecture on Nov 25 Einstein submitted the correct field equations. The published paper (Einstein 1915d) appeared on December 2, and it did not mention Hilbert.
• Hilbert's paper took considerably longer to appear. He had galley proofs that were marked "December 6" by the printer in December 1915. Most of the galley proofs have been preserved, but about a quarter of a page is missing.[1] The extant part of the proofs contains Hilbert's action from which the field equations can be obtained by taking a variational derivative, and using the contracted Bianchi identity derived in theorem III of Hilbert's paper, though this was not done in the extant proofs.
• Hilbert rewrote his paper for publication (in Mar 1916), changing the treatment of the energy theorem, dropping a non-covariant gauge condition on the coordinates to produce a covariant theory, and adding a new credit to Einstein for introducing the gravitational potentials g_μν into the theory of gravity. In the final paper he said his differential equations seemed to agree with the "magnificent theory of general relativity established by Einstein in his later papers"^[3]
• The events of late November through December 1915 caused bad feelings from Einstein towards Hilbert. In a November 25 letter to Zangger, Einstein accused Hilbert (without mentioning his name) of attempts to appropriate ('nostrify') his theory. On Dec 4, Hilbert nominated Einstein for election as a corresponding member of the Göttingen Mathematical Society. In a December 20 letter to Hilbert, Einstein proposed to settle the dispute.
• The 1916 paper was rewritten and republished in 1924 [Hil24], where Hilbert wrote: Einstein [...] kehrt schließlich in seinen letzten Publikationen geradewegs zu den Gleichungen meiner Theorie zurück. (Einstein [...] in his most recent publications, returns directly to the equations of my theory.)^[4] This has been interpreted by some readers as a claim by Hilbert that General Relativity is his theory. Some claim also that Hilbert claimed priority in a letter to Schwarzschild^{[citation needed]}.

[edit] Disputed claims

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

[edit] Special relativity

• To what degree Einstein was familiar with Poincaré's work
  • It is known that Einstein was familiar with [Poi02], but it is not known to what extent he was familiar with other work of Poincaré in 1905. However it is known that he knew [Poi00] in 1906, because he quoted it in [Ein06].
• Lorentz' paper [Lor04] containing the transformations bearing his name appeared in 1904. The question is whether Einstein was familiar in 1905 with either this paper itself or a review of it (which appeared in the Annalen der Physik), and whether these are the transformations that Einstein was referring to.
• To what degree Einstein was following other physicists' work at the time. Some authors claim that Einstein worked in relative isolation and with restricted access to the physics literature in 1905. Others, however, disagree; a personal friend of Einstein, Maurice Solovine, later acknowledged that he and Einstein both pored for weeks over Poincaré's 1902 book, keeping them "breathless for weeks on end" [Rot06].
• To what degree his wife, Mileva Marić, may have contributed to Einstein's work.

[edit] General relativity

• Whether Einstein got the correct mathematical formulation for general relativity from Hilbert, or formulated it independently. Points at issue:
  • The content of Hilbert's November 16 letter/postcard to Einstein is not known. It is however, clear from Einstein's response that it was an account of Hilbert's work.
  • It is not known what was on the missing part of Hilbert's printer proofs. The missing portion is large enough to have contained the field equations in an explicit form. There are several competing speculations about the content of the missing piece.
  • Based on the above, it is not known whether Hilbert had formulated the field equations in an explicit form before December 6 (the date of the printer's proofs) or not.
  • It is known from the proofs that Hilbert introduced four non-covariant equations in order to specific the gravitational potentials g and that this approach was dropped from his revised paper.
• Whether Hilbert ever tried to claim priority for the field equations - it seems clear that he regarded the theory of general relativity as Einstein's theory.
• What Hilbert thought he was referring to when he used the term "equations of my theory" about Einstein's research.

