Figures of light in the early history of relativity (1905–1914). (English) Zbl 1402.83016
Rowe, David E. (ed.) et al., Beyond Einstein. Perspectives on geometry, gravitation, and cosmology in the twentieth century. Selected papers based on the presentations at the conference, Mainz, Germany, September 22–26, 2008. New York, NY: Birkhäuser (ISBN 978-1-4939-7706-2/hbk; 978-1-4939-7708-6/ebook). Einstein Studies 14, 3-50 (2018).
Summary: Albert Einstein’s bold assertion of the form invariance of the equation of a spherical light wave with respect to inertial frames of reference [A. Einstein, Ann. der Phys. (4) 17, 891–921 (1905; JFM 36.0920.02)] became, in the space of 6 years, the preferred foundation of his theory of relativity. Early on, however, Einstein’s universal light-sphere invariance was challenged on epistemological grounds by Henri Poincaré, who promoted an alternative demonstration of the foundations of relativity theory based on the notion of a light ellipsoid. A third figure of light, Hermann Minkowski’s lightcone also provided a new means of envisioning the foundations of relativity. Drawing in part on archival sources, this paper shows how an informal, international group of physicists, mathematicians, and engineers, including Einstein, Paul Langevin, Poincaré, Hermann Minkowski, Ebenezer Cunningham, Harry Bateman, Otto Berg, Max Planck, Max von Laue, A. A. Robb, and Ludwig Silberstein, employed figures of light during the formative
years of relativity theory in their discovery of the salient features of the relativistic worldview.
For the entire collection see [Zbl 1403.83002].
For the entire collection see [Zbl 1403.83002].
MSC:
| 83-03 | History of relativity and gravitational theory |
| 01A60 | History of mathematics in the 20th century |
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 83A05 | Special relativity |
Citations:
JFM 36.0920.02References:
| [1] | Abraham, M. (1905). \(Theorie der Elektrizität, Volume 2, Elektromagnetische Theorie der Strahlung\). Leipzig: Teubner. · JFM 36.0906.02 |
| [2] | Balàzs, N. L. (1972). The acceptability of physical theories: Poincaré versus Einstein. In L. O’Raifeartaigh (Ed.) \(General relativity: Papers in Honour of J. L. Synge\) (pp. 21-34). Oxford: Oxford University Press. |
| [3] | Barrow-Green, J., & Gray, J. (2006). Geometry at Cambridge, 1863-1940. \(Historia Mathematica, 33\)(3), 315-356. · Zbl 1101.01007 · doi:10.1016/j.hm.2005.09.002 |
| [4] | Bateman, H. (1908). On conformal transformations of a space of four dimensions and their application to geometrical optics. \(Report-British Association, 78\), 627-629. |
| [5] | Bateman, H. (1909). The conformal transformations of a space of four dimensions and their applications to geometrical optics. \(Proceedings of the London Mathematical Society, 7\), 70-89. · JFM 40.0710.02 · doi:10.1112/plms/s2-7.1.70 |
| [6] | Bateman, H. (1910a). The physical aspect of time. \(Memoirs and Proceedings, Manchester Literary and Philosophical Society, 54\)(14), 1-13. · JFM 41.0756.02 |
| [7] | Bateman, H. (1910b). The relation between electromagnetism and geometry. \(Philosophical Magazine, 20\), 623-628. · JFM 41.0952.05 |
| [8] | Bateman, H. (1910c). The transformations of the electrodynamical equations. \(Proceedings of the London Mathematical Society, 8\), 223-264. · JFM 41.0942.03 · doi:10.1112/plms/s2-8.1.223 |
| [9] | Bateman, H. (1912). Some geometrical theorems connected with Laplace’s equation and the equation of wave motion. \(American Journal of Mathematics, 34\), 325-360. · JFM 43.0449.02 · doi:10.2307/2370223 |
| [10] | Berg, O. (1910). Das Relativitätsprinzip der Elektrodynamik. \(Abhandlungen der Fries’schen Schule, 3\), 333-382. |
| [11] | Bergson, H. (1922). \(Durée et simultanéité : à propos de la théorie d’Einstein\). Paris: Alcan. · JFM 48.1063.02 |
