|Hendrik Antoon Lorentz|
18 July 1853|
4 February 1928 74) (aged|
|Alma mater||University of Leiden|
|Doctoral advisor||Pieter Rijke|
Hendrik Antoon Lorentz (18 July 1853 – 4 February 1928) 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. He also derived the transformation equations which formed the basis of the special relativity theory of Albert Einstein.
According to the biography published by the Nobel Foundation, "It may well be said that Lorentz was regarded by all theoretical physicists as the world's leading spirit, who completed what was left unfinished by his predecessors and prepared the ground for the fruitful reception of the new ideas based on the quantum theory." For this he received many honours and distinctions during his life, including—from 1925 to his death in 1928—the role of Chairman of the exclusive International Committee on Intellectual Cooperation.
Hendrik Lorentz was born in Arnhem, Gelderland (The Netherlands), the son of Gerrit Frederik Lorentz (1822–1893), a well-off nurseryman, and Geertruida van Ginkel (1826–1861). In 1862, after his mother's death, his father married Luberta Hupkes. Despite being raised as a Protestant, he was a freethinker in religious matters. From 1866 to 1869 he attended the "Hogere Burger School" in Arnhem, a new type of public high school recently established by Johan Rudolph Thorbecke. His results in school were exemplary; not only did he excel in the physical sciences and math, but also in English, French, and German. In 1870 he passed the exams in classical languages which were then required for admission to University.
Lorentz studied physics and mathematics at the Leiden University, where he was strongly influenced by the teaching of astronomy professor Frederik Kaiser; it was his influence that led him to become a physicist. After earning a bachelor's degree, he returned to Arnhem in 1871 to teach night school classes in mathematics, but he continued his studies in Leiden in addition to his teaching position. In 1875 Lorentz earned a doctoral degree under Pieter Rijke on a thesis entitled "Over de theorie der terugkaatsing en breking van het licht" (On the theory of reflection and refraction of light), in which he refined the electromagnetic theory of James Clerk Maxwell.
Professor in Leiden
On 17 November 1877, only 24 years of age, Hendrik Antoon Lorentz was appointed to the newly established chair in theoretical physics at the University of Leiden. The position had initially been offered to Johan van der Waals, but he opted for a position at the Universiteit van Amsterdam at the last moment. On 25 January 1878 Lorentz delivered his inaugural lecture on "De moleculaire theoriën in de natuurkunde" (The molecular theories in physics). In 1881 he became member of the Royal Netherlands Academy of Arts and Sciences.
During the first twenty years in Leiden, Lorentz was primarily interested in the theory of electromagnetism to explain the relationship of electricity, magnetism, and light. After that, he extended his research to a much wider area while still focusing on theoretical physics. Lorentz made significant contributions to fields ranging from hydrodynamics to general relativity. His most important contributions were in the area of electromagnetism, the electron theory, and relativity.
Lorentz theorized that atoms might consist of charged particles and suggested that the oscillations of these charged particles were the source of light. When a colleague and former student of Lorentz's, Pieter Zeeman, discovered the Zeeman effect in 1896, Lorentz supplied its theoretical interpretation. The experimental and theoretical work was honored with the Nobel prize in physics in 1902. Lorentz' name is now associated with the Lorentz-Lorenz formula, the Lorentz force, the Lorentzian distribution, and the Lorentz transformation.
Electrodynamics and relativity
In 1892 and 1895 Lorentz worked on describing electromagnetic phenomena (the propagation of light) in reference frames that move relative to the luminiferous aether. He discovered that the transition from one to another reference frame could be simplified by using a new time variable which he called local time. The local time depended on the universal time and the location under consideration. By that, he could explain the aberration of light and the result of the Fizeau experiment. Lorentz's publications made use of the term local time without giving a detailed interpretation of its physical relevance. In 1900 and 1904, Henri Poincaré called local time Lorentz's "most ingenious idea" and illustrated it by showing that clocks in moving frames are synchronized by exchanging light signals that are assumed to travel at the same speed against and with the motion of the frame (see Einstein synchronisation and Relativity of simultaneity). In 1892, with the attempt to explain the Michelson-Morley experiment, Lorentz also proposed that moving bodies contract in the direction of motion (see length contraction; George FitzGerald had already arrived at this conclusion in 1889).
