Abstract
The most general form of transformations of space-time coordinates in Special Theory of Relativity based solely on physical assumptions is described. Only the linearity of space-time transformations and the constancy of the speed of light are used as assumptions. The application to tachyonic motion is indicated.
Highlights
In almost all textbooks on Special Relativity [1] it is claimed that fundamental transformations of space-time coordinates (x, t) are of the form of Lorentz transformations t → t′ = γ t
The present paper provides a firm theoretical basis for tachyonic physics
We have shown that superluminal motions are permitted by Special Relativity in the same way as the subluminal motions are
Summary
In almost all textbooks on Special Relativity [1] it is claimed that fundamental transformations of space-time coordinates (x, t) are of the form of Lorentz transformations t → t′ = γ t. Lorentz derived his transformations from the requirement of covariance of the vacuum Maxwell equations under linear transformations of space-time coordinates. It is known that in any medium the Maxwell equations are covariant under linear transformations and under arbitrary transformations of space-time coordinates. The Lorentz derivation of Lorentz transformations used additional particular assumption that the basic Maxwell equations are the vacuum Maxwell equations. Einstein [3], in his derivation of the space-time transformations, used particular information on the Doppler effect and assumed the equality of two-way velocities of light.
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