Leipzig: F.W. Vogel, 1909.
First edition of Minkowski’s famous lecture on his theory of four-dimensional space-time, the first published account of this theory to be illustrated with ‘spacetime diagrams’, which were widely used later by Stephen Hawking, Roger Penrose and others in the development of general relativity. “In ‘Space and Time’, read by Minkowski in Cologne only a few months before his death, he introduced the notion that made possible the expansion of the relativity theory of Einstein from its specific (1905) to its general form (1916). Minkowski’s space-time hypothesis was in effect a restatement of Einstein’s basic principle in a form that greatly enhanced its plausibility and also introduced important new developments. Hitherto natural phenomena had been thought to occur in a space of three dimensions and to flow uniformly through time. Minkowski maintained that the separation of time and space is a false conception; that time itself is a dimension, comparable to length, breadth, and height; and that therefore the true conception of reality was constituted by a space-time continuum possessing these four dimensions” (Printing and the Mind of Man). “The laws of physics were written in the language of the geometry of this four dimensional space ... Physics had become geometry, and it was a stunning achievement” (Gerber, pp. 358-9). “‘Raum und Zeit’ was originally published in Vol. II (1909) of the Verhandlungen of the Deutscher Naturforscher und Aertze [offered here]; it was later reprinted in the Jahresbericht der Deutschen Mathematiker Vereinigung” (Norman). It is most commonly encountered in the separate (and later) printing from the Jahresbericht published as a tribute after Minkowski’s sudden and tragic death. An outstanding copy of the first printing of this landmark lecture, rare in the original printed wrappers.
Barchas 1440 (Verhandlungen journal issue); Honeyman 2231 & Norman 1514 (both listing separate printing from Jahresbericht); PMM 401 (Jahresbericht journal issue). Einstein, ‘Autobiographical notes,’ in Albert Einstein: Philosopher-Scientist. Paul A. Schilpp ed. (1969), pp. 1-94. Gerber, The Language of Physics: The Calculus and the Development of Theoretical Physics in Europe, 1750-1914, 1988; Gray, The Symbolic Universe: Geometry and Physics 1890-1930, 1999; Petkov, Space, Time, and Spacetime. Physical and Philosophical Implications of Minkowski’s Unification of Space and Time, 2010; Walter, ‘The Historical Origins of Spacetime,’ pp. 27-38 in Ashtekar & Petkov (eds.), The Springer Handbook of Spacetime, 2014.
“Minkowski’s … ‘Space and Time’ lecture given in Cologne in 1908, began with these words: ‘The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.’ He ended as follows: 'The validity without exception of the world postulate [i.e., the relativity postulate], I like to think, is the true nucleus of an electromagnetic image of the world, which, discovered by Lorentz, and further revealed by Einstein, now lies open in the full light of day’. It is hardly surprising that these opening and closing statements caused a tremendous stir among his listeners, though probably few of them followed the lucid remarks he made in the body of the speech. Minkowski did not live to see his lecture appear in print. In January 1909 he died of appendicitis. [David] Hilbert called him ‘a gift of heaven’ when he spoke in his memory” (Pais, p. 152).
“The impact of Minkowski’s ideas on the twentieth century physics has been so immense that one cannot imagine modern physics without the notion of spacetime. It would hardly be an exaggeration to say that spacetime has been the greatest discovery in physics of all times. The only other discovery that comes close to spacetime is Einstein’s general relativity, which revealed that gravity is a manifestation of the curvature of spacetime. But it was the discovery of spacetime which paved the way for this deep understanding of what gravity really is” (Petkov, p. v).
Initially, Einstein was not impressed by Minkowski’s four-dimensional formulation of special relativity, describing it as ‘überflüssige Gelehrsamkeit’ (superfluous learnedness), but he soon realized that his theory of gravity would be impossible without Minkowski’s revolutionary contributions. At the beginning of his 1916 paper on general relativity Einstein wrote: “The generalization of the theory of relativity has been facilitated considerably by Minkowski, a mathematician who was the first one to recognize the formal equivalence of space coordinates and the time coordinate, and utilize this in the construction of the theory.” In 1946 in his ‘Autobiographical Notes’ (p. 59), Einstein summarized Minkowski’s main contribution: “Minkowski’s important contribution to the theory lies in the following: Before Minkowski’s investigation it was necessary to carry out a Lorentz transformation on a law in order to test its invariance under such transformations; he, on the other hand, succeeded in introducing a formalism such that the mathematical form of the law itself guarantees its invariance under Lorentz transformations. By creating a four-dimensional tensor-calculus he achieved the same thing for the four-dimensional space which the ordinary vector calculus achieves for the three spatial dimensions. He also showed that the Lorentz transformation (apart from a different algebraic sign due to the special character of time) is nothing but a rotation of the coordinate system in the four-dimensional space.”