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

[edit] Special Relativity

Main articles: History of special relativity and Lorentz ether theory

[edit] Comments by Lorentz, Poincaré, and Einstein

Lorentz, Poincaré

In a paper that was written in 1914 and published in 1921,^[5] Lorentz appreciated the Palermo paper (1906)^[6] of Poincaré on relativity. Lorentz stated:

“

Indeed I have not given the most appropriate transformation for some physical quantities encountered in the formulae. This was done by Poincaré and later by Einstein and Minkowski. [..] I had not thought of the straight path leading to them, since I considered there was an essential difference between the reference systems x, y, z, t and x', y', z', t'. In one of them were used - such was my reasoning - coordinate axes with a defnite position in ether and what could be termed true time; in the other, on the contrary, one simply dealt with auxiliary quantities introduced with the aid of a mathematical trick. [..] I have not established the principle of relativity as rigorously and universally true. Poincaré, on the other hand, has obtained a perfect invariance of the electro-magnetic equations, and he has formulated 'the postulate of relativity', terms which he was the first to employ. [..] Let's add that while thus correcting the imperfections of my work he never blamed me for them.[7]

”

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:^[8]

“

[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:^[9]

“

[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:^[10]

“

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,^[11] 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: ^[11]

“

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:^[12]

“

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.[13] 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^[14] 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." And in 1910^[15] and 1912^[16] Einstein explained that he borrowed the principle of the constancy of light from Lorentz's immobile ether, but he recognized that this principle together with the principle of relativity makes the ether useless and leads to special relativity. It is also known^[17] that he read Poincaré's 1902-book „Science and hypothesis“ before 1905, which included:

• philosophical assessments on the relativity of space, time, and simultaneity
• the definition of the principle of relativity and the opinion that a violation of that principle can never be detected
• the possible non-existence of the ether
• many remarks on the non-Euclidean geometry.

Einstein refers to Poincaré in connection with the inertia of energy in 1906^[18] and the non-Euclidean geometry in 1921,^[19] but not in connection with the Lorentz transformation, the relativity principle or the synchronisation procedure by light signals. However, in the last years before Einstein's death he acknowledged some of Poincaré's contributions (according to Darrigol, maybe because his biographer Pais in 1950 sent him a copy of Poincarè's Palermo paper, which he hadn't read before). Einstein wrote in 1953:^[20]

“

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.

”

[edit] Historians of special relativity

In his well-known „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.^[21] However, the predominant majority of the historians of science like Gerald Holton,^[22] Arthur I. Miller,^[23] Abraham Pais,^[24] John Stachel^[25] or Olivier Darrigol^[26] and physicists like Max Born^[27] or Wolfgang Pauli^[28] have other points of view. It's true that Lorentz and Poincaré developed the mathematics of special relativity, and many scientists originally spoke about the „Lorentz-Einstein theory“. But Einstein was the first (contrary to Lorentz and Poincaré) to banish the (classical) ether out of physics, which lead to a fundamental new approach to physics.

[edit] General Relativity

[edit] Did Hilbert claim priority for parts of General Relativity?

Kip Thorne concludes, 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...".^[29] 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."^[30]

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

• Hilbert's article (dated 20 November 1915), when it appeared in 1916, contained the text "Die so zu Stande kommenden Differentialgleichungen der Gravitation sind, wie mir scheint, mit der von Einstein in seinen späteren Abhandlungen aufgestellten großzügigen Theorie der allgemeinen Relativität in gutem Einklang." - in translation, "It appears to me that the differential equations of gravitation arrived at in [my] way are in agreement with those of Einstein in his subsequent papers setting forth the broad theory of general relativity[.]"^[31] Bjerknes claims that "subsequent" refers to Einstein publishing the equations after Hilbert.^[32] Bjerknes further points out that, "It is interesting to note that Hilbert changed a key phrase in the published paper, which appeared after Einstein had plagiarized Hilbert's equations, from: 'in dem von Einstein geforderten Sinne' or, 'in the sense requested by Einstein' in the proofs at page 13, to: 'in dem von Einstein dargelegten Sinne' or, 'in the sense stated by Einstein” in the published paper at page 407, which indicates that it was Einstein who adopted Hilbert's solution, without an attribution."^[33]
• Wuensch ^[34] points out that Hilbert refers to the field equations of gravity as "meine Theorie" ("my theory") in his February 6, 1916 letter to Schwarzschild.
• Mehra ^[35] and Bjerknes^[36] point out that Hilbert's 1924 version of the article contained the sentence "..und andererseits auch Einstein, obwohl wiederholt von abweichenden und unter sich verschiedenen Ansätzen ausgehend, kehrt schließlich in seinen letzten Publikationen geradenwegs zu den Gleichungen meiner Theorie zurück" - "Einstein [. . .] in his last publications ultimately returns directly to the equations of my theory."^[37].
• Sauer says the "the independence of Einstein's discovery was never a point of dispute between Einstein and Hilbert ... Hilbert claimed priority for the introduction of the Riemann scalar into the action principle and the derivation of the field equations from it, "^[38] (Sauer mentions a letter and a draft letter where Hilbert defends his priority for the action functional) "and Einstein admitted publicly that Hilbert (and Lorentz) had succeeded in giving the equations of general relativity a particularly lucid form by deriving them from a single variational principle"^{[citation needed]}. Sauer also stated, "And in a draft of a letter to Weyl, dated 22 April 1918, written after he had read the proofs of the first edition of Weyl's 'Raum-Zeit-Materie' Hilbert also objected to being slighted in Weyl's exposition. In this letter again 'in particular the use of the Riemannian curvature [scalar] in the Hamiltonian integral' ('insbesondere die Verwendung der Riemannschen Kruemmung unter dem Hamiltonschen Integral') was claimed as one of his original contributions. SUB Cod. Ms. Hilbert 457/17."^[39]
• Bjerknes points out that Einstein wrote to Hilbert on 20 December 1915 that there was an "ill-feeling between us" and claims that this hostility was the result of Einstein's alleged use of Hilbert's equations without an attribution.^[40] CRS claim that this hostility resulted from, in Einstein's words, Hilbert's alleged attempt to "nostrify" Einstein's theory.^[41]

