Apr 24, 2015 10:43 AM By Chris Weller 

Ph.D. student Zakaryah Abdulkarim, M.D., shows how to create the illusion of invisibility in the lab (photomontage). Staffan Larsson

The candidates for credit[edit]

Undisputed and well known facts[edit]

Special relativity[edit]

• In 1889, ([Poi89]), Henri Poincaré argued that the ether might be unobservable, in which case the existence of the ether is a metaphysical question, and he suggested that some day the ether concept would be thrown aside as useless. However, in the same book (Ch. 10) he considered the ether a "convenient hypothesis" and continued to use the concept also in later papers in 1908 ([Poi08], Book 3) and 1912 ([Poi13], Ch. 6).
• In 1895, Poincaré argued that experiments like that of Michelson–Morley show that it seems to be impossible to detect the absolute motion of matter or the relative motion of matter in relation to the ether. In [Poi00] he called this the Principle of Relative Motion, i.e., that the laws of movement should be the same in all inertial frames. Alternative terms used by Poincaré were "relativity of space" and "principle of relativity".^[2] In 1904 he expanded that principle by saying: "The principle of relativity, according to which the laws of physical phenomena must be the same for a stationary observer as for one carried along in a uniform motion of translation, so that we have no means, and can have none, of determining whether or not we are being carried along in such a motion." However, he also stated that we do not know if this principle will turn out to be true, but that it is interesting to determine what the principle implies.
• In [Poi00], Poincaré published a paper in which he said that radiation could be considered as a fictitious fluid with an equivalent mass of . He derived this interpretation from Lorentz's 'theory of electrons' which incorporated Maxwell's radiation pressure.
• Poincaré had described a synchronization procedure for clocks at rest relative to each other in [Poi00] and again in [Poi04]. So two events, which are simultaneous in one frame of reference, are not simultaneous in another frame. It is very similar to the one later proposed by Einstein.^[3] However, Poincaré distinguished between "local" or "apparent" time of moving clocks, and the "true" time of resting clocks in the ether. In [Poi02] he argued that "some day, no doubt, the ether will be thrown aside as useless".
• Lorentz' paper [Lor04] containing the transformations bearing his name appeared in 1904.
• Albert Einstein in [Ein05c] derived the Lorentz equations by using the principle of constancy of velocity of light and the relativity principle. He was the first to argue that those principles (along with certain other basic assumptions about the homogeneity and isotropy of space, usually taken for granted by theorists) are sufficient to derive the theory. See Postulates of special relativity. He said: "The introduction of a luminiferous ether will prove to be superfluous inasmuch as the view here to be developed will not require an absolutely stationary space provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place." * Einstein's Elektrodynamik paper [Ein05c] contains no formal references to other literature. It does mention, in §9, part II, that the results of the paper are in agreement with Lorentz's electrodynamics. Poincaré is not mentioned in this paper, although he is cited formally in a paper on special relativity written by Einstein the following year.
• In 1905 Einstein was the first to suggest that when a material body lost energy (either radiation or heat) of amount , its mass decreased by the amount .^[4]
• Hermann Minkowski showed in 1907 that the theory of special relativity could be elegantly described using a four-dimensional spacetime, which combines the dimension of time with the three dimensions of space.
• Einstein in 1920 returned to a concept of aether having no state of motion.^[5][6]

General relativity[edit]

• 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.^[7] Grossmann identified the contracted Riemann tensor as the key for the solution of the problem posed by Einstein. 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 [Ein15a], [Ein15b], [Ein15c], [Ein15d].
• 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 ;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 : 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 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"^[8]
• 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.)^[9]

Disputed claims[edit]

Special relativity[edit]

• 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).
• 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].
• Whether his wife, Mileva Marić, may have contributed to Einstein's work, although Einstein scholars say that there is no substantive evidence that she made significant contributions.^[1]

General relativity[edit]

• 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.^[10]
• 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^{[according to whom?]} 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 specify the gravitational potentials 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. Hilbert made a similar remark in a letter to Karl Schwarzschild.^{[B 1]}

Special Relativity[edit]

Historians of special relativity[edit]

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[edit]

Lorentz[edit]

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.

[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.

[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.

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[edit]

Einstein[edit]

...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).

• detailed philosophical assessments on the relativity of space, time, and simultaneity
• discussion of the reliance on conventions regarding the use of light signals for the synchronization of clocks
• the definition of the principle of relativity and the conjecture that a violation of that principle can never be detected empirically
• the possible redundancy of the ether hypothesis
• detailed remarks on the physical status of non-Euclidean geometry.

