chapter  27
3 Pages

The Space-Time Continuum of the General Theory of Relativity is not a Euclidean Continuum

But the considerations of Sections 25 and 26 show us the way to surmount this difficulty. We refer the four-dimensional space-time continuum in an arbitrary manner to Gauss coordinates. We assign to every point of the continuum (event) four numbers, x1, x2, x3, x4 (co-ordinates), which have not the least direct physical significance, but only serve the purpose of numbering the points of the continuum in a definite but arbitrary manner. This arrangement does not even need to be of such a kind that we must regard x1, x2, x3, as “space” co-ordinates and x4 as a “time” co-ordinate.