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

[edit] 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. This changed in 1978, when a November 18, 1915 letter from Einstein to Hilbert^{[citation needed]} resurfaced, confirming the arrival of a letter in which Hilbert explained his theory. While most authors were reluctant to use the harsh word 'plagiarism', many felt that Einstein's conception of his November 25 paper was guided by the information he had received from Hilbert. For instance, Albrecht Fölsing wrote the following 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? ^[42]

In their 1997 Science paper [Cor97] attempting to refute this theory, Corry, Renn and Stachel quote the above passage and admit that

the arguments by which Einstein is exculpated are rather weak, turning on his slowness in fully grasping Hilbert's mathematics.

A discussion of the controversy around this paper is given below.

Among others, Bjerknes, Sommer and Wuensch defend the view that Einstein's paper was motivated by the information obtained from Hilbert. The following sources are being used as evidence:

• Hilbert's letter to Einstein mentioned above. More recently, it became known that Einstein was also given notes of Hilbert's November 16 talk about his theory^[43].
• Bjerknes notes that Einstein's November 18 paper on the perihelion motion of Mercury still refers to the false field equations of November 4 and 11 as the correct ones, changing this position only in a footnote added to the paper. This indicates that Einstein may have changed his mind about the earlier field equations at the very time he received Hilbert's letter.^[44]
• In addition, evidence from letters of Hilbert, Einstein, and other scientists may be used in attempts to make guesses about the content of Hilbert's letter to Einstein, which is not preserved, or of Hilbert's lecture in Göttingen on November 16.

People who try to defend Einstein's priority [Cor97] or the view that both authors did their work independently [Tod06] may use the following arguments:

• They may argue that Hilbert modified his paper in December 1915, and that the extant part of the printer proofs does not have the explicit field equations. This is the point of view defended by Corry, Renn, Stachel, and Sauer.
• Sauer (1999) and Todorov (2005) agree with Corry, Renn and Satchel that Hilbert's proofs show that Hilbert had originally presented a non-covariant theory, which was dropped from the revised paper. Corry et al quote from the proofs: "Since our mathematical theorem ... can provide only ten essentially independent equations for the 14 potentials [...] and further, maintaining general covariance makes quite impossible more than ten essential independent equations [...] then, in order to keep the deterministic characteristic of the fundamental equations of physics [...] four further non-covariant equations ... [are] unavoidable." (proofs, pages 3 and 4. Corry et al) Hilbert derives these four extra equations and continues "these four differential equations [...] supplement the gravitational equations [...] to yield a system of 14 equations for the 14 potentials g^μν, q_s: the system of fundamental equations of physics". (proofs, page 7. Corry et al). Hilbert's first theory (lecture Nov 16, lecture Nov 20, proofs Dec 6) was titled "The fundamental equations of Physics". In proposing non-covariant fundamental equations, based on the Ricci tensor but restricted in this way, Hilbert was following the causality requirement that Einstein and Grassman had introduced in the Entwurf papers of 1913 (Sauer, 1999).