In 1899 and again in 1904, Lorentz added time dilation to his transformations and published what Poincaré in 1905 named Lorentz transformations. It was apparently unknown to Lorentz that Joseph Larmor had used identical transformations to describe orbiting electrons in 1897. Larmor's and Lorentz's equations look somewhat dissimilar, but they are algebraically equivalent to those presented by Poincaré and Einstein in 1905. Lorentz's 1904 paper includes the covariant formulation of electrodynamics, in which electrodynamic phenomena in different reference frames are described by identical equations with well defined transformation properties. The paper clearly recognizes the significance of this formulation, namely that the outcomes of electrodynamic experiments do not depend on the relative motion of the reference frame. The 1904 paper includes a detailed discussion of the increase of the inertial mass of rapidly moving objects in a useless attempt to make momentum look exactly like Newtonian momentum; it was also an attempt to explain the length contraction as the accumulation of "stuff" onto mass making it slow and contract.
Lorentz and special relativity
In 1905, Einstein would use many of the concepts, mathematical tools and results Lorentz discussed to write his paper entitled "On the Electrodynamics of Moving Bodies", known today as the theory of special relativity. Because Lorentz laid the fundamentals for the work by Einstein, this theory was originally called the Lorentz-Einstein theory.
In 1906, Lorentz's electron theory received a full-fledged treatment in his lectures at Columbia University, published under the title The Theory of Electrons.
The increase of mass was the first prediction of Lorentz and Einstein to be tested, but some experiments by Kaufmann appeared to show a slightly different mass increase; this led Lorentz to the famous remark that he was "au bout de mon latin" ("at the end of my [knowledge of] Latin" = at his wit's end) The confirmation of his prediction had to wait until 1908 and later (see Kaufmann–Bucherer–Neumann experiments).
Lorentz published a series of papers dealing with what he called "Einstein's principle of relativity". For instance, in 1909, 1910, 1914. In his 1906 lectures published with additions in 1909 in the book "The theory of electrons" (updated in 1915), he spoke affirmatively of Einstein's theory:
It will be clear by what has been said that the impressions received by the two observers A0 and A would be alike in all respects. It would be impossible to decide which of them moves or stands still with respect to the ether, and there would be no reason for preferring the times and lengths measured by the one to those determined by the other, nor for saying that either of them is in possession of the "true" times or the "true" lengths. This is a point which Einstein has laid particular stress on, in a theory in which he starts from what he calls the principle of relativity, [...] I cannot speak here of the many highly interesting applications which Einstein has made of this principle. His results concerning electromagnetic and optical phenomena ... agree in the main with those which we have obtained in the preceding pages, the chief difference being that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle. [...] It would be unjust not to add that, besides the fascinating boldness of its starting point, Einstein's theory has another marked advantage over mine. Whereas I have not been able to obtain for the equations referred to moving axes exactly the same form as for those which apply to a stationary system, Einstein has accomplished this by means of a system of new variables slightly different from those which I have introduced.
Though Lorentz still maintained that there is an (undetectable) aether in which resting clocks indicate the "true time":
1909: Yet, I think, something may also be claimed in favour of the form in which I have presented the theory. I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter.
1910: Provided that there is an aether, then under all systems x, y, z, t, one is preferred by the fact, that the coordinate axes as well as the clocks are resting in the aether. If one connects with this the idea (which I would abandon only reluctantly) that space and time are completely different things, and that there is a "true time" (simultaneity thus would be independent of the location, in agreement with the circumstance that we can have the idea of infinitely great velocities), then it can be easily seen that this true time should be indicated by clocks at rest in the aether. However, if the relativity principle had general validity in nature, one wouldn't be in the position to determine, whether the reference system just used is the preferred one. Then one comes to the same results, as if one (following Einstein and Minkowski) deny the existence of the aether and of true time, and to see all reference systems as equally valid. Which of these two ways of thinking one is following, can surely be left to the individual.
Indeed, for some of the physical quantities which enter the formulas, I did not indicate the transformation which suits best. That was done by Poincaré and then by Mr. Einstein and Minkowski [...] I did not succeed in obtaining the exact invariance of the equations [...] Poincaré, on the contrary, obtained a perfect invariance of the equations of electrodynamics, and he formulated the "postulate of relativity", terms which he was the first to employ. [...] Let us add that by correcting the imperfections of my work he never reproached me for them.
