International audienceHermann Minkowski's spacetime theory scandalized physicists, in part because of its challenge to received notions of the geometric nature of physical space and time.La théorie de l'espace-temps de Hermann Minkowski a scandalisait les physiciens à cause de sa mise en cause des idées reçues de la nature géométrique de l'espace et du temps

Walter, Scott,

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Hermann Minkowski and the scandal of spacetimeScott WalterTo cite this version:Scott Walter. Hermann Minkowski and the scandal of spacetime. ESI News, 2008, 3 (1), pp.6-8.<halshs-00319209>HAL Id: halshs-00319209https://halshs.archives-ouvertes.fr/halshs-00319209Submitted on 6 Sep 2008HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike 4.0 InternationalLicenseHermann Minkowski and the Scandal of SpacetimeScott Walter (walter [at] univ-nancy2.fr)Preprint of an article published in ESI News (3(1), Spring 2008, pp. 6–8When Hermann Minkowski’s first paper on relativity theory [8] appeared inApril 1908, it was met with an immediate, largely critical response. His paperpurported to extend the reach of the principle of relativity to the electrody-namics of moving media, but one of the founders of relativity theory, the youngAlbert Einstein, along with his co-author Jakob Laub, found Minkowski’s theoryto be wanting on physical and formal grounds alike. The lesson in physics de-livered by his two former students did not merit a rejoinder, but their summarydismissal of his sophisticated four-dimensional formalism for physics appears tohave given Minkowski pause.The necessity of such a formalism for physics was stressed by Minkowskiin a lecture entitled “Raum und Zeit,” delivered at the annual meeting of theGerman Association for Natural Scientists and Physicians in Cologne, on 21September 1908. Minkowski argued famously in Cologne that certain circum-stances required scientists to discard the view of physical space as a Euclideanthree-space, in favor of a four-dimensional world with a geometry character-ized by the invariance of a certain quadratic form. Delivered in grand style,Minkowski’s lecture appears to have struck a chord, generating a reaction thatwas phenomenal in terms of sheer publication numbers and disciplinary breadth.Historians have naturally sought to explain this burst of interest in relativ-ity theory. According to one current of thought, Minkowski added nothing ofsubstance to Einstein’s theory of relativity, but expressed relativist ideas moreforcefully and memorably than Einstein [4, 3]. It has also been suggested thatMinkowski supplied a mathematical imprimatur to relativity theory, therebyreassuring those who had doubted its internal coherence [5]. A third expla-nation claims that Minkowski’s explicit appeal to “pre-established harmony”between pure mathematics and physics resonated with Wilhelmine scientistsand philosophers, just when such Leibnizian ideas were undergoing a revival inphilosophical circles [9].The lack of historical consensus on the reasons for the sharp post-1908 up-swing in the fortunes of special relativity reflects, to a certain extent, the varied,conflicting accounts provided by the historical actors themselves [12]. A focuson the disciplinary reception of Minkowski’s theory, however, shows a commonconcern over the adequacy of Euclidean geometry for the foundations of physics.Much of the excitement generated by Minkowski’s Cologne lecture among scien-tists and philosophers arose from an idea that was scandalous when announcedon September 21, 1908, but which was soon assimilated, first by theorists andthen by the scientific community at large: Euclidean geometry was no longeradequate to the task of describing physical reality, and had to be replaced bythe geometry of a four-dimensional space Minkowski named the “world” (Welt).The scandalous nature of spacetime is brought into focus first by examiningthe situation of physical geometry at the time of Minkowski’s first lecture onrelativity in 1907, and then by following the evolution of his definition of the“world” in his writings on relativity. For the sake of concision, these prelimi-nary observations are omitted here, in favor of a few examples of the reactionsustained by Minkowski’s radical worldview on the part of a few of his mostcapable readers in physics. (For an expanded version of this narrative see [16].)1The published version of “Raum und Zeit” sparked an explosion of pub-lications in relativity theory, with the number of papers on relativity triplingbetween 1908 (32 papers) and 1910 (95 papers) [14]. This sudden