• One may attempt to reconstruct the way in which Einstein may have arrived at the field equations independently. This is, for instance, done in the paper of Logunov, Mestvirishvili and Petrov quoted below [Log04]. Renn and Sauer [Ren96] investigate the notebook used by Einstein in 1912 and claim he was close to the correct theory at that time. However, it seems that their source does not contain the correct field equations but only their linearized form.

[edit] Attackers and defenders

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

[edit] Sir Edmund Whittaker (1954)

In 1954 Sir Edmund Taylor Whittaker, an English historian of science, credited Poincaré with the equation E = mc², 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 (1954). Whittaker also claimed that David Hilbert had derived the theory of General Relativity from an elegant variational principle nearly simultaneously with Einstein.

[edit] G. H. Keswani (1965)

In a 1965 series of articles tracing the history of relativity [Kes65], 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". ^[45]. 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"^[46]

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."^[47]

Keswani did not accept the criticism, and replied in two letters also published in the same journal ([Kes66a] and [Kes66b]) - 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."^[48]

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).

[edit] Kip Thorne and general relativity (1994)

In his 1994 book "Black Holes and Time Warps: Einstein's Outrageous Legacy" [Tho94], Kip Thorne wrote of General Relativity and the Einstein field equations:

• "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: the recognition that tidal gravity must be the same thing as a warpage of spacetime, the vision that the law of warpage must obey the relativity principle, and the first 90 percent of that law, the Einstein field equation. In fact without Einstein the general relativistic laws of gravity might not have been discovered until several decades later." ^[49]

• "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."^[50]

[edit] Albrecht Folsing on the Hilbert-Einstein interaction (1998)

From Folsing's 1998 Einstein biography (footnote references in the quote are from the original text):

During the decisive phase Einstein even had a congenial colleague, though this caused him more annoyance than joy, as it seemed to threaten his primacy. "Only one colleague truly understood it, and he now tries skillfully to appropriate it."²⁹ he complained to Zangger about what he evidently regarded as an attempt at plagiarism. This colleague was none other than David Hilbert, with whom, as recently as the summer, Einstein had been "absolutely delighted." What must have irritated Einstein was that Hilbert had published the correct field equations first—a few days before Einstein.

Einstein presented his equations in Berlin on November 25, 1915, but six days earlier, on November 20, Hilbert—had derived the identical field equations for which Einstein had been searching such a long time.³¹ How had this happened?

David Hilbert had concerned himself intensively with physics for a number of years; had read everything about electrons, matter, and fields: and in this context had invited Einstein to Göttingen toward the end of June 1915 to lecture on relativity theory. Einstein had stayed at the Hilberts' home, and one must assume that the week he and Hilbert spent together would have consisted of dawn-to-dusk discussions of physics. They continued their debate in writing, although Felix Klein records that "they talked past one another, as happens not infrequently between simultaneously producing mathematicians."³² Hilbert was in fact aiming at greater things than Einstein: at a theory of the entire physical world, of matter and fields, of universe and electrons—and in a strictly axiomatic structure.

In November, when Einstein was totally absorbed in his theory of gravitation, he essentially corresponded only with Hilbert, sending Hilbert his publications and, on November 18, thanking him for a draft of his treatise. Einstein must have received that treatise 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 "appropriated" Hilbert? This is not really probable: Hilbert's treatise was exceedingly involved, or indeed confused—according to Felix Klein, it was the kind of work "that no one understands unless he has already mastered the whole subject."³³ It cannot be entirely ruled out that Hilbert's treatise made Einstein aware of some weakness in his own equations. Nevertheless, his 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.

For a few weeks relations between Einstein and Hilbert were clouded; at least, we know that Einstein was convinced that his Göttingen lectures and some of his other thoughts had—perhaps inadvertently—been plagiarized by Hilbert. It may well be, though, that he was somewhat mollified when he saw the printed version of Hilbert's treatise, since Hilbert, in the very first sentence, paid tribute to "the gigantic problems raised by Einstein and the brilliant methods developed by him for their solution,"³⁴ which represented the prerequisites of a new approach to the fundamentals of physics. Thirty years later, Einstein told his assistant Ernst G. Straus, who in turn after another thirty years told Abraham Pais, that "Hilbert had sent him a written apology, informing him that he had 'quite forgotten that lecture.' "³⁵ If that is what happened, then it must have satisfied Einstein, for just before Christmas he wrote to Hilbert: "There has been between us something like a bad feeling, the cause of which I don't wish to analyze further. I struggled against a resulting sense of bitterness, and I did so with complete success. I once more think of you in unclouded friendship, and would ask you to try to do likewise toward me. It is, objectively speaking, a pity if two fellows who have worked their way out of this shabby world cannot find pleasure in one another."³⁶ The reconciliation worked so well that no one else seems to have noticed any friction, and a legend arose that there had never been anything but friendly feelings between Einstein and Hilbert.³⁷ Hilbert, like all his other colleagues, acknowledged Einstein as the sole creator of relativity theory.

