Relativity priority dispute
Encyclopedia
Albert Einstein
presented the theories of Special Relativity
and General Relativity
in groundbreaking publications that either contained no formal references to previous literature, or referred only to a small number of his predecessors for fundamental results on which he based his theories, most notably to the work of Hendrik Lorentz
for special relativity, and to the work of Gauss
, Riemann
, and Mach
for general relativity. Subsequently claims have been put forward about both theories, asserting that they were formulated, either wholly or in part, by others before Einstein. At issue is the extent to which Einstein and various other individuals should be credited for the formulation of these theories, based on priority considerations.
The general history of the development of these theories, including the contributions made by many other scientists, is found at History of special relativity
and History of general relativity
.
, the most important names that are mentioned in discussions about the distribution of credit are Albert Einstein
, Hendrik Lorentz
, Henri Poincaré
, and Hermann Minkowski
. Consideration is also given to numerous other scientists for either anticipations of some aspects of the theory, or else for contributions to the development or elaboration of the theory. These include Woldemar Voigt
, August Föppl
, Joseph Larmor
, Emil Cohn
, Friedrich Hasenöhrl
, Max Planck
, Max von Laue
, Gilbert Newton Lewis and Richard Chase Tolman, etc. In addition, polemics exist about alleged contributions of others such as Olinto De Pretto
, and Einstein's first wife Mileva Marić
, although these are not considered to have any foundation by serious scholars.
Concerning general relativity
, there is a controversy about the amount of credit that should go to Einstein, Grossmann, and David Hilbert
. Many others (such as Gauss
, Riemann
, William Kingdon Clifford
, Ricci
, and Levi-Civita
) contributed to the development of the mathematical tools and geometrical ideas underlying the theory. Also polemics exist about alleged contributions of others such as Paul Gerber
.
There are a large number of opinions related to these involving questions of "who should get the credit" - these are not enumerated here.
claimed that relativity is the creation of Lorentz and Poincaré and attributed to Einstein's papers only little importance. However, most historians of science, like Gerald Holton
, Arthur I. Miller, Abraham Pais
, John Stachel
, or Olivier Darrigol have other points of view. They admit that Lorentz and Poincaré developed the mathematics of special relativity, and many scientists originally spoke about the „Lorentz-Einstein theory“. But they argue that it was Einstein who completely eliminated the classical ether and demonstrated the relativity of space and time. They also argue that Poincaré demonstrated the relativity of space and time only in his philosophical writings, but in his physical papers he maintained the ether as a privileged frame of reference that is perfectly undetectable, and continued (like Lorentz) to distinguish between "real" lengths and times measured by observers at rest within the aether, and "apparent" lengths and times measured by observers in motion within the aether. Darrigol summarizes:
In a paper that was written in 1914 and published in 1921,
Lorentz appreciated Poincaré's Palermo paper (1906) of Poincaré on relativity. Lorentz stated:
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:
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:
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:
Poincaré
Poincaré attributed the development of the new mechanics almost entirely to Lorentz. He only mentioned Einstein in connection with the photoelectric effect
, 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:
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
:
Einstein wrote in 1907 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 and 1912 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 that he read Poincaré's 1902-book „Science and hypothesis“ before 1905, which included:
Einstein refers to Poincaré in connection with the inertia of energy in 1906 and the non-Euclidean geometry in 1921, 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 said that he had not read before). Einstein wrote in 1953:
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...". 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."
Arguments have been made that Hilbert claimed priority for the field equations themselves; the sources cited for this are:
So far, there seems to be no consensus that these statements form a clear claim by Hilbert to have published the field equations first.
independently. While Hilbert's paper was submitted somewhat earlier than Einstein's, it only appeared in 1916, after Einstein's field equations paper had appeared in print. For this reason there was no good reason to suspect plagiarism on either side. In 1978, a November 18, 1915 letter from Einstein to Hilbert resurfaced, in which Einstein thanked Hilbert for sending an explanation of Hilbert's work. This was not unexpected to most scholars, who were well aware of the correspondence between Hilbert and Einstein that November, and who continued to hold the view expressed by Albrecht Fölsing
in his Einstein biography:
In the very next sentence, after asking the rhetorical question, Folsing answers it with "This is not really probable...", and then goes on to explain in detail why
In their 1997 Science paper, Corry, Renn and Stachel quote the above passage and comment that "the arguments by which Einstein is exculpated are rather weak, turning on his slowness in fully grasping Hilbert's mathematics", and so they attempted to find more definitive evidence of the relationship between the work of Hilbert and Einstein, basing their work largely on a recently discovered pre-print of Hilbert's paper. A discussion of the controversy around this paper is given below.
Those who contend that Einstein's paper was motivated by the information obtained from Hilbert have referred to the following sources:
Those who contend that Einstein's work takes priority over Hilberts, or that both authors did their work independently have used the following arguments:
, 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. He credited Poincaré and Lorentz, and especially alluded to Lorentz's 1904-paper (dated by Whittaker as 1903), Poincaré's St. Louis speech (The Principles of Mathematical Physics) of September 1904, and Poincaré's June 1905-paper. Whittaker attributed to Einstein's relativity paper only little importance, i.e., the formulation of the Doppler and aberration formulas.
(1960, 1973). He argued that there are fundamental differences between the theories of Einstein on one hand, and Poincaré and Lorentz on the other hand. Einstein radically reformulated the concepts of space and time, and by that removed "absolute space" and thus the stationary luminiferous aether from physics. On the other hand, Poincaré and Lorentz still adhered to the stationary aether concept, and tried only to modify Newtonian dynamics, not to replace it. Holton argued, that "Poincaré's silence" (i.e., why Poincaré never mentioned Einstein's contributions to relativity) was due to their fundamental different conceptual viewpoints. Einstein's views on space and time and the abandonment of the aether were, according to Holton, not acceptable to Poincaré, therefore the latter only referred to Lorentz as the creator of the "new mechanics". Holton also pointed out that although Poincaré's 1904 St. Louis speech was "acute and penetrating", it was only qualitative in nature, thus it cannot be interpreted as containing special relativity. He also alluded to mistakes of Whittaker, like predating Lorentz's 1904-paper to 1903.
Similar views as Holton's were later (1967, 1970) also expressed by his former student, Stanley Goldberg.
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"
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."
Keswani did not accept the criticism, and replied in two letters also published in the same journal ( and - 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."
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).
argued that Poincaré "comes near" to discover special relativity (in his St. Louis lecture of September 1904, and the June 1905 paper), but eventually he failed, because in 1904 and also later in 1909, Poincaré treated length contraction
as a third independent hypothesis besides the relativity principle and the constancy of the speed of light. According to Pais, Poincaré thus never understood (or at least he never accepted) special relativity, in which the whole theory including length contraction can simply be derived from two postulates. Consequently, he sharply criticized Whittaker's chapter on the "Relativity theory of Poincaré and Lorentz", saying "how well the author's lack of physical insight matches his ignorance of the literature", although Pais admitted that the first book of Whittaker's "History of Aether and Electricity" is a masterpiece.
