Relativity and Cosmology


The Lorentz Transformation from Light-Speed Invariance Alone

Authors: Steven Kenneth Kauffmann

The derivation of the Lorentz transformation normally rests on two a priori demands, namely that reversing the direction of the transformation's constant-velocity boost inverts the transformation, and that the transformation leaves light-speed invariant. It is notable, however, that the simple light-clock concept, which is rooted entirely in light-speed invariance, immediately implies reciprocal time dilation, and it has been demonstrated that reciprocal time dilation implies length contraction. Reciprocal time dilation and length contraction are the pivotal consequences of the Lorentz transformation, so demanding only inertial transformation-invariance of light-speed apparently already uniquely produces the Lorentz transformation. We show that the demand of x-direction inertial transformation-invariance of the light-cone space-time locus uniquely produces the x-direction Lorentz transformation, and also that the demand of x-direction inertial transformation-invariance of light speed itself has the same consequence; in the latter case the velocity, instead of the space-time, version of the general x-direction inertial transformation must be used. The x-direction Lorentz transformation is also uniquely produced by the reciprocal time dilation and length contraction implications of light clocks.

Comments: 8 Pages.

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Submission history

[v1] 2018-02-21 23:25:05
[v2] 2018-02-22 08:48:55 (removed)
[v3] 2018-02-24 23:04:46 (removed)
[v4] 2018-02-27 06:40:20 (removed)
[v5] 2018-03-02 05:00:16 (removed)
[v6] 2018-03-03 07:32:04 (removed)
[v7] 2018-03-04 16:38:30 (removed)
[v8] 2018-03-06 09:35:53 (removed)
[v9] 2018-03-08 23:25:32 (removed)
[vA] 2018-03-10 18:28:40 (removed)
[vB] 2018-03-11 19:47:18

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