Relativity
The Special and General Theory
relativity, the "time" x4, enters into natural laws in the same form as the space co-ordinates x1, x2, x3.
A four-dimensional continuum described by the "co-ordinates" x1, x2, x3, x4, was called "world" by Minkowski, who also termed a point-event a "world-point." From a "happening" in three-dimensional space, physics becomes, as it were, an "existence" in the four-dimensional "world."
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
| x'12 + x'22 + x'32 = 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."
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