Hermann Minkowski was born on 22 June 1864, in Alexotas, then in Russia, now the city of Kaunas in Lithuania. His parents were German and, from Alexotas, they moved back to their native land, in fact to Königsberg (now Kaliningrad in Russia), when he was only 8 years old. After attending the Gymnasium in Königsberg he attended the University there from which he was to receive his doctorate in 1885. As a young student, in 1883, he won the Grand Prix of the Academy of Sciences in Paris for his work on number theory. From Königsberg, he moved to a position at the University of Bonn in 1887. In 1896, after a brief return to Königsberg, he was appointed to a position at the Polytechnic in Zürich where he was one of Einstein’s teachers. Einstein apparently thought Minkowski an excellent teacher of mathematics. Minkowski’s view of Einstein, at the time, was less kind. In 1902 he moved again, this time to a chair at the University of Göttingen, where he remained for the remainder of his relatively short life, dying in 1909 at the age of only 44. In Göttingen, under the influence of David Hilbert, he became interested in mathematical physics.
In October 1907 Hilbert and Minkowski conducted a joint seminar at Göttingen on the equations of electrodynamics in which they studied Einstein’s 1905 paper ‘Zur Elektrodynamik bewegter Körper’ (Annalen der Physik 17, pp. 891-921), and Poincaré’s 1906 article ‘Sur la dynamique de l’électron’ (Rendiconti del Circolo Matematico di Palermo 21, pp. 129-76). Participants in the seminar included Max von Laue, Max Born, Max Abraham and Arnold Sommerfeld. On November 5 Minkowski delivered a talk to the Göttingen Mathematical Society entitled ‘The Principle of Relativity’; it was not published until 1915 (‘Das Relativitätsprinzip,’ Annalen der Physik 47, pp. 927-38). Minkowski opened his talk by declaring that recent developments in the electromagnetic theory of light had given rise to a completely new conception of space and time, namely, as a four-dimensional, non-Euclidean manifold. He introduced many of the mathematical concepts and terms that have come to be associated with his name and that became standard in any discussion of relativity, but he did not treat them systematically at this stage.
Minkowski’s second talk, “The Basic Equations of Electromagnetic Processes in Moving Bodies”, was delivered at the meeting of the Göttingen Scientific Society on December 21, 1907, and published in April 1908. “It presented a new theory of the electrodynamics of moving media, incorporating formal insights of the relativity theories introduced earlier by Einstein, Poincaré and Planck. For example, it took over the fact that the Lorentz transformations form a group, and that Maxwell’s equations are covariant under this group. Minkowski also shared Poincaré’s view of the Lorentz transformation as a rotation in a four-dimensional space with one imaginary coordinate. These insights Minkowski developed and presented in an original, four-dimensional approach to the Maxwell-Lorentz vacuum equations, the electrodynamics of moving media, and in an appendix, Lorentz-covariant mechanics” (Gray, p. 102).
““The basic equations” made for challenging reading. It was packed with new notation, terminology, and calculation rules, it made scant reference to the scientific literature, and offered no figures or diagrams … Few were impressed at first by Minkowski’s innovations in spacetime geometry and four-dimensional vector calculus. Shortly after “The basic equations” appeared in print, two of Minkowski’s former students, Einstein and Laub, discovered what they believed to be an infelicity in Minkowski’s definition of ponderomotive force density. These two young physicists were more impressed by Minkowski’s electrodynamics of moving media than by the novel four-dimensional formalism in which it was couched, which seemed far too laborious. Ostensibly as a service to the community, Einstein and [Jakob] Laub re-expressed Minkowski’s theory in terms of ordinary vector analysis [‘Über die elektromagnetischen Grundgleichungen für bewegte Körper’, Annalen der Physik 26, 1908, pp. 532-540] …
“The form Minkowski gave to his theory of moving media in “The basic equations” had been judged unwieldy by a founder of relativity theory, and in the circumstances, decisive action was called for if his formalism was not to be ignored. In September 1908, during the annual meeting of the German Association of Natural Scientists and Physicians in Cologne, Minkowski took action, by affirming the reality of the four-dimensional “world”, and its necessity for physics … One way for Minkowski to persuade physicists of the value of his spacetime approach to understanding physical interactions was to appeal to their visual intuition. From the standpoint of visual aids, the contrast between Minkowski’s two publications on spacetime is remarkable: where “The basic equations” is bereft of diagrams and illustrations, Minkowski’s Cologne lecture makes effective use of diagrams in two and three dimensions. For instance, Minkowski employed a two-dimensional spacetime diagrams to illustrate FitzGerald-Lorentz contraction of an electron, and the lightcone structure of spacetime” (Walter, pp. 14-17).
Pp. 4-9 in Verhandlungen der Gesellschaft Deutscher Naturforscher und Ärzte. 80 Versammlung zu Cöln. 20. – 28. September 1908. Zweiter Theil, 1. Häfte. Large 8vo (255 x 180 mm), pp. x, 218. Original printed wrappers, uncut, spine strip and corners with light wear.