Lorentz and general relativity
Lorentz was one of few scientists who supported Einstein's search for general relativity from the beginning – he wrote several research papers and discussed with Einstein personally and by letter. For instance, he attempted to combine Einstein's formalism with Hamilton's principle (1915), and to reformulate it in a coordinate-free way (1916). Lorentz wrote in 1919:
The total eclipse of the sun of May 29, resulted in a striking confirmation of the new theory of the universal attractive power of gravitation developed by Albert Einstein, and thus reinforced the conviction that the defining of this theory is one of the most important steps ever taken in the domain of natural science.
Lorentz and quantum mechanics
Lorentz gave a series of lectures in the Fall of 1926 at Cornell University on the new quantum mechanics, in which he presented Erwin Schrödinger's wave mechanics. A typescript of the lecture notes is available.
Einstein wrote of Lorentz:
1928: The enormous significance of his work consisted therein, that it forms the basis for the theory of atoms and for the general and special theories of relativity. The special theory was a more detailed expose of those concepts which are found in Lorentz's research of 1895.
1953: For me personally he meant more than all the others I have met on my life's journey.
The most satisfactory theory is that of Lorentz; it is unquestionably the theory that best explains the known facts, the one that throws into relief the greatest number of known relations ... it is due to Lorentz that the results of Fizeau on the optics of moving bodies, the laws of normal and abnormal dispersion and of absorption are connected with each other ... Look at the ease with which the new Zeeman phenomenon found its place, and even aided the classification of Faraday's magnetic rotation, which had defied all Maxwell's efforts.
Paul Langevin (1911) said of Lorentz:
It will be Lorentz's main claim to fame that he demonstrated that the fundamental equations of electromagnetism also allow of a group of transformations that enables them to resume the same form when a transition is made from one reference system to another. This group differs fundamentally from the above group as regards transformations of space and time.''
Lorentz and Emil Wiechert had an interesting correspondence on the topics of electromagnetism and the theory of relativity, and Lorentz explained his ideas in letters to Wiechert. The correspondence between Lorentz and Wiechert has been published by Wilfried Schröder.
Lorentz was chairman of the first Solvay Conference held in Brussels in the autumn of 1911. Shortly after the conference, Poincaré wrote an essay on quantum physics which gives an indication of Lorentz's status at the time:
... at every moment [the twenty physicists from different countries] could be heard talking of the [quantum mechanics] which they contrasted with the old mechanics. Now what was the old mechanics? Was it that of Newton, the one which still reigned uncontested at the close of the nineteenth century? No, it was the mechanics of Lorentz, the one dealing with the principle of relativity; the one which, hardly five years ago, seemed to be the height of boldness.
Change of priorities
In 1910 Lorentz decided to reorganize his life. His teaching and management duties at Leiden University were taking up too much of his time leaving him little time for research. In 1912, he resigned from his chair of theoretical physics to become curator of the "Physics Cabinet" at Teylers Museum in Haarlem. He remained connected to Leiden University as an external professor, and his "Monday morning lectures" on new developments in theoretical physics soon became legendary.
Lorentz initially asked Einstein to succeed him as professor of theoretical physics at Leiden. However, Einstein could not accept because he had just accepted a position at ETH Zurich. Einstein had no regrets in this matter, since the prospect of having to fill Lorentz's shoes made him shiver. Instead Lorentz appointed Paul Ehrenfest as his successor in the chair of theoretical physics at the Leiden University, who would found the Institute for Theoretical Physics which would become known as the Lorentz Institute.
After World War I, Lorentz was one of the driving forces behind the founding of the "Wetenschappelijke Commissie van Advies en Onderzoek in het Belang van Volkswelvaart en Weerbaarheid", a committee which was to harness the scientific potential united in the Royal Netherlands Academy of Arts and Sciences (KNAW) for solving civil problems such as food shortage which had resulted from the war. Lorentz was appointed chair of the committee. However, despite the best efforts of many of the participants the committee would harvest little success. The only exception being that it ultimately resulted in the founding of TNO, the Netherlands Organisation for Applied Scientific Research.
