On the Intrinsically Ambiguous Nature of Space-Time Diagrams

Elie During

doi:10.4245/sponge.v6i1.18645

Abstract

When the German mathematician Hermann Minkowski first introduced the space-time diagrams that came to be associated with his name, the idea of picturing motion by geometric means, holding time as a fourth dimension of space, was hardly new. But the pictorial device invented by Minkowski was tailor-made for a peculiar variety of space-time: the one imposed by the kinematics of Einstein’s special theory of relativity, with its unified, non-Euclidean underlying geometric structure. By plo tting two or more reference frames in relative motion on the same picture, Minkowski managed to exhibit the geometric basis of such relativistic phenomena as time dilation, length contraction or the dislocation of simultaneity. These disconcerting effects were shown to result from arbitrary projections within four-dimensional space-time. In that respect, Minkowski diagrams are fundamentally different from ordinary space-time graphs. The best way to understand their specificity is to realize how productively ambiguous they are.

Highlights

When the German mathematician Hermann Minkowski first introduced the space-time diagrams that came to be associated with his name, the idea of picturing motion by geometric means, holding time as a fourth dimension of space, was hardly new
The trick was to make sense of the troublesome fact that the speed of light was constant in empty space without giving up the principle of relativity inherited from Galilean physics, i.e. the equivalence of all kinematical perspectives a ached to reference frames in uniform motion relative to each other (“inertial frames”)
Space-Time Diagrams well-established that Henri Poincaré had hit upon the geometric structure underlying such a framework some time before Einstein’s revolutionary 1905 paper, for reasons that need not concern us here, he did not bother to figure out all its physical implications