He also argued that Lorentz never abandoned the stationary aether concept, either before or after 1905:
), which hindered many to give him due credit. In his opinion, Poincaré was rather a "structural realist" and from that he concludes, that Poincaré actually adhered to the relativity of time and space, while his allusions to the aether are of secondary importance. He continues, that due to his treatment of gravitation and four-dimensional space, Poincaré's 1905/6-paper was superior to Einstein's 1905-paper. Yet Zahar gives also credit to Einstein, who introduced Mass–Energy equivalence, and also transcended special relativity by taking a path leading to the development of general relativity.
(1995) argued that there is a debate over the respective contributions of Lorentz, Poincaré and Einstein to relativity. These questions depend on the definition of relativity, and Stachel argued that kinematics and the new view of space and time is the core of special relativity, and dynamical theories must be formulated in accordance with this scheme. Based on this definition, Einstein is the main originator of the modern understanding of special relativity. In his opinion, Lorentz interpreted the Lorentz transformation only as a mathematical device, while Poincaré's thinking was much nearer to the modern understanding of relativity. Yet Poincaré still believed in the dynamical effects of the aether and distinguished between observers being at rest or in motion with respect to it. Stachel wrote: "He never organized his many brilliant insights into a coherent theory that resolutely discarded the aether and the absolute time or transcended its electrodynamic origins to derive a new kinematics of space and time on a formulation of the relativity principle that makes no reference to the ether".
compared the approaches of both Poincaré and Einstein to reformulate the concepts of space and time. He wrote: "Did Einstein really discover relativity? Did Poincaré already have it? These old questions have grown as tedious as they are fruitless". This is because it depends on the question, which parts of relativity one considers as essential: the rejection of the aether, the Lorentz transformation, the connection with the nature of space and time, predictions of experimental results, or other parts. For Galison, it is more important to acknowledge that both thinkers were concerned with clock synchronization problems, and thus both developed the new operational meaning of simultaneity. However, while Poincaré followed a constructive approach and still adhered to the concepts of Lorentz's stationary aether and the distinction between "apparent" and "true" times, Einstein abandoned the aether and therefore all times in different inertial frames are equally valid. Galison argued that this does not mean that Poincaré was conservative, since Poincaré often alluded to the revolutionary character of the "new mechanics" of Lorentz.
's book about Poincaré's relativity theory, there is an English translation (on p. 113, using modern notations) of the part of Poincaré's 1900 article containing E=mc2. Logunov states that Poincaré's two 1905 papers are superior to Einstein's 1905 paper. According to Logunov, Poincaré was the first scientist to recognize the importance of invariance under the Poincaré group as a guideline for developing new theories in physics. In chapter 9 of this book, Logunov points out that Poincaré's second paper was the first one to formulate a complete theory of relativistic dynamics, containing the correct relativistic analogue of Newton's F=ma.
On p. 142, Logunov points out that Einstein wrote reviews for the Beiblätter Annalen der Physik, writing 21 reviews in 1905. In his view, this contradicts the claims that Einstein worked in relative isolation and with limited access to the scientific literature. Among the papers reviewed in the Beiblätter in the fourth (of 24) issue of 1905, there is a review of Lorentz' 1904-paper by Richard Gans
, which contains the Lorentz transformations. In Logunov's view, this supports the view that Einstein was familiar with the Lorentz' paper containing the correct relativistic transformation in early 1905, while his June 1905 paper does not mention Lorentz in connection with this result.
(2005) (who favors a dynamical view of relativistic effects similar to Lorentz, but "without a hidden aether frame") wrote about the road to special relativity from Michelson to Einstein in section 4:
Regarding Lorentz's work before 1905, Brown wrote about the development of Lorentz's "theorem of corresponding states
" and then continued:
Then the contribution Poincaré's to relativity:
However, Brown continued with the reasons which speak against Poincaré's co-discovery:
Brown denies the idea of other authors and historians, that the major difference between Einstein and his predecessors is Einstein's rejection of the aether, because, it is always possible to add for whatever reason the notion of a privileged frame to special relativity, as long as one accepts that it will remain unobservable, and also Poincaré argued that "some day, no doubt, the aether will thrown aside as useless". However, Brown gave some examples, what in his opinion were the new features in Einstein's work:
After that, Brown develops his own dynamical interpretation of special relativity as opposed to the kinematical approach of Einstein's 1905 paper (although he says that this dynamical view is already contained in Einstein's 1905-paper, "masqueraded in the language of kinematics", p. 82), and the modern understanding of space-time.
.
entitled "Belated Decision in the Hilbert-Einstein Priority Dispute" http://www.garfield.library.upenn.edu/histcomp/einstein-a_all-w-citing-pre-56_e/node/12342.html, concluding that Hilbert had not anticipated Einstein's equations.
Friedwardt Winterberg
, a professor of physics at the University of Nevada, Reno
, disputed http://web.archive.org/web/20070629183442/http://physics.unr.edu/faculty/winterberg/Hilbert-Einstein.pdf 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 Fölsing (1997) and Sauer (1999) according to which Hilbert invited Einstein to Göttingen to give a week of lectures on general relativity in June 1915, which however does not necessarily contradict Winterberg. Hilbert at the time was looking for physics problems to solve.
A short reply to Winterberg's article could be found at http://www.mpiwg-berlin.mpg.de/texts/Winterberg-Antwort.pdf; the original long reply can be accessed via the Internet Archive
at http://web.archive.org/web/20050313161944/http://www.mpiwg-berlin.mpg.de/texts/Winterberg-Antwort.html. 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 http://www.mpiwg-berlin.mpg.de/texts/Winterberg-Antwort.html 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, says of the debate:
In the paper recommended by Todorov as calm and non-confrontational, Tilman Sauer concludes that the printer's proofs show conclusively that Einstein did not plagiarize Hilbert, stating
Max Born's letters to David Hilbert, quoted in Wuensch, is quoted by Todorov as evidence that Einstein's thinking towards general covariance was influenced by the competition with Hilbert.
Todorov ends his paper by stating:
is a former Vice President of the Soviet Academy of Sciences and currently the Scientific advisor of the Institute for High Energy Physics.http://www.biograph.comstar.ru/bank/logunov.htmhttp://www.ihep.su/ihep/info/contact.htm 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:
and Kaluza
expert, responded to Bjerknes, Winterberg and Logunov's criticisms of the Corry/Renn/Stachel paper in a book which appeared in 2005, wherein she defends the view that the cut to Hilbert's printer proofs was made in recent times. Moreover, she presents a theory about what might have been on the missing part of the proofs, based upon her knowledge of Hilbert's papers and lectures.