| [12] | Blumenthal, O. (Ed.). (1913). \(Das Relativitätsprinzip; Eine Sammlung von Abhandlungen\). Leipzig: Teubner. · JFM 44.0770.01 |
| [13] | Born, M. (1909). Die Theorie des starren Elektrons in der Kinematik des Relativitätsprinzips. \(Annalen der Physik, 335\), 1-56. · JFM 40.0930.02 · doi:10.1002/andp.19093351102 |
| [14] | Born, M. (1912). Besprechung von Max Laue, Das Relativitätsprinzip. \(Physikalische Zeitschrift, 13\), 175-176. |
| [15] | Born, M. (1914). Besprechung von Max Weinstein, Die Physik der bewegten Materie und die Relativitätstheorie. \(Physikalische Zeitschrift, 15\), 676. |
| [16] | Born, M. (1920). \(Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen\). Berlin: Springer. · JFM 47.0778.02 · doi:10.1007/978-3-662-41810-9 |
| [17] | Born, M. (1959). Erinnerungen an Hermann Minkowski zur 50. Wiederkehr seines Todestages. \(Naturwissenschaften, 46\)(17), 501-505. · doi:10.1007/BF00703530 |
| [18] | Bridgman, P. W. (1916). Tolman’s principle of similitude. \(Physical Review, 8\), 423-431. · doi:10.1103/PhysRev.8.423 |
| [19] | Briginshaw, A. J. (1979). The axiomatic geometry of space-time: An assessment of the work of A. A. Robb. \(Centaurus, 22\)(4), 315-323. · Zbl 0412.01013 · doi:10.1111/j.1600-0498.1979.tb00595.x |
| [20] | Bromwich, T. J. I. (1901). Conformal space transformations. \(Proceedings of the London Mathematical Society, 33\)(749), 185-192. · JFM 32.0679.01 |
| [21] | Brown, H. R. (2005). \(Physical relativity: Space-time structure from a dynamical perspective\). Oxford: Oxford University Press. · Zbl 1084.83001 · doi:10.1093/0199275831.001.0001 |
| [22] | Bucherer, A. H. (1907). On a new principle of relativity in electromagnetism. \(Philosophical Magazine, 13\), 413-420. · JFM 38.0871.03 |
| [23] | Bucherer, A. H. (1908a). Messungen an Becquerelstrahlen; die experimentelle Bestätigung der Lorentz-Einsteinschen Theorie. \(Physikalische Zeitschrift, 9\), 755-762. |
| [24] | Bucherer, A. H. (1908b). On the principle of relativity and on the electromagnetic mass of the electron; a reply to Mr. E. Cunningham. \(Philosophical Magazine, 15\), 316-318. · JFM 39.0911.02 |
| [25] | Buchwald, J. Z. (1985). \(From Maxwell to microphysics\). Chicago: University of Chicago Press. |
| [26] | Cat, J. (2016). Images and logic of the light cone: Tracking Robb’s postulational turn in physical geometry. \(Revista de Humanidades de Valparaiso, 4\)(8), 43-105. · doi:10.22370/rhv.2016.8.498 |
| [27] | Cunningham, E. (1907). On the electromagnetic mass of a moving electron. \(Philosophical Magazine\), 14:538-547. · JFM 38.0866.01 |
| [28] | Cunningham, E. (1910). The principle of relativity in electrodynamics and an extension thereof. \(Proceedings of the London Mathematical Society, 8\), 77-98. · JFM 40.0928.01 · doi:10.1112/plms/s2-8.1.77 |
| [29] | Cunningham, E. (1911). The principle of relativity. \(Report-British Association, 81\):236-245. · JFM 43.0774.01 |
| [30] | Cunningham, E. (1914). \(The principle of relativity\). Cambridge: Cambridge University Press. · JFM 45.1150.04 |
| [31] | Cuvaj, C. (1970). \(A history of relativity: The role of Henri Poincaré and Paul Langevin\). PhD thesis, Yeshiva University, New York. |
| [32] | Darrigol, O. (1995). Henri Poincaré’s criticism of fin de siècle electrodynamics. \(Studies in History and Philosophy of Modern Physics, 26\), 1-44. · Zbl 1222.78003 · doi:10.1016/1355-2198(95)00003-C |
| [33] | Darrigol, O. (1996). The electrodynamic origins of relativity theory. \(Historical Studies in the Physical and Biological Sciences, 26\)(2), 241-312. · doi:10.2307/27757763 |
| [34] | Darrigol, O. (2000). \(Electrodynamics from Ampère to Einstein\). Oxford: Oxford University Press. · Zbl 0954.78001 |
