April 19, 2014

Hermann Minkowski: Einstein’s Fellow

Hermann Minkowski (June 22, 1864 – January 12, 1909) was a German mathematician of Jewish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.
Hermann Minkowski was born in Aleksotas, a suburb of Kaunas, in Lithuania, to a family of Lithuanian Jewish descent. Hermann was educated in Germany at the Albertina University of Königsberg, where he achieved his doctorate in 1885 under direction of Ferdinand von Lindemann. While still a student at Königsberg, in 1883 he was awarded the Mathematics Prize of the French Academy of Sciences for his manuscript on the theory of quadratic forms. He also became a friend of another German mathematician, David Hilbert. His brother, Oskar Minkowski (1858–1931), was a well-known physician and researcher.
Minkowski taught at the universities of Bonn, Göttingen, Königsberg and Zürich. At the Eidgenössische Polytechnikum, today the ETH Zurich, he was one of Einstein’s teachers.
Minkowski explored the arithmetic of quadratic forms, especially concerning n variables, and his research into that topic led him to consider certain geometric properties in a space of n dimensions. In 1896, he presented his geometry of numbers, a geometrical method that solved problems in number theory.
In 1902, he joined the Mathematics Department of Göttingen and became one of the close colleagues of David Hilbert, whom he first met in Königsberg. Constantin Carathéodory was one of his students there.
Although Minkowski mathematic works were successful but the most glorious were his achievements in the science of physics.
By 1907 Minkowski realized that the special theory of relativity, introduced by Albert Einstein in 1905 and based on previous work of Lorentz and Poincaré, could be best understood in a four dimensional space, since known as “Minkowski spacetime”, in which time and space are not separated entities but intermingled in a four dimensional space-time, and in which the Lorentz geometry of special relativity can be nicely represented.
By his scientific intuition he found the most actual problems in the science of physics and foreseen the development of new ideas of Hendrik Lorentz and Albert Einstein. That assisted him to create a hypothesis of the space and time unity, to determine a geometric structure of that space – time unity. These ideas were published first time in Köln, 1908 at the conference of nature scientists and medics.
The primary idea of the unity of space and time to the solid four-dimensional continuum was the analysis of transformations by Lorentz. Minkowski first realized the importance of the Lorentz transformation ideas. He stated that in the four-dimensional world one point has four coordinates: three of them are space coordinates which defines the event location ant the fourth coordinate – the time of that event. This four-dimensional space is called an event space or Minkowski space.
Minkowski created a principle of relativity of all physical occurrences: physical laws are invariantic by the aspect of Lorentz transformations. He began to use the concept of the four-dimensional forces (Minkowski forces, etc.).
It would be unavailable to create the general theory of relativity without Minkowski ideas. His works created a perfect form to the theory of relativity and assisted to spread it to the other branches of the science of physics.
Minkowski has made a revolution in the science of physics by creation of the new concept of space-time unity, later scientists developing the theory of relativity based their works on this concept.


  1. Roger says:

    Minkowski got the idea of 4-dimensional space-time from Poincare. Einstein did not understand it at all when Minkowski published it in 1908.

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