She defends the view that knowledge of Hilbert's November 16, 1915 letter was crucial to Einstein's development of the field equations: Einstein arrived at the correct field equations only with Hilbert's help ("nach großer Anstrengung mit Hilfe Hilberts"), but nevertheless calls Einstein's reaction (his negative comments on Hilbert in the November 26 letter to Zangger) "understandable" ("Einsteins Reaktion ist verständlich") because Einstein had worked on the problem for a long time.
According to her publisher, Wuensch concludes though that:
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.http://www.dpg-tagungen.de/program/muenchen/gr302.pdf
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").
[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) "Two Papers of Henri Poincaré on Mathematical Physics," 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
[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] : . See also the English translation
[Poi02] :
[Poi04] : English translation as The Principles of Mathematical Physics, in "The value of science" (1905a), Ch. 7-9.
[Poi05] :
[Poi06a] :
[Poi08] :
[Poi13] :
[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
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
presented the theories of Special Relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
and General Relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
in groundbreaking publications that either contained no formal references to previous literature, or referred only to a small number of his predecessors for fundamental results on which he based his theories, most notably to the work of Hendrik Lorentz
Hendrik Lorentz
Hendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
for special relativity, and to the work of Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
, Riemann
Bernhard Riemann
Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity....
, and Mach
Ernst Mach
Ernst Mach was an Austrian physicist and philosopher, noted for his contributions to physics such as the Mach number and the study of shock waves...
for general relativity. Subsequently claims have been put forward about both theories, asserting that they were formulated, either wholly or in part, by others before Einstein. At issue is the extent to which Einstein and various other individuals should be credited for the formulation of these theories, based on priority considerations.
The general history of the development of these theories, including the contributions made by many other scientists, is found at History of special relativity
History of special relativity
The history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others...
and History of general relativity
History of general relativity
-Overview:General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915...
.
The candidates for credit
Concerning special relativitySpecial relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
, the most important names that are mentioned in discussions about the distribution of credit are Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
, Hendrik Lorentz
Hendrik Lorentz
Hendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
, Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
, and Hermann Minkowski
Hermann Minkowski
Hermann Minkowski was a German mathematician of Ashkenazi Jewish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.- Life and work :Hermann Minkowski was born...
. Consideration is also given to numerous other scientists for either anticipations of some aspects of the theory, or else for contributions to the development or elaboration of the theory. These include Woldemar Voigt
Woldemar Voigt
Woldemar Voigt was a German physicist, who taught at the Georg August University of Göttingen. Voigt eventually went on to head the Mathematical Physics Department at Göttingen and was succeeded in 1914 by Peter Debye, who took charge of the theoretical department of the Physical Institute...
, August Föppl
August Föppl
August Otto Föppl was a professor of Technical Mechanics and Graphical Statics at the Technical University of Munich, Germany...
, Joseph Larmor
Joseph Larmor
Sir Joseph Larmor , a physicist and mathematician who made innovations in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter...
, Emil Cohn
Emil Cohn
Emil Georg Cohn , was a German physicist.-Life:Cohn was born in Neustrelitz, Mecklenburg on 28 September 1854. He was the son of August Cohn, a lawyer, and Charlotte Cohn. At the age of 17, Cohn began to study jurisprudence at the University of Leipzig...
, Friedrich Hasenöhrl
Friedrich Hasenöhrl
Friedrich Hasenöhrl , was an Austro-Hungarian physicist.-Life:Friedrich Hasenöhrl was born in Vienna, Austria in 1874. His father was a lawyer and his mother belonged to a prominent aristocratic family...
, Max Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...
, Max von Laue
Max von Laue
Max Theodor Felix von Laue was a German physicist who won the Nobel Prize in Physics in 1914 for his discovery of the diffraction of X-rays by crystals...
, Gilbert Newton Lewis and Richard Chase Tolman, etc. In addition, polemics exist about alleged contributions of others such as Olinto De Pretto
Olinto De Pretto
Olinto De Pretto was an Italian industrialist, physicist and geologist from Schio, Vicenza. He is credited with being the first person to derive the precise formula E=mc2 and is also the first to conclude that radioactive decay of uranium and thorium was an example of energy transformation from...
, and Einstein's first wife Mileva Marić
Mileva Maric
Mileva Marić was one of the first women to study mathematics and physics in Europe...
, although these are not considered to have any foundation by serious scholars.
Concerning general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, there is a controversy about the amount of credit that should go to Einstein, Grossmann, and David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
. Many others (such as Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
, Riemann
Bernhard Riemann
Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity....
, William Kingdon Clifford
William Kingdon Clifford
William Kingdon Clifford FRS was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour, with interesting applications in contemporary mathematical physics...
, Ricci
Gregorio Ricci-Curbastro
Gregorio Ricci-Curbastro was an Italian mathematician. He was born at Lugo di Romagna. He is most famous as the inventor of the tensor calculus but published important work in many fields....
, and Levi-Civita
Tullio Levi-Civita
Tullio Levi-Civita, FRS was an Italian mathematician, most famous for his work on absolute differential calculus and its applications to the theory of relativity, but who also made significant contributions in other areas. He was a pupil of Gregorio Ricci-Curbastro, the inventor of tensor calculus...
) contributed to the development of the mathematical tools and geometrical ideas underlying the theory. Also polemics exist about alleged contributions of others such as Paul Gerber
Paul Gerber
Paul Gerber was a German physicist. He studied in Berlin from 1872-1875. In 1877 he became a teacher at the Realgymnasium in Stargard in Pommern...
.
Special relativity
- In 1889, ([Poi89]), Henri PoincaréHenri PoincaréJules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
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". 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 electronsLorentz ether theoryWhat is now often called Lorentz Ether theory has its roots in Hendrik Lorentz's "Theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century....
' 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. However, Poincaré distinguished between "local" or "apparent" time of moving clocks, and the "true" time of resting clocks in the ether.
- Lorentz' paper [Lor04] containing the transformations bearing his name appeared in 1904.
- Albert EinsteinAlbert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
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 relativityPostulates of special relativity- Postulates of special relativity :1. First postulate 2. Second postulate - Alternate Derivations 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 
. - Hermann MinkowskiHermann MinkowskiHermann Minkowski was a German mathematician of Ashkenazi Jewish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.- Life and work :Hermann Minkowski was born...
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.
General relativity
- The proposal to describe gravity by means of a pseudo-Riemannian metric was first made by Einstein and GrossmannMarcel GrossmannMarcel Grossmann was a mathematician of Jewish ancestry, and a friend and classmate of Albert Einstein. He became a Professor of Mathematics at the Federal Polytechnic Institute in Zurich, today the ETH Zurich, specializing in descriptive geometry....
in the so called Entwurf theory published 1913 . This was followed by several attempts of Einstein to find valid field equations for this theory of gravity. - David HilbertDavid HilbertDavid Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
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.http://termessos.de/prooffotos.htm The extant part of the proofs contains Hilbert's actionEinstein-Hilbert actionThe Einstein–Hilbert action in general relativity is the action that yields the Einstein's field equations through the principle of least 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" - 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.)
