Mechanical and Maxwell’s equations relative to an observer and principle of general relativity

Abstract

The principle of general relativity states that every observer has the right to analyze the physical world from his point of view. However, a transcription code is necessary to compare different descriptions. It is just this code that allows to obtain a physics that is universal in the class of observers. First of all, an observer, identified with a frame of reference R, must have procedures not only to attribute coordinates to each event but also to measure any physical quantity. In the literature, formal procedures are proposed to derive physical quantities and equations relative to an observer starting from the absolute ones. In this paper, these formal approaches are shown to be equivalent to entrust the proper inertial frame [Formula: see text] at an event [Formula: see text] to carry out the measure of physical quantities. Then the observer R adopts the results obtained by [Formula: see text] without introducing his own measures. Since these adopted measures are carried out in the absence of gravitation, the obtained relative equations describe how the evolution with respect to R of proper quantities is modified by gravitation. Finally, after determining the transformation of proper quantities in going from R to another frame R’, a principle of general relativity is formulated in an appropriate class of observers.