(Source: Folsing, "Albert Einstein")^[51]

From the publication date of his book, it appears that Folsing did not know of the printer proofs discussed in [Cor97].

[edit] 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" [2], concluding that Hilbert had not anticipated Einstein's equations.

Friedwardt Winterberg, a professor of physics at the University of Nevada, Reno, disputed [3] 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 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 Folsing (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 [4]; the original long reply can be accessed via the Internet Archive at [5]. 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."

As of September 2006, the Max Planck Institute of Berlin has replaced the short reply with a note [6] saying that the society "distances itself from statements published on this website [...] concerning Prof. Friedwart Winterberg" and stating that "the Max Planck Institute will not take a position in [this] scientific dispute".

Ivan Todorov, in a paper published on ArXiv (Todorov 2005), 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 (Sau 99) 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 (1999) 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.

Bjerknes ^[52] has disputed Sauer's conclusion,

[. . .]Dr. Sauer's vague and arbitrary arguments regarding Einstein's plagiarism do not follow from his premises. There is no evidence or circumstance which would preclude Einstein's plagiarism. On the contrary, the evidence and the circumstances surrounding Einstein’s publication of the generally covariant field equations of gravitation containing the trace term on 25 November 1915 prove beyond any reasonable doubt that Einstein plagiarized them from David Hilbert.

Max Born's letter to David Hilbert, quoted in Wuensch ^[53] vindicates Bjerknes's view there is a real possibility that Einstein copied from Hilbert.^[54]

Logunov (2004) commenting on the "Belated decision" paper, but not aware of the Born letter, concludes

Their [Hilbert's and Einstein's] pathways were different but they led exactly to the same result. Nobody "nostrified" the other ... 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.[12]

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.

[edit] Richard Moody (2003)

An article by Richard Moody in Nexus magazine repeated many of Bjerknes' claims, and also stated that in Einstein's 1935 paper, "Elementary Derivation of the Equivalence of Mass and Energy", he wrote "The question as to the independence of those relations is a natural one because the Lorentz transformation, the real basis of special relativity theory..." [7].

Sample quote from the article:

When the scandal breaks, the physics community, Einstein's supporters and the media will attempt to downplay the negative news and put a positive spin on it. However, their efforts will be shown up when Einstein's paper, "On the Electrodynamics of Moving Bodies", is seen for what it is: the consummate act of plagiarism in the 20th century.

[edit] Olivier Darrigol on Special Relativity (2004)

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

• "By 1905 Poincaré's and Einstein's reflections on the electrodynamics of moving bodies led them to postulate the universal validity of the relativity principle, according to which the outcome of any conceivable experiment is independent of the inertial frame of reference in which it is performed. In particular, they both assumed that the velocity of light measured in different inertial frames was the same. They further argued that the space and time measured by observers belonging to different inertial systems were related to each other through the Lorentz transformations. They both recognized that the Maxwell-Lorentz equations of electrodynamics were left invariant by these transformations. They both required that every law of physics should be invariant under these transformations. They both gave the relativistic laws of motion. They both recognized that the relativity principle and the energy principle led to paradoxes when conjointly applied to radiation processes. On several points - namely, the relativity principle, the physical interpretation of Lorentz's transformations (to first order), and the radiation paradoxes - Poincaré's relevant publications antedated Einstein's relativity paper of 1905 by at least five years, and his suggestions were radically new when they first appeared. On the remaining points, publication was nearly simultaneous."