| [35] | Darrigol, O. (2014). \(Physics and necessity: Rationalist pursuits from the Cartesian past to the quantum present\). Oxford: Oxford University Press. · doi:10.1093/acprof:oso/9780198712886.001.0001 |
| [36] | Darrigol, O. (2015). Poincaré and light. In B. Duplantier & V. Rivasseau (Eds.), \(Henri Poincaré, 1912-2012\). \(Progress in mathematical physics\) (Vol. 67, pp. 1-50). Berlin: Springer. · Zbl 1319.01014 |
| [37] | Du Pasquier, L.-G. (1922). \(Le principe de la relativité et les théories d’Einstein\). Paris: Doin. · JFM 48.1062.03 |
| [38] | Einstein, A. (1905). Zur Elektrodynamik bewegter Körper. \(Annalen der Physik, 322\), 891-921. · JFM 36.0920.02 · doi:10.1002/andp.19053221004 |
| [39] | Einstein, A. (1907). Relativitätsprinzip und die aus demselben gezogenen Folgerungen. \(Jahrbuch der Radioaktivität und Elektronik, 4\), 411-462. |
| [40] | Frank, P. G. (1911). Das Verhalten der elektromagnetischen Feldgleichungen gegenüber linearen Transformationen. \(Annalen der Physik, 340\), 599-607. · JFM 42.0925.01 · doi:10.1002/andp.19113400811 |
| [41] | Frank, P. G. (1947). \(Einstein: His life and times\). New York: Knopf. · Zbl 0029.19601 |
| [42] | Galison, P. (1979). Minkowski’s spacetime: From visual thinking to the absolute world. \(Historical Studies in the Physical Sciences, 10\), 85-121. · doi:10.2307/27757388 |
| [43] | Galison, P. (2003). \(Einstein’s clocks and Poincaré’s maps: Empires of time\). New York: Norton. · Zbl 1066.01005 |
| [44] | Goldberg, S. (1970). In defense of Ether: The British response to Einstein’s special theory of relativity 1905-1911. \(Historical Studies in the Physical Sciences, 2\), 89-125. · doi:10.2307/27757305 |
| [45] | Gray, J. (1989). \(Ideas of space: Euclidean, non-Euclidean and relativistic\) (2nd ed.). Oxford: Clarendon. · Zbl 0672.51001 |
| [46] | Gray, J. (2013). \(Henri Poincaré: A scientific biography\). Princeton: Princeton University Press. · Zbl 1263.01002 |
| [47] | Guillaume, E. (1921). Expression mono et polyparametrique du temps dans la theorie de la relativité. In H. Villat (Ed.), \(Comptes rendus du Congrès international des mathématiciens: Strasbourg, 22-30 septembre 1920\) (pp. 594-602). Toulouse: Edouard Privat. · JFM 48.0046.06 |
| [48] | Guillaume, E. (1922). Un résultat des discussions de la théorie de la relativité d’Einstein au Collège de France. \(Revue générale des sciences pures et appliquées, 33\), 322-324. |
| [49] | Heilbron, J. L. (1963). \(Interview with Dr. Ebenezer Cunningham\). http://www.aip.org/history/catalog/icos/4565.html |
| [50] | Heilbron, J. L. (1986). \(The dilemmas of an upright man: Max Planck as spokesman for German science\). Berkeley: University of California Press. |
| [51] | Hirosige, T. (1968). Theory of relativity and the ether. \(Japanese Studies in the History of Science, 7\), 37-53. |
| [52] | Holton, G. (1965). The metaphor of space-time events in science. \(Eranos Jahrbuch, 34\), 33-78. |
| [53] | Hunt, B. J. (1986). Experimenting on the ether: Oliver J. Lodge and the great whirling machine. \(Historical Studies in the Physical Sciences, 16\), 111-134. · doi:10.2307/27757559 |
| [54] | Hunt, B. J. (1988). The origins of the FitzGerald contraction. \(British Journal for the History of Science, 21\)(1), 67-76. · doi:10.1017/S0007087400024389 |
| [55] | Jammer, M. (1979). Some foundational problems in the special theory of relativity. In G. Toraldo di Francia (Ed.), \(Problems in the foundations of physics\). \(Proceedings of the international school of physics ``Enrico Fermi”\) (Vol. 72, pp. 202-236). Amsterdam: North-Holland. · Zbl 0446.70003 |
| [56] | Janssen, M., & Mecklenburg, M. (2006). From classical to relativistic mechanics: Electromagnetic models of the electron. In V.F. Hendricks, K.F. Jørgenson, J. Lützen, & S.A. Pedersen (Eds.), \(Interactions: Mathematics, physics and philosophy, 1860-1930\) (pp. 65-134). Dordrecht: Springer. · doi:10.1007/978-1-4020-5195-1_3 |
