Authors: Eric Su
The application of symmetry to physics leads to conservation law and conserved quantity. For inertial reference frames, the reflection symmetry generates not only conservation but also transformation. Under reflection symmetry, the elapsed time is conserved in all inertial reference frames. The displacement in space is also conserved in all inertial reference frames. From the conservation of the elapsed time and the displacement, the coordinate transformation between inertial reference frame is derived. Based on the coordinate transformation, both the time transformation and the velocity transformation are also derived. The derivation shows that all three transformations are dependent exclusively on the relative motion between inertial reference frames.
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[v1] 2019-01-01 02:09:00
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