• "I turn now to basic conceptual differences. Einstein completely eliminated the ether, required that the expression of the laws of physics should be the same in any inertial frame, and introduced a "new kinematics" in which the space and time measured in different inertial systems were all on exactly the same footing. In contrast, Poincaré maintained the ether as a privileged frame of reference in which "true" space and time were defined, while he regarded the space and time measured in other frames as only "apparent." He treated the Lorentz contraction as a hypothesis regarding the effect of the edgewise motion of a rod through the ether, whereas for Einstein it was a kinematic consequence of the difference between the space and time defined by observers in relative motion. Einstein gave the operational meaning of time dilation, whereas Poincaré never discussed it. Einstein derived the expression of the Lorentz transformation from his two postulates (the relativity principle and the constancy of the velocity of light in a given inertial system), whereas Poincaré obtained these transformations as those that leave the Maxwell-Lorentz equations invariant. Whereas Einstein, having eliminated the ether, needed a second postulate, in Poincaré's view the constancy of the velocity of light (in the ether frame) derived from the assumption of a stationary ether. Einstein obtained the dynamics of any rapidly moving particle by the direct use of Lorentz covariance, whereas Poincaré reasoned according to a specific model of the electron built up in conformity with Lorentz covariance. Einstein saw that Poincaré's radiation paradoxes could be solved only by assuming the inertia of energy, whereas Poincaré never returned to this question. Lastly, Poincaré immediately proposed a relativistic modification of Newton's law of gravitation and saw the advantages of a four-vector formalism in this context, whereas Einstein waited a couple of years to address this problem complex."

(Source: Olivier Darrigol (2004): "The Mystery of the Einstein-Poincaré Connection". Isis: Vol.95, Issue 4; pg. 614, 14 pgs)

[edit] Anatoly Alexeevich Logunov (2004)

Logunov is a former Vice President of the Soviet Academy of Sciences and currently "Advisor" of the Institute for High Energy Physics.[8][9] Author of a book about Poincaré's relativity theory. 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.[10]

His book about Poincaré's relativity theory is a useful introduction to the subject. Starting on p. 113 is an English translation by V. A. Petrov, using modern notations, of the part of Poincaré's 1900 article containing E=mc². Logunov states that Poincaré's 1905 papers Sur la dynamique de l'électron (On the Dynamics of the Electron) are superior to Einstein's 1905 Elektrodynamik 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. This contradicts the claims that Einstein worked in relative isolation and with limited access to the scientific literature, claims which are usually made to exculpate Einstein from plagiarism. Among the papers reviewed in 1905 Beiblätter are a review, in the fourth (of 24) issue of 1905, of Lorentz' paper in the Versl. K. Ak. van Wet. 12(1904), p. 986 containing the Lorentz transformation. The review also contained these transformations. This supports the view that Einstein was familiar with the Lorentz' paper containing the correct relativistic transformation in early 1905, while his June 1905 Elektrodynamik paper does not mention Lorentz in connection with this result.

[edit] Jules Leveugle and Christian Marchal (2004/2005)

Similar as Anatoly A. Logunov, Christian Marchal and Jules Leveugle argue that the contribution of Albert Einstein to the special theory of relativity is minor compared to that of Henri Poincaré [11]. Compare also: Jules Leveugle, La Relativité et Einstein, Planck, Hilbert - Histoire véridique de la Théorie de la Relativité, L'Harmattan, Paris 2004.

[edit] Daniela Wuensch (2005)

Daniela Wuensch, 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" ("Einstein's Reaktion ist verständlich") because Einstein had worked on the problem for a long time.

According to her publisher, 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. [12]

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.[13]

[edit] Klaus Sommer (2005)

Klaus Sommer is a historian of science and Hilbert expert. In an article in "Physik in unserer Zeit" (Sommer 05) [14], he supports Wuensch's view that Einstein obtained 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 Einstein's behaviour in the final version of his paper, claiming 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").

[edit] See also

• Special relativity
• General relativity
• History of special relativity
• History of general relativity
• Albert Einstein
• Henri Poincare
• David Hilbert
• Twin paradox
• Equivalence principle
• List of scientific priority disputes
• Einstein-Hilbert action

[edit] Footnotes

[edit] References

[edit] Works of physics (primary sources)

[Ein05c] 

Albert Einstein: Zur Elektrodynamik bewegter Körper, Annalen der Physik 17(1905), 891-921. Received June 30, published September 26, 1905. Reprinted with comments in [Sta89], p. 276-306 English translation, with footnotes not present in the 1905 paper, available on the net

[Ein05d] 

Albert Einstein: Ist die Trägheit eines Körpers von seinem Energiegehalt abhängig?, Annalen der Physik 18(1905), 639-641, Reprinted with comments in [Sta89], Document 24 English translation available on the net

[Ein06] 

Albert Einstein: Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie Annalen der Physik 20(1906):627-633, Reprinted with comments in [Sta89], Document 35

[Ein15a]

Einstein, A. (1915) "Die Feldgleichungun der Gravitation". Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, 844-847.