General Relativity[edit]

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

• 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, "The differential equations of gravity arrived at in this way are, I think, in good agreement with those of Einstein in his later papers in which he presented his comprehensive theory of general relativity." Hilbert refers here to the "later papers" of Einstein, obviously to distinguish them from the Entwurf theory of 1913 and the preliminary papers prior to the end of November 1915 when Einstein published the equations of general relativity in their final form. Hilbert's sentence has sometimes been mis-interpreted^{[citation needed]} by replacing the word "later" with "subsequent", and suggesting that Hilbert was writing in a clairvoyant sense about papers of Einstein that would be written subsequent to the paper that Hilbert was presently writing. Serious scholars^[who?] dismiss such misconstruals as obvious nonsense.
• Wuensch ^{[B 1]} points out that Hilbert refers to the field equations of gravity as "meine Theorie" ("my theory") in his February 6, 1916 letter to Schwarzschild. This, however, is not at issue, since no one disputes that Hilbert had his own "theory", which Einstein criticized as naive and overly ambitious. Hilbert's theory was based on the work of Mie combined with Einstein's principle of general covariance, but applied to matter and electromagnetism as well as gravity.
• Mehra ^{[B 12]} and Bjerknes^{[B 13]} 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.".^[25] These statements of course do not have any particular bearing on the matter at issue. No one disputes that Hilbert has "his" theory, which was a very ambitious attempt to combine gravity with a theory of matter and electromagnetism along the lines of Mie's theory, and that his equations for gravitation agreed with those that Einstein presented beginning in his, Einstein's, Nov 25 paper (which Hilbert refers to as Einstein's later papers to distinguish them from previous theories of Einstein). None of this bears on the precise origin of the trace term in the Einstein field equations (a feature of the equations that, while theoretically significant, does not have any effect on the vacuum equations, from which all the empirical tests proposed by Einstein were derived).
• Sauer says "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, "^{[B 14]} (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 Krümmung unter dem Hamiltonschen Integral') was claimed as one of his original contributions. SUB Cod. Ms. Hilbert 457/17."^{[B 14]}
• Einstein wrote to Hilbert on 20 December 1915 that there was an "ill-feeling between us" and it has been suspected that this ill feeling was the result of Einstein's bitterness over Hilbert's "nostrification" of his (Einstein's) theory. Others have suggested that Hilbert might have felt that Einstein had derived some benefit or hints from his (Hilbert's) letters, and that those had helped him to arrive at the trace term of the field equations, and if so, that Einstein should have acknowledged this in his paper. But this is pure speculation, aside from Einstein's comment that he believed others (presumably Hilbert) had tried to "nostrify" his theory.

Did Einstein develop the field equations independently?[edit]

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]}

"[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."

• The correspondence between Hilbert and Einstein mentioned above. More recently, it became known that Einstein was also given notes of Hilbert's November 16 talk about his theory.^{[B 1]}
• Einstein's November 18 paper on the perihelion motion of Mercury, which still refers to the incomplete field equations of November 4 and 11. (The perihelion motion depends only on the vacuum equations, which are unaffected by the trace term that was added to complete the field equations.) Reference to the final form of the equations appears only in a footnote added to the paper, indicating that Einstein had not known the final form of the equations on November 18. This is not controversial, and is consistent with the well-known fact that Einstein did not complete the field equations (with the trace term) until November 25.
• 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.

• Hilbert modified his paper in December 1915, and the November 18 version sent to Einstein did not contain the final form of the field equations. 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 , : 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 Grossmann had introduced in the Entwurf papers of 1913.^{[B 14]}

• 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.^{[B 18]} Renn and Sauer^{[B 19]} investigate the notebook used by Einstein in 1912 and claim he was close to the correct theory at that time.

Attackers and defenders[edit]

Special relativity[edit]

Sir Edmund Whittaker (1954)[edit]

Gerald Holton (1960)[edit]

G. H. Keswani (1965)[edit]

Arthur I. Miller (1973)[edit]

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'".

Abraham Pais (1982)[edit]

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)[edit]

John Stachel (1995)[edit]

Peter Galison (2002)[edit]

Olivier Darrigol (2004)[edit]

• "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."

• "These differences between the two theories are sometimes regarded as implying different observable predictions even within the domain of electromagnetism and optics. In reality, there is no such disagreement, for Poincaré's ether is by assumption perfectly undetectable, and every deduction made in Einstein's theory can be translated into a deduction in Poincaré's theory ..."