| [57] | Jungnickel, C., & McCormmach, R. (1986). \(Intellectual mastery of nature: Theoretical physics from Ohm to Einstein\). Chicago: University of Chicago Press. · Zbl 1181.01032 |
| [58] | Kastrup, H. A. (2008). On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics. \(Annalen der Physik, 17\)(9), 691-704. · Zbl 1152.81300 |
| [59] | Kennedy, W. L. (2005). On Einstein’s 1905 electrodynamics paper. \(Studies in History and Philosophy of Modern Physics, 36\)(1), 61-65. · Zbl 1222.83019 · doi:10.1016/j.shpsb.2004.06.002 |
| [60] | Klein, M. J., Kox, A. J., & Schulmann, R. (Eds.). (1993). \(The collected papers of Albert Einstein, volume 5, the Swiss years: Correspondence, 1902-1914\). Princeton: Princeton University Press. · Zbl 0795.01035 |
| [61] | Kormos Buchwald, D., Sauer, T., Rosenkranz, Z., Illy, J., & Holmes, V. I. (Eds.). (2006). \(The collected papers of Albert Einstein, volume 10, the Berlin years: Correspondence, May-December 1920\). Princeton: Princeton University Press. · Zbl 1161.01022 |
| [62] | Kox, A. J. (Ed). (2008). \(The scientific correspondence of H.A. Lorentz\) (Vol. 1). Berlin: Springer. · Zbl 1161.01023 |
| [63] | Langevin, P. (1905). Sur l’origine des radiations et l’inertie électromagnétique. \(Journal de physique théorique et appliquée, 4\), 165-183. · JFM 36.0916.01 · doi:10.1051/jphystap:019050040016500 |
| [64] | Langevin, P. (1906). The relations of the physics of electrons to the other branches of science. In H. J. Rogers (Ed.), \(Congress of arts and science, universal exposition, St. Louis, 1904, volume 4: Physics, chemistry, astronomy, sciences of the Earth\), pages 121-156. Houghton, Mifflin & Co., Boston. |
| [65] | Larmor, J. (1900). \(Æther and matter\). Cambridge: Cambridge University Press. · JFM 31.0759.01 |
| [66] | Larmor, J. (1938). Alfred Arthur Robb 1873-1936. \(Obituary Notices of Fellows of the Royal Society, 2\), 315-321. · doi:10.1098/rsbm.1938.0013 |
| [67] | Laue, M. (1903). \(Über die Interferenzerscheinungen an planparallelen Platten\). PhD thesis, University of Berlin, Berlin. · JFM 35.0842.01 |
| [68] | Laue, M. (1907). Die Mitführung des Lichtes durch bewegte Körper nach dem Relativitätsprinzip. \(Annalen der Physik, 328\), 989-990. · JFM 38.0834.02 · doi:10.1002/andp.19073281015 |
| [69] | Laue, M. (1908). Die Wellenstrahlung einer bewegten Punktladung nach dem Relativitätsprinzip. \(Berichte der Deutschen Physikalischen Gesellschaft, 10\), 838-844. · JFM 39.0909.01 |
| [70] | Laue, M. (1911a). \(Das Relativitätsprinzip\). Braunschweig: Vieweg. |
| [71] | Laue, M. (1911b). Zur Dynamik der Relativitätstheorie. \(Annalen der Physik, 340\), 524-542. · JFM 42.0725.02 · doi:10.1002/andp.19113400808 |
| [72] | Laue, M. (1912). Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung. \(Physikalische Zeitschrift, 13\), 118-120. · JFM 43.0779.02 |
| [73] | Lémeray, M. (1912). Sur un théorème de M. Einstein. \(Comptes rendus hebdomadaires de l’Académie des sciences de Paris, 155\), 1224-1227. · JFM 43.0961.03 |
| [74] | Lie, S., & Scheffers, G. (1893). \(Vorlesungen über continuierliche Gruppen mit geometrischen und anderen Anwendungen\). Leipzig: Teubner. · JFM 25.0623.02 |
| [75] | Liénard, A. (1898). Champ électrique et magnétique produit par une charge concentrée en un point et animée d’un mouvement quelconque. \(Éclairage électrique, 16\), 5-14, 53-59, 106-112. |
| [76] | Lorentz, H. A. (1897). Ueber den Einfluss magnetischer Kräfte auf die Emission des Lichtes. \(Annalen der Physik, 299\), 278-284. · JFM 28.0791.03 · doi:10.1002/andp.18972991341 |
| [77] | Lorentz, H. A. (1904). Electromagnetic phenomena in a system moving with any velocity less than that of light. \(Proceedings of the Section of Sciences, Koninklijke Akademie van Wetenschappen te Amsterdam, 6\), 809-831. |