upswing inthe interest is clearly a complex historical phenomenon requiring careful study,for the theory of relativity carried different meaning for different observers [2].While Minkowski’s spacetime theory is conceptually and formally distinct fromEinstein’s special relativity theory and the Lorentz-Poincare´ relativity theory,the history of its reception is similarly polysemous. For example, a disciplinaryanalysis of the reception of Minkowski’s Cologne lecture reveals a overwhelm-ingly positive response on the part of mathematicians, and a decidedly mixedreaction on the part of physicists [14]. A close examination of the physicists’response to Minkowski’s lecture shows that what they objected to above all inMinkowski’s view was the idea that Euclidean space was no longer adequate forunderstanding physical phenomena. The range of response among physicists toMinkowski’s attack on Euclidean space, we will see here, went fairly smoothlyfrom cognitive shock and outright denial, on one end, to unreserved enthusiasmand collaborative extension on the other end.Among the physicists shocked by Minkowski’s spacetime theory was Danzig’sMax Wien, an experimental physicist. In a letter to the Munich theoreti-cal physicist Arnold Sommerfeld, Max Wien described his experience readingMinkowski’s Cologne lecture as provoking “a slight brain-shiver, now space andtime appear conglomerated together in a gray, miserable chaos” [1, p. 71]. Hiscousin Willy Wien, director of the Wu¨rzburg Physical Institute and co-editor ofAnnalen der Physik, was shocked, too, but it wasn’t the loss of Euclidean spacethat bothered him so much as Minkowski’s claim that circumstances forcedspacetime geometry on physicists. The entire Minkowskian system, Wien saidin a 1909 lecture, “evokes the conviction that the facts would have to join it asa fully internal consequence.” Wien would have none of this, as he felt that thetouchstone of physics was experiment, not abstract mathematical deduction.“For the physicist,” Wien concluded his lecture, “Nature alone must make thefinal decision” [15].On the opposite end of the spectrum of response to Minkowski’s attack onEuclidean space, Max Born and Arnold Sommerfeld saw in Minkowski space-time the future of theoretical physics. Both men had close ties to Minkowski,and upon the latter’s untimely death on 12 January 1909, each took up thecause of promoting a spacetime approach to physics. In a crucial contributionto Minkowski’s program, Sommerfeld transformed Minkowski’s unorthodox ma-trix calculus into a four-dimensional vector algebra and analysis [10, 11], basedon the notational conventions he had introduced in 1904 as editor of the physicsvolumes of Felix Klein’s monumental Encyclopedia of Mathematical Sciences In-cluding Applications. Sommerfeld’s streamlined spacetime formalism was takenover and extended by Max Laue, then working in Sommerfeld’s institute inMunich, for use in the first German textbook on relativity theory [6]. Laue’stextbook was hugely successful, and effectively established the Sommerfeld-Laueformalism as the standard for research in relativity physics.Sommerfeld insisted upon the simplification afforded to calculation by theadoption of a spacetime approach, and left aside Minkowski’s philosophical in-terpretation of spacetime, with one exception. In the introduction to his 1910reformulation of Minkowski’s matrix calculus, Sommerfeld echoed Minkowski’sbelief that absolute space should vanish from physics, to be replaced by the2“absolute world” of Minkowski spacetime [10, p. 749]. This exchange of abso-lutes, Euclidean 3-space for Minkowski spacetime, was clearly designed to calmphysicists shocked by Minkowski’s high-handed dismissal of Euclidean space asthe frame adequate for understanding physical phenomena.Between the extremes represented by the responses of Max Wien and ArnoldSommerfeld emerged the mainstream response to Minkowski’s interpretation.The latter is well represented by remarks expressed by Max Laue in his influ-ential relativity textbook, mentioned above. Laue considered Minkowski space-time as an “almost indispensable resource” for precise mathematical operationsin relativity [6, p. 46]. He expressed reservations, however, about Minkowski’sphilosophy, in that the geometrical interpretation (or “analogy”) of the Lorentztransformation called upon a space of four dimensions. One could avail oneselfof the new four-dimensional formalism, Laue assured his readers, even if onewas not blessed with Minkowski’s spacetime-intuition, and without committingoneself to the existence of Minkowski’s four-dimensional