[Ein15b]

Einstein, A. (1915) "Zur allgemeinen Relativatstheorie", Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, 778-786

[Ein15c]

Einstein, A. (1915) "Erklarung der Perihelbewegung des Merkur aus der allgemeinen Relatvitatstheorie", Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, 799-801

[Ein15d]

Einstein, A. (1915) "Zur allgemeinen Relativatstheorie", Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, 831-839

[Ein16]

Einstein, A. (1916) "Die Grundlage der allgemeinen Relativitätstheorie", Annalen der Physik, 49

[Hil24]

Hilbert, D., Die Grundlagen der Physik - Mathematische Annalen, 92, 1924 - "meiner theorie" quote on page 2 - online at Uni Göttingen - index of journal

[Lan05]

Langevin, P. (1905) "Sur l'origine des radiations et l'inertie électromagnétique", Journal de Physique Théorique et Appliquée, 4, pp.165-183.

[Lan14]

Langevin, P. (1914) "Le Physicien" in Henri Poincaré Librairie (Felix Alcan 1914) pp. 115-202.

[Lor99]

Lorentz, H. A. (1899) "Simplified Theory of Electrical and Optical Phenomena in Moving Systems", Proc. Acad. Science Amsterdam, I, 427-43.

[Lor04]

Lorentz, H. A. (1904) "Electromagnetic Phenomena in a System Moving with Any Velocity Less Than That of Light", Proc. Acad. Science Amsterdam, IV, 669-78.

[Lor11]

Lorentz, H. A. (1911) Amsterdam Versl. XX, 87

[Lor14]

Lorentz, H. A. (1914) "Deux Memoires de Henri Poincaré," Acta Mathematica 38: 293, p.1921.

[Pla07]

Planck, M. (1907) Berlin Sitz., 542

[Pla08]

Planck, M. (1908) Verh. d. Deutsch. Phys. Ges. X, p218, and Phys. ZS, IX, 828

[Poi97]

Poincaré, H. (1897) "The Relativity of Space", article in English translation

[Poi00] 

Henri Poincaré: La théorie de Lorentz et le principe de l'action et de la réaction, Archives neérlandaises des Sciences exactes et naturelles, 2e série, 5(1900), p. 252-278, Recueil de Travaux offert à M. Lorentz à l'occasion du 25e anniversaire de son doctorat, Reprinted in Oeuvres, vol. IX, p. 454-488. An English translation, put into modern notation by V. A. Petrov, is given in [Log05, p. 113-120]

[Poi02] 

Henri Poincaré: La science et l'hypothèse, E. Flamarion, Paris, 1902. Electronic version, english translation thereof.

[Poi04a] 

Henri Poincaré: L'état actuel et l'avenir de la physique mathématique., Bulletin des sciences mathématiques 28(1904), 302-324. Address delivered before the Section of Applied Mathematics of the International Congress of Arts and Science, St. Louis, September 24, 1904

[Poi04b] 

Henri Poincaré: The Present and the Future of Mathematical Physics, Bull. Amer. Math. Soc., 12(1906), 240-260, engl. transl. of [Poi04a] by J. W. Young.

[Poi04c] 

Henri Poincaré: The Present and the Future of Mathematical Physics, Bull. Amer. Math. Soc. (new series), 37(2000), 25-38, reprint of [Poi04b]

[Poi04d]

Poincaré, H. (1904) "La valeur de la Science"

[Poi05] 

Henri Poincaré: Sur la dynamique de l'électron, Comptes rendus de l'Académie des Sciences, 140(1905), p. 1504-1508. Reprinted in Oeuvres, vol. IX, p. 489-493

[Poi06a] 

Henri Poincaré: Sur la dynamique de l'électron, Rendiconti del Circolo matematico di Palermo, 21(1906), 129-176. Submitted July 23, 1905. Reprinted in Oeuvres, vol. IX, 494-550

"Sur la dynamique de l'electron"

[Poi13]