| [78] | Lorentz, H. A. (1909). \(The theory of electrons and its application to the phenomena of light and radiant heat\). New York: Columbia University Press. · JFM 40.0922.01 |
| [79] | Lorentz, H. A. (1916). \(The theory of electrons and its application to the phenomena of light and radiant heat\) (2nd ed.). Leipzig: Teubner. · JFM 46.1359.01 |
| [80] | Lorenz, L. V. (1867). On the identity of the vibrations of light with electrical currents. \(Philosophical Magazine, 34\)(230), 287-301. |
| [81] | Maltese, G., & Orlando, L. (1995). The definition of rigidity in the special theory of relativity and the genesis of the general theory of relativity. \(Studies in History and Philosophy of Modern Physics, 26\)(3), 263-306. · Zbl 1222.83011 · doi:10.1016/1355-2198(95)00017-8 |
| [82] | Manegold, K.-H. (1970). \(Universität, Technische Hochschule und Industrie\). Berlin: Duncker & Humblot. |
| [83] | Martínez, A. A. (2009). \(Kinematics: The lost origins of Einstein’s relativity\). Baltimore: Johns Hopkins University Press. · Zbl 1179.83002 |
| [84] | McCrea, W. H. (1978). Ebenezer Cunningham. \(Bulletin of the London Mathematical Society, 10\)(1), 116-126. · Zbl 0373.01010 · doi:10.1112/blms/10.1.116 |
| [85] | Miller, A. I. (1973). A study of Henri Poincaré’s ‘Sur la dynamique de l’électron’. \(Archive for History of Exact Sciences, 10\), 207-328. · doi:10.1007/BF00412332 |
| [86] | Miller, A. I. (1976). On Einstein, light quanta, radiation and relativity in 1905. \(American Journal of Physics, 44\)(10), 912-923. · doi:10.1119/1.10229 |
| [87] | Miller, A. I. (1981). \(Albert Einstein’s special theory of relativity: Emergence (1905) and early interpretation\). Reading, MA: Addison-Wesley. |
| [88] | Minkowski, H. (1908). Die Grundgleichungen für die electromagnetischen Vorgänge in bewegten Körpern. \(Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 1908\), 53-111. · JFM 39.0909.02 |
| [89] | Minkowski, H. (1909). Raum und Zeit. \(Jahresbericht der deutschen Mathematiker-Vereinigung, 18\), 75-88. · JFM 40.0094.01 |
| [90] | Minkowski, H. (1915). Das Relativitätsprinzip. \(Jahresbericht der deutschen Mathematiker-Vereinigung, 24\), 372-382. · JFM 46.1283.05 |
| [91] | Neumann, C. G. (1870). \(Ueber die Principien der Galilei-Newton’schen Theorie\). Leipzig: Teubner. · JFM 02.0039.03 |
| [92] | Newman, E. T., & Price, R. H. (2010). The Lorentz transformation: Simplification through complexification. \(American Journal of Physics, 78\)(1), 14-19. · doi:10.1119/1.3216468 |
| [93] | Norton, J. D. (1992). Einstein, Nordström and the early demise of Lorentz-covariant theories of gravitation. \(Archive for History of Exact Sciences, 45\), 17-94. · Zbl 0768.01011 · doi:10.1007/BF00375886 |
| [94] | Penrose, R. (1959). The apparent shape of a relativistically moving sphere. \(Proceedings of the Cambridge Philosophical Society, 55\), 137-139. · doi:10.1017/S0305004100033776 |
| [95] | Planck, M. (1907). Zur Dynamik bewegter Systeme. \(Sitzungsberichte der königliche preußischen Akademie der Wissenschaften, 29\), 542-570. · JFM 38.0718.03 |
| [96] | Planck, M. (1910). \(Acht Vorlesungen über theoretische Physik\). Leipzig: Hirzel. · JFM 41.0868.01 |
| [97] | Poincaré, H. (1891). Sur la théorie des oscillations hertziennes. \(Comptes rendus hebdomadaires de l’Académie des sciences de Paris, 113\), 515-519. · JFM 23.1149.03 |
| [98] | Poincaré, H. (1901). \(Électricité et optique: la lumière et les théories électrodynamiques\). Paris: Carré et Naud. |
| [99] | Poincaré, H. (1904). L’état actuel et l’avenir de la physique mathématique. \(Bulletin des sciences mathématiques, 28\), 302-324. · JFM 35.0068.03 |
| [100] | Poincaré, H. (1905a). \(Science and hypothesis\). London: Walter Scott. |
