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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.
[14] Cf. the somewhat more detailed discussion in Appendix II.
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. Minkowski s work is doubtless difficult of access to anyone
inexperienced in mathematics, but since it is not necessary to have a
very exact grasp of this work in order to understand the fundamental
ideas of either the special or the general theory of relativity, I
shall leave it here at present, and revert to it only towards the end
of Part II.
PART II: THE GENERAL THEORY OF RELATIVITY
XVIII.
SPECIAL AND GENERAL PRINCIPLE OF RELATIVITY
The basal principle, which was the pivot of all our previous
considerations, was the _special_ principle of relativity, _i.e._ the
principle of the physical relativity of all _uniform_ motion. Let as
once more analyse its meaning carefully.
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