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).
- 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 SolovineMaurice SolovineMaurice Solovine was a Romanian philosopher and mathematician.As a young student of philosophy in Bern Solovine applied to study physics with Albert Einstein in response to an advert...
, 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 MarićMileva MaricMileva Marić was one of the first women to study mathematics and physics in Europe...
, may have contributed to Einstein's work, although this question is not considered to have any foundation by serious scholars.
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 StachelJohn StachelJohn Stachel is an American physicist and philosopher of science.Stachel earned his PhD at Stevens Institute of Technology in Physics about a topic in General relativity in 1958...
, 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. - 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 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 SchwarzschildKarl SchwarzschildKarl Schwarzschild was a German physicist. He is also the father of astrophysicist Martin Schwarzschild.He is best known for providing the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-rotating mass, which he accomplished...
.
There are a large number of opinions related to these involving questions of "who should get the credit" - these are not enumerated here.
Historians of special relativity
In his History of the theories of ether and electricity from 1953, E. T. WhittakerE. T. Whittaker
Edmund Taylor Whittaker FRS FRSE was an English mathematician who contributed widely to applied mathematics, mathematical physics and the theory of special functions. He had a particular interest in numerical analysis, but also worked on celestial mechanics and the history of physics...
claimed that relativity is the creation of Lorentz and Poincaré and attributed to Einstein's papers only little importance. However, most historians of science, like Gerald Holton
Gerald Holton
Gerald Holton is Mallinckrodt Research Professor of Physics and Research Professor of the History of Science, Emeritus, at Harvard University.Born 1922 in Berlin, he grew up in Vienna before emigrating in 1938...
, Arthur I. Miller, Abraham Pais
Abraham Pais
Abraham Pais was a Dutch-born American physicist and science historian. Pais earned his Ph.D. from University of Utrecht just prior to a Nazi ban on Jewish participation in Dutch universities during World War II...
, John Stachel
John Stachel
John Stachel is an American physicist and philosopher of science.Stachel earned his PhD at Stevens Institute of Technology in Physics about a topic in General relativity in 1958...
, or Olivier Darrigol have other points of view. They admit that Lorentz and Poincaré developed the mathematics of special relativity, and many scientists originally spoke about the „Lorentz-Einstein theory“. But they argue that it was Einstein who completely eliminated the classical ether and demonstrated the relativity of space and time. They also argue that Poincaré demonstrated the relativity of space and time only in his philosophical writings, but in his physical papers he maintained the ether as a privileged frame of reference that is perfectly undetectable, and continued (like Lorentz) to distinguish between "real" lengths and times measured by observers at rest within the aether, and "apparent" lengths and times measured by observers in motion within the aether. Darrigol summarizes:
Most of the components of Einstein's paper appeared in others' anterior works on the electrodynamics of moving bodies. Poincaré and Alfred BuchererAlfred BuchererAlfred Heinrich Bucherer was a German physicist, who is known for his experiments on relativistic mass...
had the relativity principle. LorentzHendrik LorentzHendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
and LarmorJoseph LarmorSir Joseph Larmor , a physicist and mathematician who made innovations in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter...
had most of the Lorentz transformations, Poincaré had them all. CohnEmil CohnEmil Georg Cohn , was a German physicist.-Life:Cohn was born in Neustrelitz, Mecklenburg on 28 September 1854. He was the son of August Cohn, a lawyer, and Charlotte Cohn. At the age of 17, Cohn began to study jurisprudence at the University of Leipzig...
and Bucherer rejected the ether. Poincaré, Cohn, and AbrahamMax AbrahamMax Abraham was a German physicist.Abraham was born in Danzig, Imperial Germany to a family of Jewish merchants. His father was Moritz Abraham and his mother was Selma Moritzsohn. Attending the University of Berlin, he studied under Max Planck. He graduated in 1897...
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.
Comments by Lorentz, Poincaré, and Einstein
Lorentz, PoincaréIn a paper that was written in 1914 and published in 1921,
Lorentz appreciated Poincaré's Palermo paper (1906) of Poincaré on relativity. Lorentz stated:
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:
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:
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:
Poincaré
Poincaré attributed the development of the new mechanics almost entirely to Lorentz. He only mentioned Einstein in connection with the photoelectric effect
Photoelectric effect
In the photoelectric effect, electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as photoelectrons...
, 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
Old quantum theory
The old quantum theory was a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was a collection of heuristic prescriptions which are now understood to be the first quantum corrections to classical mechanics...
. He wrote:
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
Max Planck Institute for the History of Science
The Max Planck Institute for the History of Science in Berlin was established in March 1994. Its research is primarily devoted to a theoretically oriented history of science, principally of the natural sciences, but with methodological perspectives drawn from the cognitive sciences and from...
wrote on Einstein's contributions to the Annalen der Physik
Annalen der Physik
Annalen der Physik is one of the oldest physics journals worldwide. The journal publishes original, peer-reviewed papers in the areas of experimental, theoretical, applied and mathematical physics and related areas...
:
Einstein wrote in 1907 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 and 1912 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 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 geometryNon-Euclidean geometryNon-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
.
Einstein refers to Poincaré in connection with the inertia of energy in 1906 and the non-Euclidean geometry in 1921, 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 said that he had not read before). Einstein wrote in 1953:
Did Hilbert claim priority for parts of General Relativity?
Kip ThorneKip Thorne
Kip Stephen Thorne is an American theoretical physicist, known for his prolific contributions in gravitation physics and astrophysics and for having trained a generation of scientists...
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...". 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."
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, "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 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 dismiss such misconstruals as obvious nonsense.
- Wuensch 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 and Bjerknes 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.". 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 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, " (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". 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."
- 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.
So far, there seems to be no consensus that these statements form a clear claim by Hilbert to have published the field equations first.
Did Einstein develop the field equations independently?
For a long time, it was believed that Einstein and Hilbert found the field equations of gravityEinstein field equations
The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
independently. While Hilbert's paper was submitted somewhat earlier than Einstein's, it only appeared in 1916, after Einstein's field equations paper had appeared in print. For this reason there was no good reason to suspect plagiarism on either side. In 1978, a November 18, 1915 letter from Einstein to Hilbert resurfaced, in which Einstein thanked Hilbert for sending an explanation of Hilbert's work. This was not unexpected to most scholars, who were well aware of the correspondence between Hilbert and Einstein that November, and who continued to hold the view expressed by Albrecht Fölsing
Albrecht Fölsing
Albrecht Fölsing is a trained physicist turned into a scientific journalist. Having studied physics in Berlin, Philadelphia, and Hamburg, he worked as an academic research assistant for the German electron synchrotron named Desy. In the years 1973-2001, Fölsing was head of the Nature and Science...
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?