| [101] | Poincaré, H. (1905b). Sur la dynamique de l’électron. \(Comptes rendus hebdomadaires de l’Académie des sciences de Paris, 140\), 1504-1508. · JFM 36.0911.02 |
| [102] | Poincaré, H. (1906). Sur la dynamique de l’électron. \(Rendiconti del circolo matematico di Palermo, 21\), 129-176. · JFM 37.0886.01 · doi:10.1007/BF03013466 |
| [103] | Poincaré, H. (1907). La relativité de l’espace. \(Année psychologique, 13\), 1-17. · doi:10.3406/psy.1906.1285 |
| [104] | Poincaré, H. (1908a). La dynamique de l’électron. \(Revue générale des sciences pures et appliquées, 19\), 386-402. · JFM 39.0911.08 |
| [105] | Poincaré, H. (1908b). \(Science et méthode\). Paris: Flammarion. |
| [106] | Poincaré, H. (1909). La mécanique nouvelle. \(Revue scientifique, 12\), 170-177. · JFM 40.1017.01 |
| [107] | Poincaré, H. (1913). \(La dynamique de l’électron\). Paris: Dumas. · JFM 44.1028.07 |
| [108] | Poincaré, H. (1953). Les limites de la loi de Newton. \(Bulletin astronomique, 17\)(3), 21-269. |
| [109] | Pyenson, L. (1979). Physics in the shadow of mathematics: The Göttingen electron-theory seminar of 1905. \(Archive for History of Exact Sciences, 21\)(1), 55-89. · Zbl 0417.01006 · doi:10.1007/BF00327873 |
| [110] | Renn, J. (2007). The third way to general relativity. In J. Renn (Ed.), \(The genesis of general relativity, volume 3, gravitation in the twilight of classical physics: Between mechanics, field theory, and astronomy\). \(The genesis of general relativity\) (pages 21-75). Berlin: Springer. |
| [111] | Reynolds, W. F. (1993). Hyperbolic geometry on a hyperboloid. \(American Mathematical Monthly, 100\), 442-455. · Zbl 0789.51020 · doi:10.1080/00029890.1993.11990430 |
| [112] | Ribaucour, A. (1870). Sur la déformation des surfaces. \(Comptes rendus hebdomadaires de l’Académie des sciences de Paris, 70\), 330-333. · JFM 02.0630.01 |
| [113] | Robb, A. A. (1904). \(Beiträge zur Theorie des Zeemaneffektes\). PhD thesis, Georg-Augusta Universität Göttingen, Leipzig. · JFM 35.0900.01 · doi:10.1002/andp.19043201106 |
| [114] | Robb, A. A. (1911). \(Optical geometry of motion: A new view of the theory of relativity\). Cambridge: W. Heffer and Sons. · JFM 43.0559.02 |
| [115] | Rohrlich, F. (2007). \(Classical charged particles\) (3rd ed.). Singapore: World Scientific. · Zbl 1187.78001 · doi:10.1142/6220 |
| [116] | Rosser, W. G. V. (1967). \(Introductory relativity\). London: Butterworth. |
| [117] | Rowe, D. E. (1989). Klein, Hilbert, and the Göttingen mathematical tradition. In K. M. Olesko (Ed.), \(Science in Germany\). \(Osiris\) (Vol. 5, pp. 186-213). Philadelphia: History of Science Society. · Zbl 0894.01003 · doi:10.1086/368687 |
| [118] | Rowe, D. E. (1999). The Göttingen response to general relativity and Emmy Noether’s theorems. In J. Gray (Ed.), \(The symbolic universe: Geometry and physics, 1890-1930\) (pp. 189-233). Oxford: Oxford University Press. · Zbl 1059.01511 |
| [119] | Rowe, D. E. (2008). Max von Laue’s role in the relativity revolution. \(Mathematical Intelligencer, 30\)(3), 54-60. · Zbl 1200.01024 · doi:10.1007/BF02985380 |
| [120] | Rowe, D. E. (2009). A look back at Hermann Minkowski’s Cologne lecture ‘Raum und Zeit’. \(Mathematical Intelligencer, 31\)(2), 27-39. · Zbl 1172.01010 · doi:10.1007/s00283-009-9027-0 |
| [121] | Sánchez-Ron, J. M. (1987). The reception of special relativity in Great Britain. In T. F. Glick (Ed.), \(The comparative reception of relativity\). \(Boston studies in the philosophy of science\) (pp. 27-58). Dordrecht: Reidel. · doi:10.1007/978-94-009-3875-5_2 |
| [122] | Searle, G. F. C. (1897). On the steady motion of an electrified ellipsoid. \(Philosophical Magazine, 44\), 329-341. · JFM 28.0784.01 |
| [123] | Seelig, C. (1960). \(Albert Einstein: Leben und Werk eines Genies unserer Zeit\). Zürich: Europa Verlag. |
| [124] | Silberstein, L. (1914). \(The theory of relativity\). London: Macmillan. · JFM 45.1150.07 |
