Lorentz semigroup



Abstract



An attempt is made to construct a semigroup generalization of the relativistic invariance principle for transformation between inertial and arbitrary non-inertial coordinates.



Preface



It is convenient to express the motion of the non-inertial observer by means of her proper acceleration because this quantity is directly observable and makes no reference to external inertial frames. Following this strategy the non-inertial observer metric is expected to depend on the proper acceleration history of the non-inertial observer. We shall be particularly concerned with what can be actually measured by the non-inertial observer, and our construction will depend on an observable definition of the coordinates (radar coordinates) and on an observable

and intrinsic description of the non-inertial observer motion (the proper acceleration).

As mentioned, the non-inertial observer can construct coordinates using different methods. The transformation between inertial and non-inertial coordinates should reduce to a Lorentz transformation if the observer has

vanishing acceleration. However, this requirement is too weak to determine a unique solution. There are at least three possibilities that have been considered: radar coordinates,[1],[2],[3],[4] Fermi coordinates[5],[6],[7],[8] and Møller coordinates [9],[10],[11],[12],[13],[14].



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