Lorentz was also asked by the Dutch government to chair a committee to calculate some of the effects of the proposed Afsluitdijk (Enclosure Dam) flood control dam on water levels in the Waddenzee. Hydraulic engineering was mainly an empirical science at that time, but the disturbance of the tidal flow caused by the Afsluitdijk was so unprecedented that the empirical rules could not be trusted. Originally Lorentz was only supposed to have a coordinating role in the committee, but it quickly became apparent that Lorentz was the only physicist to have any fundamental traction on the problem. In the period 1918 till 1926, Lorentz invested a large portion of his time in the problem. Lorentz proposed to start from the basic hydrodynamic equations of motion and solve the problem numerically. This was feasible for a "human computer", because of the quasi-one-dimensional nature of the water flow in the Waddenzee. The Afsluitdijk was completed in 1932 and the predictions of Lorentz and his committee turned out to be remarkably accurate. One of the two sets of locks in the Afsluitdijk was named after him.
In January 1928, Lorentz became seriously ill, and died shortly after on February 4. The respect in which he was held in the Netherlands is apparent from Owen Willans Richardson's description of his funeral:
- The funeral took place at Haarlem at noon on Friday, February 10. At the stroke of twelve the State telegraph and telephone services of Holland were suspended for three minutes as a revered tribute to the greatest man the Netherlands has produced in our time. It was attended by many colleagues and distinguished physicists from foreign countries. The President, Sir Ernest Rutherford, represented the Royal Society and made an appreciative oration by the graveside.
Unique 1928 film footage of the funeral procession with a lead carriage followed by ten mourners, followed by a carriage with the coffin, followed in turn by at least four more carriages, passing by a crowd at the Grote Markt, Haarlem from the Zijlstraat to the Smedestraat, and then back again through the Grote Houtstraat towards the Barteljorisstraat, on the way to the "Algemene Begraafplaats" at the Kleverlaan (northern Haarlem cemetery) has been digitized on YouTube. Einstein gave a eulogy at a memorial service at Leiden University.
Richardson describes Lorentz as:
- [A] man of remarkable intellectual powers ... . Although steeped in his own investigation of the moment, he always seemed to have in his immediate grasp its ramifications into every corner of the universe. ... The singular clearness of his writings provides a striking reflection of his wonderful powers in this respect. .... He possessed and successfully employed the mental vivacity which is necessary to follow the interplay of discussion, the insight which is required to extract those statements which illuminate the real difficulties, and the wisdom to lead the discussion among fruitful channels, and he did this so skillfully that the process was hardly perceptible.
M. J. Klein (1967) wrote of Lorentz's reputation in the 1920s:
- For many years physicists had always been eager "to hear what Lorentz will say about it" when a new theory was advanced, and, even at seventy-two, he did not disappoint them.
In addition to the Nobel prize, Lorentz received a great many honours for his outstanding work. He was elected a Foreign Member of the Royal Society (ForMemRS) in 1905. The Society awarded him their Rumford Medal in 1908 and their Copley Medal in 1918.
- List of things named after Hendrik Antoon Lorentz
- Geertruida de Haas-Lorentz
- Lorentz factor
- Lorentz force
- Lorentz Medal
- Lorentz (crater)
|Wikisource has original works written by or about:|
|German Wikisource has original text related to this article:|
Many papers by Lorentz (mostly in English) are available for online viewing in the Proceedings of the Royal Netherlands Academy of Arts and Science, Amsterdam.
- Lorentz, Hendrik Antoon (1900), "Considerations on Gravitation", Proc. Acad. Science Amsterdam, 2: 559–574
- Lorentz, Hendrik Antoon (1927–1931), Lectures on Theoretical Physics (vol. I-III), New York, [NY.]: Macmillan & Co., (Vol. I online)
- Russell McCormmach. "Lorentz, Hendrik Antoon". Complete Dictionary of Scientific Biography. Retrieved 25 April 2012.
Although he grew up in Protestant circles, he was a freethinker in religious matters; he regularly attended the local French church to improve his French.
- Kox, Anne J. (2011). "Hendrik Antoon Lorentz (in Dutch)". Nederlands Tijdschirft voor Natuurkunde. 77 (12): 441.
- Macrossan, Michael N. (1986), "A note on relativity before Einstein", Brit. J. Phil. Sci., 37 (2): 232–234, doi:10.1093/bjps/37.2.232
- Miller, Arthur I. (1981). Albert Einstein’s special theory of relativity. Emergence (1905) and early interpretation (1905–1911). Reading: Addison–Wesley. ISBN 0-201-04679-2.
- Kox, A.J. (1993). "Einstein, Lorentz, Leiden and general relativity". Class. Quantum Grav. 10: 187. Bibcode:1993CQGra..10S.187K. doi:10.1088/0264-9381/10/S/020.