| [125] | Sommerfeld, A. (1913). Anmerkungen zu Minkowski, Raum und Zeit. In O. Blumenthal (Ed.), \(Das Relativitätsprinzip; Eine Sammlung von Abhandlungen\) (pp. 69-73). Leipzig: Teubner. |
| [126] | Sommerfeld, A. (1919). \(Atombau und Spektrallinien\). Braunschweig: Vieweg. · JFM 55.1173.02 |
| [127] | Sommerfeld, A. (1948). \(Vorlesungen über theoretische Physik, Bd. 3: Elektrodynamik\). Wiesbaden: Dieterich. · Zbl 0035.12401 |
| [128] | Stachel, J., Cassidy, D. C., Renn, J., & Schulmann, R. (Eds.). (1989). \(The collected papers of Albert Einstein, volume 2, the Swiss years: Writings, 1900-1909\). Princeton: Princeton University Press. |
| [129] | Staley, R. (1998). On the histories of relativity: The propagation and elaboration of relativity theory in participant histories in Germany, 1905-1911. \(Isis, 89\)(2), 263-299. · Zbl 1135.01310 · doi:10.1086/384001 |
| [130] | Sternberg, S. (1986). Imagery in scientific thought by Arthur I. Miller. \(Mathematical Intelligencer, 8\)(2), 65-74. |
| [131] | Tanner, J. R. (Ed.). (1917). \(The historical register of the University of Cambridge, being a supplement to the calendar with a record of university offices, honours and distinctions to the year 1910\). Cambridge: Cambridge University Press. |
| [132] | Thomson, J. J. (1893). \(Notes on recent researches in electricity and magnetism: Intended as a sequel to Professor Clerk-Maxwell’s treatise on electricity and magnetism\). Oxford: Clarendon. · JFM 25.1775.07 |
| [133] | Timerding, H. E. (1912). Über ein einfaches geometrisches Bild der Raumzeitwelt Minkowskis. \(Jahresbericht der deutschen Mathematiker-Vereinigung, 21\), 274-285. · JFM 43.0779.01 |
| [134] | Timerding, H. E. (1915). Über die Raumzeitvektoren und ihre geometrische Behandlung. In K. Bergwitz (Ed.), \(Festschrift Julius Elster und Hans Geistel zum sechzigsten Geburtstage: Arbeiten aus den Gebieten der Physik, Mathematik, Chemie\) (pp. 514-520). Braunschweig: Vieweg. · JFM 45.1145.02 |
| [135] | Tolman, R. C. (1910). The second postulate of relativity. \(Physical Review 31\), 26-40. |
| [136] | Tolman, R. C. (1914). The principle of similitude. \(Physical Review, 3\), 244-255. · JFM 45.0948.03 · doi:10.1103/PhysRev.3.244 |
| [137] | Torretti, R. (1996). \(Relativity and geometry\) (2nd ed.). New York: Dover Publications. · Zbl 0515.53001 |
| [138] | von Ignatowsky, W. S. (1909). \(Die Vektoranalysis und Anwendung in der theoretischen Physik\). Leipzig: Teubner. · JFM 40.0138.01 |
| [139] | von Ignatowsky, W. S. (1910). Einige allgemeine Bemerkungen zum Relativitätsprinzip. \(Berichte der Deutschen Physikalischen Gesellschaft, 12\)(20), 788-796. |
| [140] | von Laue, M. (1913a). Das Relativitätsprinzip. \(Jahrbücher der Philosophie, 1\), 99-128. |
| [141] | von Laue, M. (1913b). \(Das Relativitätsprinzip\) (2nd ed.). Braunschweig: Vieweg. · JFM 44.0772.02 |
| [142] | von Laue, M. (1947). \(Geschichte der Physik\). Bonn: Universitäts-Verlag. · Zbl 0030.17903 |
| [143] | von Laue, M. (1952). Mein physikalischer Werdegang; eine Selbstdarstellung. In H. Hartmann (Ed.), \(Schöpfer des neuen Weltbildes: Große Physiker unserer Zeit\) (pp. 178-207). Bonn: Athenäum-Verlag. |
| [144] | von Laue, M. (1955). \(Die Relativitätstheorie: die spezielle Relativitätstheorie\) (6th ed.). Braunschweig: Vieweg. · Zbl 0068.21601 |
| [145] | von Laue, M. (1961). \(Aufsätze und Vorträge\). Braunschweig: Vieweg. · Zbl 0094.36502 |
| [146] | Walter, S. A. (1999a). Minkowski, mathematicians, and the mathematical theory of relativity. In H. Goenner, J. Renn, T. Sauer, & J. Ritter (Eds.), \(The expanding worlds of general relativity\), \(Einstein studies\) (Vol. 7, pp. 45-86). Boston: Birkhäuser. · Zbl 0943.83005 · doi:10.1007/978-1-4612-0639-2_2 |
