Minkowski’s Legacy

Today, Hermann Minkowski is most famous for introducing a two-dimensional space-time diagram to explain the Lorentz transformation of Special Relativity. Over the last century, this intuitive visual aid has helped clarify Einstein’s theory, significantly facilitating its dissemination to scientists and the general public. 

However, according to Minkowski, Einstein’s former math teacher at the Polytechnic, Einstein clarified the physical significance of Lorentz’s theory, but did not grasp the true meaning and full implication of the principle of relativity.1

Minkowski also was the first to suggest that the world may be composed of an infinite number of spaces, but his affirmation was not explicit enough for other scientists to take his hint seriously. 

Indeed, in 1908, Minkowski delivered his famous Cologne lecture Raum und Zeit (Space and Time). Explaining the natural laws of transformation between reference frames, he pointed out a subtle yet extremely important concept:

… We should then have in the world no longer the “space,” but an infinite number of spaces, analogously as there are in three-dimensional space an infinite number of planes.2

Sadly, Minkowski died soon after that lecture without having explained precisely what he meant by an infinite number of spaces. Not understanding the extreme importance of Minkowski’s declaration, no one – then or since – took his hint seriously, considering it nothing more than a grandiose announcement of the mathematician’s own relativity theory. 

Now, the Multispace Diagram brings a new understanding to this concept.


1 Scott Walter, Minkowski, Mathematicians, and the Mathematical Theory of Relativity, in H. Goenner, J. Renn, J. Ritter, T. Sauer (eds.), The Expanding Worlds of General Relativity (Einstein Studies, volume 7), pp. 45-86. Boston/Basel: Birkhäuser, 1999, page 61, or download it from here.

2 H. Minkowski, Space and Time, in The Principle of Relativity, translated by W. Perrett and G.B. Jeffery (Dover Publications, Inc., 1952), p. 79.

Posted in Mathematics, Physics

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