पृष्ठ 190 / 212

This four-dimensional "world" bears a close similarity to the

three-dimensional "space" of (Euclidean) analytical geometry. If

we introduce into the latter a new Cartesian co-ordinate system

(x′1, x′2, x′3) with the same origin, then x′1, x′2, x′3, are

linear homogeneous functions of x1, x2, x3 which identically

satisfy the equation

x1′2 + x2′2 + x3′2 = x12 + x22 + x32

The analogy with (12) is a complete one. We can regard

Minkowski's "world" in a formal manner as a four-dimensional

Euclidean space (with an imaginary time coordinate); the Lorentz

transformation corresponds to a "rotation" of the co-ordinate

system in the four-dimensional "world."

APPENDIX III

THE EXPERIMENTAL CONFIRMATION OF THE GENERAL THEORY OF RELATIVITY