Reference: Einstein’s 1920 Book
Section XXVI (Part 2)
The Space-Time Continuum of the Special Theory of Relativity Considered as a Euclidean Continuum
Please see Section XXVI at the link above.
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Summary
In the special theory of relativity, mathematical relationships are derived from the postulate that the velocity of light is same in all Galilean systems. These relationships are expressed as the equations of the Lorentz transformation. They have proved valid for the Galilean systems.
If we choose as time-variable the imaginary variable √(-1) ct instead of the real quantity t, we can regard the space-time continuum as a “Euclidean” four-dimensional continuum.
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Final Comments
The space coordinates (x, y, z) and the time coordinate (t) represent two very different dimensions in our experience; but they may be combined geometrically to form a “Euclidean” four-dimensional continuum. This continuum may be interpreted as follows.
The greater is the “duration” of substance at a location, the lesser is its flexibility at that location. Whereas, the coordinate t represents the “duration” of substance at a location in space (x, y, z); the Minkowki’s coordinate “√(-1) ct” represents the consistency of substance at that location.
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