In the very next sentence, after asking the rhetorical question, Folsing answers it with "This is not really probable...", and then goes on to explain in detail why
- "[Einstein's] eventual derivation of the equations was a logical development of his earlier arguments—in which, despite all the mathematics, physical principles invariably predominated. His approach was thus quite different from Hilbert's, and Einstein's achievements can, therefore, surely be regarded as authentic."
In their 1997 Science paper, Corry, Renn and Stachel quote the above passage and comment that "the arguments by which Einstein is exculpated are rather weak, turning on his slowness in fully grasping Hilbert's mathematics", and so they attempted to find more definitive evidence of the relationship between the work of Hilbert and Einstein, basing their work largely on a recently discovered pre-print of Hilbert's paper. A discussion of the controversy around this paper is given below.
Those who contend that Einstein's paper was motivated by the information obtained from Hilbert have referred to the following sources:
- 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.
- 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.
Those who contend that Einstein's work takes priority over Hilberts, or that both authors did their work independently have used the following arguments:
- 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 Grassman had introduced in the Entwurf papers of 1913.
- 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. Renn and Sauer investigate the notebook used by Einstein in 1912 and claim he was close to the correct theory at that time.
Attackers and defenders
This section cites notable publications where people have expressed a view on the issues outlined above.Sir Edmund Whittaker (1954)
In 1954, Sir Edmund Taylor Whittaker, an English mathematician and historian of science, credited Poincaré with the equation, 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. He credited Poincaré and Lorentz, and especially alluded to Lorentz's 1904-paper (dated by Whittaker as 1903), Poincaré's St. Louis speech (The Principles of Mathematical Physics) of September 1904, and Poincaré's June 1905-paper. Whittaker attributed to Einstein's relativity paper only little importance, i.e., the formulation of the Doppler and aberration formulas.Gerald Holton (1960)
Whittaker's claims were criticized by Gerald HoltonGerald Holton
Gerald Holton is Mallinckrodt Research Professor of Physics and Research Professor of the History of Science, Emeritus, at Harvard University.Born 1922 in Berlin, he grew up in Vienna before emigrating in 1938...
(1960, 1973). He argued that there are fundamental differences between the theories of Einstein on one hand, and Poincaré and Lorentz on the other hand. Einstein radically reformulated the concepts of space and time, and by that removed "absolute space" and thus the stationary luminiferous aether from physics. On the other hand, Poincaré and Lorentz still adhered to the stationary aether concept, and tried only to modify Newtonian dynamics, not to replace it. Holton argued, that "Poincaré's silence" (i.e., why Poincaré never mentioned Einstein's contributions to relativity) was due to their fundamental different conceptual viewpoints. Einstein's views on space and time and the abandonment of the aether were, according to Holton, not acceptable to Poincaré, therefore the latter only referred to Lorentz as the creator of the "new mechanics". Holton also pointed out that although Poincaré's 1904 St. Louis speech was "acute and penetrating", it was only qualitative in nature, thus it cannot be interpreted as containing special relativity. He also alluded to mistakes of Whittaker, like predating Lorentz's 1904-paper to 1903.
Similar views as Holton's were later (1967, 1970) also expressed by his former student, Stanley Goldberg.
G. H. Keswani (1965)
In a 1965 series of articles tracing the history of relativity, 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". This would leave the special theory of relativity as the unique theory of relativity. Keswani cited also Vladimir FockVladimir Fock
Vladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics....
for this same opinion.
This series of articles prompted responses, among others from Herbert Dingle
Herbert Dingle
Herbert Dingle , an English physicist and natural philosopher, who served as president of the Royal Astronomical Society from 1951 to 1953, is best known for his opposition to Albert Einstein's special theory of relativity and the protracted controversy that this provoked.-Biography:Dingle was born...
and Karl Popper
Karl Popper
Sir Karl Raimund Popper, CH FRS FBA was an Austro-British philosopher and a professor at the London School of Economics...
.
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"
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."
Keswani did not accept the criticism, and replied in two letters also published in the same journal ( and - 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."
Dingle commented the year after on the history of crediting: "Until the first World War, Lorentz's and Einstein's theories were regarded as different forms of the same idea, but Lorentz, having priority and being a more established figure speaking a more familiar language, was credited with it." (Dingle 1967, Nature 216 p. 119-122).
Arthur I. Miller (1973)
Miller (1973, 1981) agreed with the analysis of Holton and Goldberg, and further argued that although the terminology (like the principle of relativity) used by Poincaré and Einstein were very similar, their content differs sharply. According to Miller, Poincaré used this principle to complete the aether based "electromagnetic world-view" of Lorentz and Abraham. He also argued that Poincaré distinguished (in his July 1905 paper) between "ideal" and "real" systems and electrons. That is, Lorentz's and Poincaré's usage of reference frames lacks an unambiguous physical interpretation, because in many cases they are only mathematical tools, while in Einstein's theory the processes in inertial frames are not only mathematically, but also physically equivalent. Miller wrote in 1981:- p. 172: "Although Poincaré's principle of relativity is stated in a manner similar to Einstein's, the difference in content is sharp. The critical difference is that Poincaré's principle admits the existence of the ether, and so considers the velocity of light to be exactly c only when it is measured in coordinate systems at rest in the ether. In inertial reference systems, the velocity of light is c and is independent of the emitter's motion as a result of certain compensatory effects such as the mathematical local time and the hypothesis of an unobservable contraction. Consequently, Poincaré's extension of the relativity principle of relative motion into the dynamics of the electron resided in electromagnetic theory, and not in mechanics...Poincaré came closest to rendering electrodynamics consistent, but not to a relativity theory." p. 217: "Poincaré related the imaginary system Σ' to the ether fixed system S'".
Abraham Pais (1982)
In his Einstein biography "Subtle is the Lord" (1982), Abraham PaisAbraham Pais
Abraham Pais was a Dutch-born American physicist and science historian. Pais earned his Ph.D. from University of Utrecht just prior to a Nazi ban on Jewish participation in Dutch universities during World War II...
argued that Poincaré "comes near" to discover special relativity (in his St. Louis lecture of September 1904, and the June 1905 paper), but eventually he failed, because in 1904 and also later in 1909, Poincaré treated length contraction
Length contraction
In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer...
as a third independent hypothesis besides the relativity principle and the constancy of the speed of light. According to Pais, Poincaré thus never understood (or at least he never accepted) special relativity, in which the whole theory including length contraction can simply be derived from two postulates. Consequently, he sharply criticized Whittaker's chapter on the "Relativity theory of Poincaré and Lorentz", saying "how well the author's lack of physical insight matches his ignorance of the literature", although Pais admitted that the first book of Whittaker's "History of Aether and Electricity" is a masterpiece.
