Space Contractions, Local Light Speeds and the Question of Gauge in General Relativity

C. Y. Lo

《Chinese Journal of Physics》 41卷4期 (2003/08) Pp. 332-342

並列摘要

It is believed that, in general relativity, the choice of a gauge is still arbitrary even after the frame of reference has been chosen. For instance, it is well known that the Schwarzschild solution and the isotropic solution are considered to be physically equivalent. Here, I argue that such belief is actually incorrect. For instance, in the case of Einstein's rotating disk, once the frame of reference is chosen, the gauge has been determined for a space-time coordinate system for which, as Einstein required, time is defined ”in such a way that the rate of a clock depends upon where the clock may be.” Thus, the different space contractions from different metrics cannot both be valid physically, as both metrics have the same frame of reference. Moreover, based on the equivalence principle, Einstein pointed out that both space contraction and time dilation are measurable. Accordingly, it is proposed to measure the directional difference of local light speeds at the surface of the earth to decide which metric is more realistic.