world.By disengaging Minkowski’s spacetime ontology from the Sommerfeld-Lauespacetime calculus, Laue cleared the way for the acceptance by physicists of histensor calculus, and of spacetime geometry in general. A detailed study of thereception of Minkowski’s ideas on relativity has yet to be realized, but anecdotalevidence points to a change in attitudes toward Minkowski’s spacetime view inthe 1950s. For example, in the sixth edition of Laue’s textbook, celebrating thefiftieth anniversary of relativity theory, and marking the end of Einstein’s life, itsauthor still felt the need to warn physicists away from Minkowski’s scandalousclaim in Cologne that space and time form a unity. As if in defiance of Laue,this particular view of Minkowski’s (“Von Stund’ an . . . ”) was soon cited (inthe original German) on the title page of a rival textbook on special relativity[13]. In Laue’s opinion, however, Minkowski’s most famous phrase remained an“exaggeration” [7, p. 60].Minkowski’s carefully-crafted Cologne lecture shocked scientists’ sensibili-ties, in sharp contrast to all previous writings on relativity, including his own.The author of “Raum and Zeit” famously characterized his intuitions (Anschau-ungen) of space and time as grounded in experimental physics, and radical innature. Predictably, his lecture created a scandal for physicists in its day, butunlike most scandals, it did not fade away with the next provocation. Instead,Minkowski focused attention on how mathematics structures our understandingof the physical universe, in a way no other writer had done since Riemann, orhas managed to do since, paving the way for acceptance of even more visually-unintuitive theories to come in the early twentieth century, including generalrelativity and quantum mechanics. Minkowski’s provocation of physicists inCologne, his rejection of existing referents of time, space, and geometry, andhis appeal to subjective intuition to describe external reality may certainly bedetached from Minkowski geometry, as Laue and others wished, but not if wewant to understand the explosion of interest in relativity theory in 1909.References[1] Ulrich Benz. Arnold Sommerfeld: Lehrer und Forscher an der Schwelle zumAtomzeitalter, 1868–1951. Wissenschaftliche Verlagsgesellschaft, Stuttgart,1975.3[2] Klaus Hentschel. Interpretationen und Fehlinterpretationen der speziellenund der allgemeinen Relativita¨tstheorie durch Zeitgenossen Albert Ein-steins. Birkha¨user, Basel, 1990.[3] Tetu Hirosige. Theory of relativity and the ether. Japanese Studies in theHistory of Science, 7:37–53, 1968.[4] Gerald Holton. The metaphor of space-time events in science. EranosJahrbuch, 34:33–78, 1965.[5] Jo´zsef Illy. Revolutions in a revolution. Studies in History and Philosophyof Science, 12:173–210, 1981.[6] Max von Laue. Das Relativita¨tsprinzip. Vieweg, Braunschweig, 1911.[7] Max von Laue. Die Relativita¨tstheorie: die spezielle Relativita¨tstheorie.Vieweg, Braunschweig, 6th edition, 1955.[8] Hermann Minkowski. Die Grundgleichungen fu¨r die electromagnetis-chen Vorga¨nge in bewegten Ko¨rpern. Nachrichten von der Ko¨niglichenGesellschaft der Wissenschaften zu Go¨ttingen, pages 53–111, 1908.[9] Lewis Pyenson. The Young Einstein: The Advent of Relativity. AdamHilger, Bristol, 1985.[10] Arnold Sommerfeld. Zur Relativita¨tstheorie, I: Vierdimensionale Vektoral-gebra. Annalen der Physik, 32:749–776, 1910.[11] Arnold Sommerfeld. Zur Relativita¨tstheorie, II: Vierdimensionale Vektor-analysis. Annalen der Physik, 33:649–689, 1910.[12] Richard Staley. On the histories of relativity: propagation and elaborationof relativity theory in participant histories in Germany, 1905–1911. Isis,89:263–299, 1998.[13] John Lighton Synge. Relativity: The Special Theory. North-Holland, Am-sterdam, 1956.[14] Scott Walter. Minkowski, mathematicians, and the mathematical theoryof relativity. In Hubert Goenner, Ju¨rgen Renn, Tilman Sauer, and JimRitter, editors, The Expanding Worlds of General Relativity, volume 7 ofEinstein Studies, pages 45–86. Birkha¨user, Boston/Basel, 1999.[15] Scott Walter. The non-Euclidean style of Minkowskian relativity. In JeremyGray, editor, The Symbolic Universe: Geometry and Physics, 1890–1930,pages 91–127. Oxford University Press, Oxford, 1999.[16] Scott Walter. Minkowski’s modern world. In Vesselin Petkov, editor,Minkowski Spacetime: A Hundred Years Later. Springer, Berlin, in press.4

Hermann Minkowski and the scandal of spacetime

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Hermann Minkowski and the scandal of spacetime

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