He also argued that Lorentz never abandoned the stationary aether concept, either before or after 1905:
- p. 118: "Throughout the paper of 1895, the Fresnel aether is postulated explicitly"; p. 125: "Like Voigt before him, Lorentz regarded the transformation ... only as a convenient mathematical tool for proving a physical theorem ... he proposed to call t the general time and t' the local time. Although he didn't say it explicitly, it is evident that to him there was, so to speak, only one true time t."; p. 166: "8.3. Lorentz and the Aether... For example, Lorentz still opines that the contraction of the rods has a dynamic origin. There is no doubt that he had read and understood Einstein's papers by then. However, neither then nor later was he prepared to accept their conclusions as the definitive answer to the problems of the aether."
Elie Zahar (1983)
In several papers, Elie Zahar (1983, 2000) argued that both Einstein (in his June paper) and Poincaré (in his July paper) independently discovered special relativity. He said that "though Whittaker was unjust towards Einstein, his positive account of Poincaré's actual achievement contains much more than a simple grain of truth". According to him, it was Poincaré's unsystematic and sometimes erroneous statements regarding his philosophical papers (often connected with conventionalismConventionalism
Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on agreements in society, rather than on external reality...
), which hindered many to give him due credit. In his opinion, Poincaré was rather a "structural realist" and from that he concludes, that Poincaré actually adhered to the relativity of time and space, while his allusions to the aether are of secondary importance. He continues, that due to his treatment of gravitation and four-dimensional space, Poincaré's 1905/6-paper was superior to Einstein's 1905-paper. Yet Zahar gives also credit to Einstein, who introduced Mass–Energy equivalence, and also transcended special relativity by taking a path leading to the development of general relativity.
John Stachel (1995)
John StachelJohn Stachel
John Stachel is an American physicist and philosopher of science.Stachel earned his PhD at Stevens Institute of Technology in Physics about a topic in General relativity in 1958...
(1995) argued that there is a debate over the respective contributions of Lorentz, Poincaré and Einstein to relativity. These questions depend on the definition of relativity, and Stachel argued that kinematics and the new view of space and time is the core of special relativity, and dynamical theories must be formulated in accordance with this scheme. Based on this definition, Einstein is the main originator of the modern understanding of special relativity. In his opinion, Lorentz interpreted the Lorentz transformation only as a mathematical device, while Poincaré's thinking was much nearer to the modern understanding of relativity. Yet Poincaré still believed in the dynamical effects of the aether and distinguished between observers being at rest or in motion with respect to it. Stachel wrote: "He never organized his many brilliant insights into a coherent theory that resolutely discarded the aether and the absolute time or transcended its electrodynamic origins to derive a new kinematics of space and time on a formulation of the relativity principle that makes no reference to the ether".
Peter Galison (2002)
In his book "Einstein's clocks, Poincaré's maps" (2002),http://www.aip.org/history/einstein/essay-einsteins-time.htm Peter GalisonPeter Galison
Peter Louis Galison is the Pellegrino University Professor in History of Science and Physics at Harvard University.Galison received his Ph.D. from Harvard University in both Physics and the History of Science in 1983. His publications include Image and Logic: A Material Culture of Microphysics ...
compared the approaches of both Poincaré and Einstein to reformulate the concepts of space and time. He wrote: "Did Einstein really discover relativity? Did Poincaré already have it? These old questions have grown as tedious as they are fruitless". This is because it depends on the question, which parts of relativity one considers as essential: the rejection of the aether, the Lorentz transformation, the connection with the nature of space and time, predictions of experimental results, or other parts. For Galison, it is more important to acknowledge that both thinkers were concerned with clock synchronization problems, and thus both developed the new operational meaning of simultaneity. However, while Poincaré followed a constructive approach and still adhered to the concepts of Lorentz's stationary aether and the distinction between "apparent" and "true" times, Einstein abandoned the aether and therefore all times in different inertial frames are equally valid. Galison argued that this does not mean that Poincaré was conservative, since Poincaré often alluded to the revolutionary character of the "new mechanics" of Lorentz.
Christopher Jon Bjerknes (2003)
This author has written several books and articles claiming that Einstein plagiarized the theories of relativity. Examples are "Anticipations of Einstein in the General Theory of Relativity" and "Albert Einstein: the incorrigible plagiarist".Olivier Darrigol (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."
- "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)
In Anatoly LogunovAnatoly Logunov
Anatoly Alekseyevich Logunov is a Soviet and Russian theoretical physicist, academician of the USSR Academy of Sciences and Russian Academy of Sciences.-Relativistic theory of gravitation:...
's book about Poincaré's relativity theory, there is an English translation (on p. 113, using modern notations) of the part of Poincaré's 1900 article containing E=mc2. Logunov states that Poincaré's two 1905 papers are superior to Einstein's 1905 paper. According to Logunov, Poincaré was the first scientist to recognize the importance of invariance under the Poincaré group as a guideline for developing new theories in physics. In chapter 9 of this book, Logunov points out that Poincaré's second paper was the first one to formulate a complete theory of relativistic dynamics, containing the correct relativistic analogue of Newton's F=ma.
On p. 142, Logunov points out that Einstein wrote reviews for the Beiblätter Annalen der Physik, writing 21 reviews in 1905. In his view, this contradicts the claims that Einstein worked in relative isolation and with limited access to the scientific literature. Among the papers reviewed in the Beiblätter in the fourth (of 24) issue of 1905, there is a review of Lorentz' 1904-paper by Richard Gans
Richard Gans
Richard Martin Gans , German of Jewish origin, born in Hamburg, was the physicist who founded the Physics Institute of the National University of La Plata, Argentina...
, which contains the Lorentz transformations. In Logunov's view, this supports the view that Einstein was familiar with the Lorentz' paper containing the correct relativistic transformation in early 1905, while his June 1905 paper does not mention Lorentz in connection with this result.
Harvey R. Brown (2005)
Harvey R. BrownHarvey Brown (philosopher)
Harvey R. Brown, is a philosopher of physics. He is professor of philosophy at the University of Oxford and a Fellow of Wolfson College, Oxford, as well as a Fellow of the British Academy....
(2005) (who favors a dynamical view of relativistic effects similar to Lorentz, but "without a hidden aether frame") wrote about the road to special relativity from Michelson to Einstein in section 4:
- p. 40: "The cradle of special theory of relativity was the combination of Maxwellian electromagnetism and the electron theory of Lorentz (and to a lesser extent of Larmor) based on Fresnel's notion of the stationary aether....It is well known that Einstein's special relativity was partially motivated by this failure [to find the aether wind], but in order to understand the originality of Einstein's 1905 work it is incumbent on us to review the work of the trailblazers, and in particular Michelson, FitzGerald, Lorentz, Larmor, and Poincaré. After all they were jointly responsible for the discovery of relativistic kinematics, in form if not in content, as well as a significant portion of relativistic dynamics as well."
Regarding Lorentz's work before 1905, Brown wrote about the development of Lorentz's "theorem of corresponding states
Lorentz ether theory
What is now often called Lorentz Ether theory has its roots in Hendrik Lorentz's "Theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century....
