Authors: Steven Kenneth Kauffmann
The x-direction Galilean and Lorentz space-time transformations are both effectively two-dimensional matrix transformations, so a simple four-parameter general framework of which both are special cases is easily devised. Moreover, passing from the general space-time transformation to its velocity counterpart uniquely singles out one of those four parameters as the general transformation's intrinsic x-direction constant velocity. This allows the "principle of relativity" to be extended to such general transformations; it applies when the transformation's inversion is accomplished by reversing the sign of its intrinsic velocity. Both the Galilean and Lorentz transformations abide by the "principle of relativity", and the Galilean transformation in addition refrains from altering the time coordinate. The Michelson-Morley null result, however, motivates the Lorentz transformation to refrain from changing the speed of light, which is readily shown to be outright incompatible with transformation-invariant time. The Lorentz transformation's pairing of invariant light speed with the "relativity principle" is closely allied to its preservation of the Minkowski quadratic form.
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