Hermann Minkowski and the four-dimensional Space-Time

Hermann Minkowski

Hermann Minkowski

On June 22, 1864, German mathematician Hermann Minkowski was born. Minkowski developed the geometry of numbers and used geometrical methods to solve problems in number theory, mathematical physics, and the theory of relativity. But he is perhaps best known for his work in relativity, in which he showed in 1907 that his former student Albert Einstein’s special theory of relativity can be understood geometrically as a theory of four-dimensional space–time, since known as the “Minkowski spacetime“.

Hermann Minkowski was born in Russia, but his family returned to Germany and settled in Königsberg when he was about eight years old. It became clear quite early, that he had great talents in mathematics. Minkowski started reading the works of Dedekind, Dirichlet, and Gauss during his school years in Königsberg and enrolled at the University of Königsberg in 1880. Minkowski received his doctorate in 1885 from Königsberg for a thesis titled “Untersuchungen über quadratische Formen, Bestimmung der Anzahl verschiedener Formen, welche ein gegebenes Genus enthält”. Minkowski’s interest in quadratic forms evolved early in his university studies. In 1881, Paris’ Academy of Sciences announced that the Grand Prix for mathematical science to be awarded in 1883 would be for a solution to the problem of the number of representations of an integer as the sum of five squares. Already in 1847, Eisenstein had given a formula for the number of such representations, but without a proof of the result. At the age of 18, Minkowski reconstructed Eisenstein’s theory of quadratic forms and produced a beautiful solution to the Grand Prix problem. Henry John Stephen Smith had previously worked on the problem and also submitted his solution as well. The prize was then shared between the two mathematicians.

Starting from 1887, Minkowski spent a few years teaching in Bonn and Königsberg before being appointed to the Eidgenössische Polytechnikum Zürich. At Zurich Einstein was a student in several of the courses he gave and the two would later become interested in similar problems in relativity theory. In 1902. Minkowski accepted a chair at the University of Göttingen, which was arranged by David Hilbert. There, Minkowski became interested in mathematical physics gaining enthusiasm from Hilbert and his associates. He participated in a seminar on electron theory in 1905 and he learnt the latest results and theories in electrodynamics. Hermann Minkowski laid the mathematical foundation of the theory of relativity and developed an entirely new view of space and time. He made clear that Lorentz’ and Einstein’s work could be better understood in a non-euclidean space. Minkowski came to realize that space and time, which were previously thought to be independent, are coupled together in a four-dimensional ‘space-time continuum‘. To his major works in the field belong ‘Raum und Zeit’ [6], published in 1907, as well as ‘Zwei Abhandlungen über die Grundgleichungen der Elektrodynamik‘ published two years later. Minkowski’s space-time continuum provided a framework for later works on relativity and were used by Einstein in developing the general theory of relativity .

At yovisto academic search engine you can learn more about the theory of relativity in a lecture titled ‘Einstein for the Masses‘ by Prof. Dr. Ramamurti Shankar at Yale University.

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