Die Anschauungen über Raum und Zeit, die ich Ihnen entwickeln möchte, sind auf experimentell-physikalischem Boden erwachsen. Darin liegt ihre Stärke. Ihre Tendenz ist eine radikale. Von Stund' an sollen Raum für sich und Zeit für sich völlig zu Schatten herabsinken und nur noch eine Art Union der beiden soll Selbständigkeit bewahren.
Hermann Minkowski, opening words of his talk "Raum und Zeit" at the 80. Meeting of Natural Scientists and Physicians, Cologne 1908 (English translation see footnote).
Hermann Minkowski, 1864-1909 (from MacTutor History of Mathematics Archive)September 21, 1908, was a wonderful and sunny late-summer Monday in Cologne, Germany, where scientists from all over the country had come together for the 80th General Meeting of the Society of Natural Scientists and Physicians.
On that day, Hermann Minkowski, a well-known mathematician from Göttingen, gave a talk with the title "Raum und Zeit" – "Space and Time". In this now famous talk, Minkowski proposed a new formulation of the special theory of relativity. His formulation implied a unification of the notions of space and time, which traditionally have been seen as completely independent, to a four-dimensional entity dubbed "space-time".
Points in this "space-time" correspond to "events", e.g. things happening at a certain time and at a certain point in space, and Minkowski proposed to define a distance between events x (at time t and location x, y, z) and x' (at time t' and location x', y', z') by
distance(x, x') = c²(t−t')² − (x−x')² − (y−y')² − (z−z')²,
where c is the speed of light. The distance between two events defined in this way is, according to the special theory of relativity, the same for all observers in uniform relative motion, or, using the technical jargon, does not change under Lorentz transformations. This definition is a generalization of the Euclidean distance between two points in space, which does not change ("is invariant") under rotations, and the corresponding four-dimensional space-time is now called "Minkowski space".
All the concepts we now use to describe the kinematics of special relativity – events, worldlines, light cones – were presented in front of a large public audience for the first time one hundered years ago today, in Minkowski's lecture.
Future ("Nachkegel") and past ("Vorkegel") light cones, and timelike ("zeitartiger") and spacelike ("raumartiger") vectors in the writeup of Minkowski's talk (page 82 of Raum und Zeit, Jahresbericht der Deutschen Mathematiker-Vereinigung 18, 1909).
Worldline ("Weltlinie") of a particle in Minkowski spacetime (page 86 of Raum und Zeit).
Hermann Minkowski was born in Lithuania, and had studied mathematics at the University of Königsberg. His contributions to number theory, complex analysis and algebra had made him quite renowned at a young age, and he held positions as professor of mathematics at the universities of Bonn, Zürich (the ETH), and Göttingen. At Göttingen, he shared the interest of Hilbert in the problems of the theory of the electron and special relativity.
Curiously, his worldline hat crossed that of Albert Einstein before: Einstein, as a student of physics at Zürich, had been taught mathematics by Minkowski. But it seems that Minkowski didn't have a very good impression of his student. On the other hand, Einstein had some difficulties to make sense of the reformulation of his theory by his former teacher. Arnold Sommerfeld quotes Einstein as having said in reaction to Minkowski's work that "since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore."
But it's clear that Minkowski's four-dimensional world was an essential conceptual step in the understanding of relativity, and indispensable for the later formulation of general relativity. Unfortunately, Minkowski didn't live to see or even foster these developments. His lecture on "Space and Time" was his last scientific work – he died from a ruptured appendix in January 1909, at the age of 44.
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.
Translation by W. Perrett and G.B. Jeffery, taken from Hermann Minkowski, "Space and Time", in Hendrik A. Lorentz, Albert Einstein, Hermann Minkowski, and Hermann Weyl, The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity (Dover, New York, 1952), pages 75-91.
For more about Minkowski and his role in special relativity, see e.g. L Corry: Hermann Minkowski and the postulate of relativity, Arch. Hist. Exact Sci. 51 (1997), 273-314 (a free preprint as PDF is here), and Scott Walter: Hermann Minkowski’s approach to physics, Math Semesterber. 55 (2008) 213–235 (preprint as PDF), and Minkowski, Mathematicians, and the Mathematical Theory of Relativity, in H. Goenner, J. Renn, J. Ritter, T. Sauer (eds.): The ExpandingWorlds of General Relativity (Einstein Studies 7), Boston/Basel: Birkhäuser 1999, 45–86 (preprint as PDF).