Poincaré, H. (1913) Mathematics and Science: Last Essays, Dover 1963 (translated from Dernières Pensées posthumously published by Ernest Flammarion, 1913)

[Sta89] 

John Stachel (Ed.), The collected papers of Albert Einstein, volume 2, Princeton University Press, 1989

[edit] Secondary sources

[Bje02]

Bjerknes, Christopher Jon (2002). Einstein, the incorrigible plagiarist. Downers Grove, Illinois: XTX Inc.. ISBN 0-9719629-8-7.  Author's site

[Bje03a]

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

[Bje03b]

Bjerknes, Christopher Jon (May/June 2003). "A Response to Physics World's "Review" of Albert Einstein: The Incorrigible Plagiarist". Infinite Energy 8 (49): 65–68.  - Magazine ToC

[Bje06]

Bjerknes, Christopher Jon (2006). The manufacture and sale of Saint Einstein. ISBN.  online copy

[Bro67]

G. Burniston Brown, What's wrong with relativity, Bulletin of the Institute of Physics and Physical Society, Vol. 18 (March, 1967) pp.71—77 - online copy

[Cor97]

Leo Corry, Jürgen Renn, John Stachel: "Belated Decision in the Hilbert-Einstein Priority Dispute", SCIENCE, Vol. 278, 14 November 1997 - article text

[Cor03]

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.

[Dar04]

Olivier Darrigol (2004): "The Mystery of the Einstein-Poincaré Connection". Isis: Vol.95, Issue 4; pg. 614, 14 pgs

[Din65]

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])

[Fol98]

Albrecht Folsing: Einstein - a biography; Penguin (Non-Classics); New Ed edition (June 1, 1998). ISBN 0-14-023719-4.

[Gal03]

Galison, Peter Louis (2003) Einstein's Clocks, Poincaré's Maps: Empires of Time. Hodder & Stoughton. ISBN 0-340-79447-X.

[Ive52]

Ives, H. E., "Derivation of the Mass-Energy Relationship", article in 1952, J. Opt. Soc. Amer., 42, 540—3. (Journal of the Optical Society of America)

[Ive53]

Ives, H. E. (1953) "Note on 'Mass-Energy Relationship'", J. O. S. A., 43, 619.

[Kes65]

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.

[Kes66a]

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])

[Kes66b]

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]

[Kes83]

Keswani, G. H. and C. W. Kilmister (1983) "Initimations of relativity. Relativity before Einstein", British Journal for the Philosophy of Science 34, 343-54. ISSN 0007-0882.

[Log04] 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

[Mac86]

Macrossan, M. N. (1986) "A Note on Relativity Before Einstein", British Journal for the Philosophy of Science., 37, pp.232-34.

[Meh74]

Mehra, J. (1974) "Einstein, Hilbert, and the Theory of Gravitation" Reidel, Dordrecht, Netherlands.

[Nor93]

John D Norton (1993): "General covariance and the foundations of general relativity: eight decades of dispute", Rep. Prog. Phys. 56 (1993) 791458. - Author's Web copy (PDF) (Report on the Progress of Physics)

[Pop65]

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])

[Ren96]

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.

[Ren05]

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.

[Ris53]

Riseman, J. and I. G. Young (1953) "Mass-Energy Relationship", J. O. S. A., 43, 618.

[Rot06]

Rothman, Tony (March/April 2006). "Lost in Einstein's Shadow". American Scientist 94 (2): 112. doi:10.1511/2006.2.112. 

[Sau99]

Tilman Sauer, "The relativity of discovery: Hilbert's first note on the foundations of physics", Arch. Hist. Exact Sci., v53, 529-575 (1999)

[Som05]

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)

[Sta02]

John Stachel: John Stachel's review of Bjerknes' book [Bje02]

[Tho94]

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

[Tod06]

Todorov, Ivan T., Einstein and Hilbert: The Creation of General Relativity, Institut fuer Theoretische Physik Universitaet Goettingen, arXiv:physics/0504179v1, 25 April 2005.

[Whi53]

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.

[Win02]

Friedwart Winterberg: a critique of [Cor77] as printed in "Zeitschrift für Naturforschung" 59a, 715-719.

[Wue05] 

Daniela Wuensch, "zwei wirkliche Kerle", Neues zur Entdeckung der Gravitationsgleichungen der Allgemeinen Relativitätstheorie durch Einstein und Hilbert. Termessos, 2005, ISBN 3-938016-04-3