The Extensive Special Relativity and Comment on Local Lorentz Transformation in Varying Speed of Light Theory

TL;DR

This paper argues that local Lorentz transformations cannot support a varying speed of light and emphasizes the necessity of an invariant speed in special relativity, suggesting that VSL theories are only compatible with general relativity.

Contribution

It clarifies that local Lorentz transformations cannot justify a varying speed of light and redefines the basic principles of special relativity to include an invariant speed.

Findings

Local Lorentz transformations cannot derive a varying speed of light.

An invariant speed is necessarily derived from the principles of special relativity.

Varying speed of light theories are only compatible with general relativity.

Abstract

It is proved that local Lorentz transformations for different systems cannot derive varying speed of light. Based on the special relativity principle, an invariant speed is necessarily obtained. Therefore, the exact basic principles of the special relativity should be redefined as: I. The special relativity principle, which derives necessarily an invariant speed. II. Suppose that the invariant speed in the theory is the speed of light in the vacuum c. If the second principle does not hold, for example, the superluminal motions exist, the theory will be still the extensive special relativity, in which the formulations are the same, only c is replaced by the invariant speed. If the invariant speed are various invariant velocities, the diversity of space-time will correspond to many worlds. Varying speed of light theory is probably connected only with the general relativity.