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FOUR-DIMENSIONAL SPACE
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enters into natural laws in the same form as the space co-ordinates , , .

A four-dimensional continuum described by the “co-ordinates” , , , , 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 (, , ) with the same origin, then , , , are linear homogeneous functions of , , , which identically satisfy the equation

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 imaginary time co-ordinate); the Lorentz transformation corresponds to a “rotation” of the co-ordinate system in the four-dimensional “world.”