Relativity

by Albert Einstein

It is to be found rather in the fact of his recognition that the four-dimensional space-time continuum of the Theory of Relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space.14 In order to give due prominence to this relationship, however, we must replace the usual time co-ordinate t by an imaginary magnitude proportional to it. Under these conditions, the natural laws satisfying the demands of the (special) Theory of Relativity assume mathematical forms, in which the time co-ordinate plays exactly the same role as the three space co-ordinates. Formally, these four co-ordinates correspond exactly to the three space co-ordinates in Euclidean geometry. It must be clear even to the non-mathematician that, as a consequence of this purely formal addition to our knowledge, the theory perforce gained clearness in no mean measure.