| [147] | Walter, S. A. (1999b). The non-Euclidean style of Minkowskian relativity. In J. Gray (Ed.), \(The symbolic universe: Geometry and physics, 1890-1930\) (pp. 91-127). Oxford: Oxford University Press. · Zbl 1059.01513 |
| [148] | Walter, S. A. (2007). Breaking in the 4-vectors: The four-dimensional movement in gravitation, 1905-1910. In J. Renn & M. Schemmel (Eds.), \(The genesis of general relativity, volume 3: Theories of gravitation in the twilight of classical physics\) (pp. 193-252). Berlin: Springer. |
| [149] | Walter, S. A. (2008). Hermann Minkowski’s approach to physics. \(Mathematische Semesterberichte, 55\)(2), 213-235. · Zbl 1168.01009 · doi:10.1007/s00591-008-0044-4 |
| [150] | Walter, S. A. (2009). Hypothesis and convention in Poincaré’s defense of Galilei spacetime. In M. Heidelberger & G. Schiemann (Eds.), \(The significance of the hypothetical in the natural sciences\) (pp. 193-219). Berlin: Walter de Gruyter. |
| [151] | Walter, S. A. (2010). Minkowski’s modern world. In V. Petkov (Ed.), \(Minkowski spacetime: A hundred years later\). \(Fundamental theories of physics\) (Vol. 165, pp. 43-61). Berlin: Springer. · Zbl 1208.83016 |
| [152] | Walter, S. A. (2011). Henri Poincaré, theoretical physics and relativity theory in Paris. In K.-H. Schlote & M. Schneider (Eds.), \(Mathematics meets physics: A contribution to their interaction in the 19th and the first half of the 20th century\) (pp. 213-239). Frankfurt am Main: Harri Deutsch. |
| [153] | Walter, S. A. (2014). Poincaré on clocks in motion. \(Studies in History and Philosophy of Modern Physics, 47\)(1), 131-141. · Zbl 1294.83002 · doi:10.1016/j.shpsb.2014.01.003 |
| [154] | Walter, S. A. (2017). Henri Poincaré’s life, science, and life in science. \(Historia Mathematica, 44\)(4), 425-435. · Zbl 1378.00086 · doi:10.1016/j.hm.2017.05.001 |
| [155] | Walter, S. A. (2018). Poincaré-week in Göttingen, in light of the Hilbert-Poincaré correspondence of 1908-1909. In M. T. Borgato, E. Neuenschwander & I. Passeron (Eds.), Mathematical correspondences and critical editions (pp. 189-202). Basel: Birkhäuser. |
| [156] | Walter, S. A., Bolmont, E., & Coret, A. (Eds.). (2007b). \(La correspondance d’Henri Poincaré, volume 2: La correspondance entre Henri Poincaré et les physiciens, chimistes et ingénieurs\). Basel: Birkhäuser. · Zbl 1196.01030 |
| [157] | Walter, S. A., Nabonnand, P., & Rollet, L. (Eds.). (2016). \(Henri Poincaré papers\). http://henripoincarepapers.univ-nantes.fr. |
| [158] | Warwick, A. C. (2003). \(Masters of theory: Cambridge and the rise of mathematical physics\). Chicago: University of Chicago. · Zbl 1127.01001 · doi:10.7208/chicago/9780226873763.001.0001 |
| [159] | Weyl, H. (1922). Das Raumproblem. \(Jahresbericht der deutschen Mathematiker-Vereinigung, 31\), 205-221. |
| [160] | Whittaker, E. T. (1951). \(A history of the theories of aether and electricity\). London: T. Nelson. · Zbl 0043.24503 |
| [161] | Wiechert, E. (1900). Elektrodynamische Elementargesetze. In J. Bosscha (Ed.), \(Recueil de travaux offerts par les auteurs à H. A. Lorentz\). \(Archives néerlandaises des sciences exactes et naturelles\) (Vol. 5, pp. 549-573). The Hague: Nijhoff. · JFM 31.0826.01 |
| [162] | Wiechert, E. (1911). Relativitätsprinzip und Äther. \(Physikalische Zeitschrift, 12\), 689-707, 737-758. · JFM 42.0733.01 |
| [163] | Williamson, R. B. (1977). Logical economy in Einstein’s ‘on the electrodynamics of moving bodies’. \(Studies in History and Philosophy of Science, 8\)(1), 46-60. · doi:10.1016/0039-3681(77)90018-8 |
| [164] | Wright, S. P. (1975). \(Henri Poincaré: A developmental study of his philosophical and scientific thought\). PhD thesis, Harvard University, Cambridge, MA. |
| [165] | Zahar, E. · Zbl 1222.00019 · doi:10.1016/S1355-2198(96)00027-5 |
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