" and then continued:
- p. 54: "Lorentz's interpretation of these transformations is not the one Einstein would given them and which is standardly embraced today. Indeed, until Lorentz came to terms with Einstein's 1905 work, and somehow despite Poincaré's warning, he continued to believe that the true coordinate transformations were the Galilean ones, and that the 'Lorentz' transformations ... were merely a useful formal device..." p. 56. "Lorentz consistently failed to understand the operational significance of his notions of 'local' time...He did however have an intimation of time dilation in 1899, but inevitably there are caveats...The hypotheses of Lorentz's system were starting to pile up, and the spectre of ad hocness was increasingly hard to ignore."
Then the contribution Poincaré's to relativity:
- p. 62: "Indeed, the claim that this giant of pure and applied mathematics co-discovered special relativity is not uncommon, and it is not hard to see why. Poincaré was the first to extend the relativity principle to optics and electrodynamics exactly. Whereas Lorentz, in his theorem of corresponding states, had from 1899 effectively assumed this extension of the relativity principle up to second-order effects, Poincaré took it to hold for all orders. Poincaré was the first to show that Maxwell’s equations with source terms are strictly Lorentz covariant. … Poincaré was the first to use the generalized relativity principle as a constraint on the form of the coordinate transformations. He recognized that the relativity principle implies that the transformations form a group, and in further appealing to spatial isotropy. … Poincaré was the first to see the connection between Lorentz’s ‘local time’, and the issue of clock synchrony. … It is fair to say that Poincaré was the first to understand the relativity of simultaneity, and the conventionality of distant simultaneity. Poincaré anticipated Minkowski’s interpretation of the Lorentz transformations as a passive, rigid rotation within a four-dimensional pseudo-Euclidean space-time. He was also aware that the electromagnetic potentials transform in the manner of what is now called a Minkowski 4-vector. He anticipated the major results of relativistic dynamics (and in particular the relativistic relations between force, momentum and velocity), but not E=mc² in its full generality."
However, Brown continued with the reasons which speak against Poincaré's co-discovery:
- p. 63-64: "What are the grounds for denying Poincaré the title of co-discoverer of special relativity? ... Although Poincaré understood independently of Einstein how the Lorentz transformations give rise to non-Galilean transformation rules for velocities (indeed Poincaré derived the correct relativistic rules), it is not clear that he had a full appreciation of the modern operational significance attached to coordinate transformations.... he did not seem to understand the role played by the second-order terms in the transformation. Compared with the cases of Lorentz and Larmor, it is even less clear that Poincaré understood either length contraction or time dilation to be a consequence of the coordinate transformation.... What Poincaré was holding out for was no less than a new theory of ether and matter - something far more ambitions than what appeared in Einstein's 1905 relativity paper...p. 65. Like Einstein half a decade later, Poincaré wanted new physics, not a reinterpretations or reorganization of existing notions."
Brown denies the idea of other authors and historians, that the major difference between Einstein and his predecessors is Einstein's rejection of the aether, because, it is always possible to add for whatever reason the notion of a privileged frame to special relativity, as long as one accepts that it will remain unobservable, and also Poincaré argued that "some day, no doubt, the aether will thrown aside as useless". However, Brown gave some examples, what in his opinion were the new features in Einstein's work:
- p. 66: "The full meaning of relativistic kinematics was simply not properly understood before Einstein. Nor was the 'theory of relativity' as Einstein articulated it in 1905 anticipated even in its programmatic form." p. 69. "How did Albert Einstein...arrive at his special theory of relativity?...I want only to stress that it is impossible to understand Einstein's discovery (if that is the right word) of special relativity without taking on board the impacts of the quantum in physics." p. 81. "In this respect [Brown refers to the conventional nature of distant simultaneity] Einstein was doing little more than expanding on a theme that Poincaré had already introduced. Where Einstein goes well beyond the great mathematician is in his treatment of the coordinate transformations... In particular, the extraction of the phenomena of length contraction and time dilation directly from the Lorentz transformations in section 4 of the 1905 paper is completely original."
After that, Brown develops his own dynamical interpretation of special relativity as opposed to the kinematical approach of Einstein's 1905 paper (although he says that this dynamical view is already contained in Einstein's 1905-paper, "masqueraded in the language of kinematics", p. 82), and the modern understanding of space-time.
Roger Cerf (2006)
Roger Cerf (2006) gave priority to Einstein for developing special relativity, and criticized the assertions of Leveugle and others concerning the priority of Poincaré. While Cerf agreed that Poincaré made important contributions to relativity, he argued (following Pais) that Poincaré "stopped short before the crucial step" because he handled length contraction as a "third hypothesis", therefore Poincaré lacked a complete understanding of the basic principles of relativity. "Einstein’s crucial step was that he abandoned the mechanistic ether in favor of a new kinematics." He also denies the idea, that Poincaré invented E=mc² in its modern relativistic sense, because he did not realize the implications of this relationship. Cerf considers Leveugle's Hilbert-Planck-Einstein connection an implausible conspiracy theoryConspiracy theory
A conspiracy theory explains an event as being the result of an alleged plot by a covert group or organization or, more broadly, the idea that important political, social or economic events are the products of secret plots that are largely unknown to the general public.-Usage:The term "conspiracy...
.
Shaul Katzir (2005)
Katzir (2005) argued that "Poincaré’s work should not be seen as an attempt to formulate special relativity, but as an independent attempt to resolve questions in electrodynamics." Contrary to Miller and others, Katzir thinks that Poincaré's development of electrodynamics led him to the rejection of the pure electromagnetic world-view (due to the non-electromagnetic Poincaré-Stresses introduced in 1905), and Poincaré's theory represents a "relativistic physics" which is guided by the relativity principle. In this physics, however, "Lorentz’s theory and Newton’s theory remained as the fundamental bases of electrodynamics and gravitation."Scott Walter (2005, 2007)
Walter (2005) argues that both Poincaré and Einstein put forward the theory of relativity in 1905. And in 2007 he wrote, that although Poincaré formally introduced four-dimensional spacetime in 1905/6, he was still clinging to the idea of "Galilei spacetime". That is, Poincaré preferred Lorentz covariance over Galilei covariance when it is about phenomena accessible to experimental tests; yet in terms of space and time, Poincaré preferred Galilei spacetime over Minkowski spacetime, and length contraction and time dilation "are merely apparent phenomena due to motion with respect to the ether". This is the fundamental difference in the two principal approaches to relativity theory, namely that of "Lorentz and Poincaré" on one side, and "Einstein and Minkowski" on the other side.E.T. Whittaker
Whittaker (1954) stated that David Hilbert had derived the theory of General Relativity from an elegant variational principle almost simultaneously with Einstein's discovery of the theory.Albrecht Fölsing on the Hilbert-Einstein interaction (1993)
From Fölsing's 1993 (English translation 1998) Einstein biography (footnote references in the quote are from the original text and the actual notes are not reproduced here):- 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. StrausErnst G. StrausErnst Gabor Straus was a German-American mathematician who helped found the theories of Euclidean Ramsey theory and of the arithmetic properties of analytic functions...
