Reciprocity Principle and the Lorentz Transformations

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Abstract
By using the principle of relativity, together with the customary assumptions concerning the nature of the space‐time manifold in special relativity, namely, space‐time homogeneity and isotropy of space, a simple but rigorous proof is given of the reciprocity relation for the relative motion of two inertial frames of reference, which is usually assumed as a postulate in the standard derivations of the Lorentz transformations without the principle of invariance of light velocity. A critical discussion is set forth of the question of eliminating the transformations with invariant imaginary velocity, which one unavoidably obtains together with the Lorentz transformations and the Galilean ones in adopting a procedure of this kind.

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