By Laboratoire Gravitation et Cosmologie Relativistes Universite Pierre et Marie Curie et CNRS Institut HenriPoincare Paris

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**Extra resources for Gravitation, Geometry and Relativistic Physics**

**Example text**

Einstein arrived at the conclusion that “within special relativity theory there is no place for a satisfactory theory of gravity”. In Einstein’s general relativity theory, special relativity theory is certainly not satisfied, it is considered a limit case. In 1955 A. Einstein wrote: ≪An essential achievement of general relativity theory consists in that it has saved physics from the necessity of introducing an “inertial reference system” (or “inertial reference systems”)≫. However, even now, there exists absolutely no experimental or observational fact that could testify to the violation of special relativity theory.

The physical meaning of local time was uncovered by H. Poincar´e. In the article “The theory of Lorentz and the principle of equal action and reaction“, published in 1900, he wrote about the local time τ , defined as follows (Translation from French by V. A. Petrov): “I assume observers, situated at different points, to compare their clocks with the aid of light signals; they correct these signals for the transmission time, but, without knowing the relative motion they are undergoing and, consequently, considering the signals to propagate with the same velocity in both directions, they limit themselves to performing observations by sending signals from A to B and, then, from B to A.

Electrodynamics . . 49 Galilean transformations x = X − vT, Y = Y ′, Z = Z′ and rewrite the preceding equation of spherical wave in the following form 2 cT 2 v2 1− 2 c − 2xvT − x2 − Y ′2 − Z ′2 = 0. The requirement of relativity principle here is reduced to necessity that the electromagnetic wave in a new inertial reference system K ′ has to be also spherical having its center at the origin of this reference system. Having this in mind we transform the above equation (as done before) to the following form c2 T ′2 − X ′2 − Y ′2 − Z ′2 = 0.