, 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.
Cory/Renn/Stachel and Friedwardt Winterberg (1997/2003)
In 1997, Cory, Renn and Stachel published a 3-page article in ScienceScience (journal)
Science is the academic journal of the American Association for the Advancement of Science and is one of the world's top scientific journals....
entitled "Belated Decision in the Hilbert-Einstein Priority Dispute" http://www.garfield.library.upenn.edu/histcomp/einstein-a_all-w-citing-pre-56_e/node/12342.html, concluding that Hilbert had not anticipated Einstein's equations.
Friedwardt Winterberg
Friedwardt Winterberg
Friedwardt Winterberg is a German-American theoretical physicist and research professor at the University of Nevada, Reno. With more than 260 publications and three books, he is known for his research in areas spanning general relativity, Planck scale physics, nuclear fusion, and plasmas...
, a professor of physics at the University of Nevada, Reno
University of Nevada, Reno
The University of Nevada, Reno , is a teaching and research university established in 1874 and located in Reno, Nevada, USA...
, disputed http://web.archive.org/web/20070629183442/http://physics.unr.edu/faculty/winterberg/Hilbert-Einstein.pdf 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 Fölsing (1997) and Sauer (1999) according to which Hilbert invited Einstein to Göttingen to give a week of lectures on general relativity in June 1915, which however does not necessarily contradict Winterberg. Hilbert at the time was looking for physics problems to solve.
A short reply to Winterberg's article could be found at http://www.mpiwg-berlin.mpg.de/texts/Winterberg-Antwort.pdf; the original long reply can be accessed via the Internet Archive
Internet Archive
The Internet Archive is a non-profit digital library with the stated mission of "universal access to all knowledge". It offers permanent storage and access to collections of digitized materials, including websites, music, moving images, and nearly 3 million public domain books. The Internet Archive...
at http://web.archive.org/web/20050313161944/http://www.mpiwg-berlin.mpg.de/texts/Winterberg-Antwort.html. In this reply, Winterberg's hypothesis is called "paranoid
Conspiracy theory
A conspiracy theory explains an event as being the result of an alleged plot by a covert group or organization or, more broadly, the idea that important political, social or economic events are the products of secret plots that are largely unknown to the general public.-Usage:The term "conspiracy...
" 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 http://www.mpiwg-berlin.mpg.de/texts/Winterberg-Antwort.html 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, 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 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 concludes that the printer's proofs show conclusively that Einstein did not plagiarize Hilbert, stating
- any possibility that Einstein took the clue for the final step toward his field equations from Hilbert's note [Nov 20, 1915] is now definitely precluded.
Max Born's letters to David Hilbert, quoted in Wuensch, is quoted by Todorov as evidence that Einstein's thinking towards general covariance was influenced by the competition with Hilbert.
Todorov ends his paper by stating:
- Einstein and Hilbert had the moral strength and wisdom - after a month of intense competition, from which, in a final account, everybody (including science itself) profited - to avoid a lifelong priority dispute (something in which Leibniz and Newton failed). It would be a shame to subsequent generations of scientists and historians of science to try to undo their achievement.
Anatoly Alexeevich Logunov on general relativity (2004)
Anatoly LogunovAnatoly Logunov
Anatoly Alekseyevich Logunov is a Soviet and Russian theoretical physicist, academician of the USSR Academy of Sciences and Russian Academy of Sciences.-Relativistic theory of gravitation:...
is a former Vice President of the Soviet Academy of Sciences and currently the Scientific advisor of the Institute for High Energy Physics.http://www.biograph.comstar.ru/bank/logunov.htmhttp://www.ihep.su/ihep/info/contact.htm 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.
Daniela Wuensch (2005)
Daniela Wuensch, a historian of science and a HilbertDavid Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
and Kaluza
Theodor Kaluza
Theodor Franz Eduard Kaluza was a German mathematician and physicist known for the Kaluza-Klein theory involving field equations in five-dimensional space...
expert, responded to Bjerknes, Winterberg and Logunov's criticisms of the Corry/Renn/Stachel paper in a book which appeared in 2005, wherein she defends the view that the cut to Hilbert's printer proofs was made in recent times. Moreover, she presents a theory about what might have been on the missing part of the proofs, based upon her knowledge of Hilbert's papers and lectures.
She defends the view that knowledge of Hilbert's November 16, 1915 letter was crucial to Einstein's development of the field equations: Einstein arrived at the correct field equations only with Hilbert's help ("nach großer Anstrengung mit Hilfe Hilberts"), but nevertheless calls Einstein's reaction (his negative comments on Hilbert in the November 26 letter to Zangger) "understandable" ("Einsteins Reaktion ist verständlich") because Einstein had worked on the problem for a long time.
According to her publisher, 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. http://termessos.de/einsteinhilbertdispute.htm
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.http://www.dpg-tagungen.de/program/muenchen/gr302.pdf
Klaus Sommer (2005)
Klaus Sommer is a historian of science and Hilbert expert. In an article in "Physik in unserer Zeit", 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").
See also
- History of Lorentz transformationsHistory of lorentz transformationsThe Lorentz transformations relate the space-time coordinates, relative to a particular inertial frame of reference , and the coordinates of the same event relative to another coordinate system moving in the positive x-direction at a constant speed v, relative to the rest system...
- History of special relativityHistory of special relativityThe history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others...
- History of general relativityHistory of general relativity-Overview:General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915...
- Criticism of relativity theory#Accusations of plagiarism and priority discussions
- Henri PoincaréHenri PoincaréJules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
- David HilbertDavid HilbertDavid Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
- List of scientific priority disputes
- Multiple discoveryMultiple discoveryThe concept of multiple discovery is the hypothesis that most scientific discoveries and inventions are made independently and more or less simultaneously by multiple scientists and inventors...
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) "Two Papers of Henri Poincaré on Mathematical Physics," 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
[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] : . See also the English translation
[Poi02] :
[Poi04] : English translation as The Principles of Mathematical Physics, in "The value of science" (1905a), Ch. 7-9.
[Poi05] :
[Poi06a] :
[Poi08] :
[Poi13] :
[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
Secondary sources
- 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)
- Ives, H. E. (1953) "Note on 'Mass-Energy Relationship'", J. O. S. A., 43, 619.
- Keswani, G. H. and C. W. Kilmister (1983) "Initimations of relativity. Relativity before Einstein", British Journal for the Philosophy of Science 34, 343-54. .
- Macrossan, M. N. (1986) "A Note on Relativity Before Einstein", British Journal for the Philosophy of Science., 37, pp. 232–34.
- 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)