- Janssen, M. (1992). "H. A. Lorentz's Attempt to Give a Coordinate-free Formulation of the General. Theory of Relativity.". Studies in the History of General Relativity. Boston: Birkhäuser. pp. 344–363. ISBN 0817634797.
- Pais, Abraham (1982), Subtle is the Lord: The Science and the Life of Albert Einstein, New York: Oxford University Press, ISBN 0-19-520438-7
- Justin Wintle (8 February 2002). Makers of Nineteenth Century Culture: 1800–1914. Routledge. pp. 375–. ISBN 978-0-415-26584-3. Retrieved 25 July 2012.
- Langevin, P. (1911), "The evolution of space and time", Scientia, X: 31–54 (translated by J. B. Sykes, 1973).
- (Arch. ex. hist. Sci, 1984).
- "Carlo Beenakker". Ilorentz.org. Retrieved 2012-02-01.
- Richardson, O. W. (1929), "Hendrik Antoon Lorentz", J. London Math. Soc., 4 (1): 183–192, doi:10.1112/jlms/s1-4.3.183. The biography which refers to this article (but gives no pagination details other than those of the article itself) is O'Connor, John J.; Robertson, Edmund F., "Hendrik Lorentz", MacTutor History of Mathematics archive, University of St Andrews.
- Funeral procession on YouTube Hendrik Lorentz
- Przibram, Karl (ed.); Klein, Martin J. (trans.) (1967), Letters of wave mechanics: Schrödinger, Planck, Einstein, Lorentz. Edited by Karl Przibram for the Austrian Academy of Sciences, New York, [NY.]: Philosophical Library
- de Haas-Lorentz, Geertruida L.; Fagginger Auer, Joh. C. (trans.) (1957), H.A. Lorentz: impressions of his life and work, Amsterdam: North-Holland Pub. Co.
- Langevin, Paul (1911), "L'évolution de l'espace et du temps", Scientia, X: 31–54 :n.p.
- Poincaré, Henri (1900), "La théorie de Lorentz et le principe de réaction", Archives Néerlandaises des Sciences exactes et naturelles, V: 253–278 See English translation.
- Poincaré, Henri (1902), La science et l'hypothèse, Paris, [France]: Ernest Flammarion : n.p.. The quotation is from the English translation (Poincaré, Henri (1952), Science and hypothesis, New York, [NY.]: Dover Publications, p. 175)
- Poincaré, Henri (1913), Dernières pensées, Paris, [France]: Ernest Flammarion :n.p.. The quotation in the article is from the English translation: (Poincaré, Henri; Bolduc, John W. (trans.) (1963), Mathematics and science: last essays, New York, [NY.]: Dover Publications :n.p.)
- Sri Kantha, S. Einstein and Lorentz. Nature, July 13, 1995; 376: 111. (Letter)
|Wikiquote has quotations related to: Hendrik Lorentz|
|Wikimedia Commons has media related to Hendrik Antoon Lorentz.|
- Publications of H.A. Lorentz
- Karl Grandin, ed. (1902). "Hendrik A. Lorentz Biography". Les Prix Nobel. The Nobel Foundation. Retrieved 2008-07-29.
- Works by Hendrik Antoon Lorentz at Project Gutenberg
- Works by or about Hendrik Lorentz at Internet Archive
- Works by Hendrik Lorentz at LibriVox (public domain audiobooks)
- Beenakker, Carlo, Lorentz and the Zuiderzee project, Leiden, [The Netherlands]: Instituut Lorentz, University of Leiden
- van Helden, Albert (1999), "Hendrik Antoon Lorentz 1853–1928", in van Berkel, Klaas; van Helden, Albert; Palm, Lodewijk (eds.), A History of Science in The Netherlands: Survey, Themes and Reference, Leiden, [The Netherlands]: Brill, pp. 514–518, ISBN 90-04-10006-7
- List of Ph.D. students of Hendrik Lorentz.
- O'Connor, John J.; Robertson, Edmund F., Hendrik Lorentz, MacTutor History of Mathematics archive, retrieved 2008-05-01
- Movie of Lorentz's funeral
- "Fellows of the Royal Society". London: Royal Society. Archived from the original on 2015-03-16.