• In sum, then, Einstein could have borrowed the relativity principle, the definition of simultaneity, the physical interpretation of the Lorentz transformations, and the radiation paradoxes from Poincaré. ... The wisest attitude might be to leave the coincidence of Poincaré's and Einstein's breakthroughs unexplained, ...

Anatoly Alexeevich Logunov on special relativity (2004)[edit]

Harvey R. Brown (2005)[edit]

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."

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."

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."

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."

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."

Roger Cerf (2006)[edit]

Shaul Katzir (2005)[edit]

Scott Walter (2005, 2007)[edit]

General relativity[edit]

E.T. Whittaker[edit]

Albrecht Fölsing on the Hilbert-Einstein interaction (1993)[edit]

Cory/Renn/Stachel and Friedwardt Winterberg (1997/2003)[edit]

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)).

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.

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)[edit]

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)[edit]

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. [7]

David E. Rowe (2006)[edit]

See also[edit]

• History of Lorentz transformations
• History of special relativity
• History of general relativity
• Criticism of relativity theory#Accusations of plagiarism and priority discussions
• David Hilbert
• List of scientific priority disputes
• Multiple discovery

Footnotes[edit]

References[edit]

Works of physics (primary sources)[edit]

• [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, Hendrik Antoon (1921), "Deux Mémoires de Henri Poincaré sur la Physique Mathématique" [Two Papers of Henri Poincaré on Mathematical Physics], Acta Mathematica38 (1): 293–308, doi:10.1007/BF02392073 .
• [Pla07]:Planck, M. (1907) Berlin Sitz., 542
• [Pla08]:Planck, M. (1908) Verh. d. Deutsch. Phys. Ges.X, p218, and Phys. ZS, IX, 828
• [Poi89]:Poincaré, H. (1889) Théorie mathématique de la lumière, Carré & C. Naud, Paris. Partly reprinted in [Poi02], Ch. 12.
• [Poi97]:Poincaré, H. (1897) "The Relativity of Space", article in English translation
• [Poi00] : Poincaré, Henri (1900), "La théorie de Lorentz et le principe de réaction", Archives néerlandaises des sciences exactes et naturelles5: 252–278 . See also the English translation
• [Poi02] : Poincaré, Henri (1902), Science and Hypothesis, London and Newcastle-on-Cyne (1905): The Walter Scott publishing Co. 
• [Poi04] : Poincaré, Henri (1904), "L'état actuel et l'avenir de la physique mathématique", Bulletin des Sciences Mathématiques28 (2): 302–324  English translation as The Principles of Mathematical Physics, in "The value of science" (1905a), Ch. 7-9.
• [Poi05] : Poincaré, Henri (1905b), "Sur la dynamique de l'électron" [On the Dynamics of the Electron], Comptes Rendus140: 1504–1508 
• [Poi06] : Poincaré, Henri (1906), "Sur la dynamique de l'électron" [On the Dynamics of the Electron], Rendiconti del Circolo matematico di Palermo21: 129–176, doi:10.1007/BF03013466 
• [Poi08] : Poincaré, Henri (1908), Science and Method, London: Nelson & Sons 
• [Poi13] : Poincaré, Henri (1913), Last Essays, New York: Dover Publication (1963) 
• [Ein20]: Albert Einstein: "Ether and the Theory of Relativity", An Address delivered on May 5, 1920, in the University of Leyden.
• [Sta89] : John Stachel (Ed.), The collected papers of Albert Einstein, volume 2, Princeton University Press, 1989

Citations[edit]

1. ^ Jump up to: ^abcdDaniela Wuensch, "zwei wirkliche Kerle", Neues zur Entdeckung der Gravitationsgleichungen der Allgemeinen Relativitätstheorie durch Einstein und Hilbert. Termessos, 2005, ISBN 3-938016-04-3
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4. ^ Jump up to: ^abPais, Abraham (1982), Subtle is the Lord: The Science and the Life of Albert Einstein, New York: Oxford University Press, ISBN 0-19-280672-6 
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13. Jump up ^: 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
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External links[edit]

Wikisource has original text related to this article: Poincaré: The Measure of Time

Wikisource has original text related to this article: Lorentz: Electromagnetic phenomena in a system moving with any velocity smaller than that of light

Wikisource has original text related to this article: Poincaré: The Principles of Mathematical Physics

Wikisource has original text related to this article: Poincaré: On the Dynamics of the Electron (June)

Wikisource has original text related to this article: Poincaré: On the Dynamics of the Electron (July)