A New View on Relativity: Part 1. Kinematic Relations Between Inertial and Relativistically Accelerated Systems Based on Symmetry

Abstract

Several new ideas related to Special and General Relativity are proposed. The black-box method is used for the synchronization of the clocks and the space axes between two inertial systems or two accelerated systems and for the derivation of the transformations between them. There are two consistent ways of defining the inputs and outputs to describe the transformations and relative motion between the systems. The standard approach uses a mixture of the two ways. By formulating the principle of special and general relativity as a symmetry principle we are able to specify these transformations to depend only on a constant. The transformations become Galilean if the constant is zero. Validity of the Clock Hypothesis for uniformly accelerated systems implies zero constant. If the constant is not zero, we can introduce a metric under which the transformations become self adjoint. In case of inertial systems, the metric is the Minkowski metric and we obtain a unique invariant maximal velocity. The ball of the relativistically admissible velocities is a bounded symmetric domain under projective maps. For uniformly accelerated systems the existence of an invariant \textit{maximal acceleration} is predicted. This is the only method of describing transformations between uniformly accelerated systems without assuming the Clock Hypothesis.