Einstein on the importance of x4=ict and Minkowski in the development of General Relativity.
In his wonderful book Relativity The Special and General Theory, Albert Einstein shared the central importance of Minkowski and the equation x4=ict in the development of general relativity, writing:
In order to give due prominence to this relationship, however, we must replace the usual time co-ordinate t by an imaginary magnitude ict 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.
These inadequate remarks can give the reader only a vague notion of the important idea contributed by Minkowski. Without it the general theory of relativity, of which the fundamental ideas are developed in the following pages, would perhaps have got no farther than its long clothes.
So it is that the equation x4=ict played an integral role in the development of general relativity. Do not take my word for it — heed the words of Einstein: “These inadequate remarks can give the reader only a vague notion of the important idea contributed by Minkowski.”
Enjoy Einstein’s writings on this:
It is thus a great curiosity that some modern physicists reject the equation x4=ict, even going so far as to label it as being “incorrect.” Not only is the equation x4=ict correct, but it also directly lead to one of the greatest edifices of modern science — the General Theory of Relativity.