- Hendrik A. Lorentz - Biographical, Nobelprize.org (retrieved: 4 November 2015)
- Hendrik Lorentz (1875). "Over de theorie der terugkaatsing en breking van het licht" (PDF).
- "Hendrik Antoon Lorentz (1853 - 1928)". Royal Netherlands Academy of Arts and Sciences. Retrieved 17 July 2015.
- Lorentz, Hendrik Antoon (1892), "La Théorie electromagnétique de Maxwell et son application aux corps mouvants on the Internet Archive", Archives néerlandaises des sciences exactes et naturelles, 25: 363–552 External link in
- Lorentz, Hendrik Antoon (1895), Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern, Leiden: E.J. Brill
- English Wikisource translation: Attempt of a Theory of Electrical and Optical Phenomena in Moving Bodies
- Poincaré, Henri (1900), "La théorie de Lorentz et le principe de réaction", Archives néerlandaises des sciences exactes et naturelles, 5: 252–278. See also the English translation.
- Poincaré, Henri (1904), "The Principles of Mathematical Physics", Congress of arts and science, universal exposition, St. Louis, 1904, 1, Boston and New York: Houghton, Mifflin and Company, pp. 604–622
- Lorentz, Hendrik Antoon (1892b), "The Relative Motion of the Earth and the Aether", Zittingsverlag Akad. V. Wet., 1: 74–79
- Lorentz, Hendrik Antoon (1899), "Simplified Theory of Electrical and Optical Phenomena in Moving Systems", Proceedings of the Royal Netherlands Academy of Arts and Sciences, 1: 427–442
- Lorentz, Hendrik Antoon (1904), "Electromagnetic phenomena in a system moving with any velocity smaller than that of light", Proceedings of the Royal Netherlands Academy of Arts and Sciences, 6: 809–831
- Einstein, Albert (1905), "Zur Elektrodynamik bewegter Körper" (PDF), Annalen der Physik, 322 (10): 891–921, Bibcode:1905AnP...322..891E, doi:10.1002/andp.19053221004. See also: English translation.
- Lorentz à Poincaré at the Wayback Machine (archived February 21, 2005)
- Lorentz, Hendrik Antoon (1909/16), The theory of electrons and its applications to the phenomena of light and radiant heat; a course of lectures delivered in Columbia university, New York, in March and April 1906, New York, [NY.]: Columbia University Press Check date values in:
- Lorentz, Hendrik Antoon (1910/1913). "Das Relativitätsprinzip und seine Anwendung auf einige besondere physikalische Erscheinungen". In Blumenthal, Otto; Sommerfeld, Arnold. Das Relativitätsprinzip. Eine Sammlung von Abhandlungen. pp. 74–89. Check date values in:
- English Wikisource translation: The Principle of Relativity and its Application to some Special Physical Phenomena
- Lorentz, Hendrik Antoon (1910 (published 1931)), Lectures on theoretical physics, Vol. 3, London: MacMillan Check date values in:
- Lorentz, Hendrik Antoon (1914). Das Relativitätsprinzip. Drei Vorlesungen gehalten in Teylers Stiftung zu Haarlem (1913). Leipzig and Berlin: B.G. Teubner.
- Lorentz, Hendrik Antoon (1914/21), "Deux Mémoires de Henri Poincaré sur la Physique Mathématique", Acta Mathematica, 38 (1): 293–308, doi:10.1007/BF02392073 Check date values in:
- English Wikisource translation: Two Papers of Henri Poincaré on Mathematical Physics
- Lorentz, Hendrik Antoon (1915), "On Hamilton's principle in Einstein's theory of gravitation", Proceedings of the Royal Netherlands Academy of Arts and Sciences, 19: 751–765
- Lorentz, Hendrik Antoon (1916), "On Einstein's Theory of gravitation I–IV", Proceedings of the Royal Netherlands Academy of Arts and Sciences, 19/20: 1341–1361, 2–34
- Lorentz, Hendrik Antoon (1920), The Einstein Theory of Relativity, New York: Bentano's
- Lorentz, H. A. (1926). The New Quantum Theory (PDF). Ithaca, New York: Typescript of Lecture Notes. Retrieved August 12, 2016.
- Poincaré, Henri (1902), Science and Hypothesis, London and Newcastle-on-Cyne (1905): The Walter Scott publishing Co.
- Poincaré, Henri (1913), Last Essays on the Internet Archive, New York External link in