Alternative realization for the composition of relativistic velocities

M. Fernández-Guasti

doi:10.1117/12.894342

28 September 2011 Alternative realization for the composition of relativistic velocities

M. Fernández-Guasti

Proceedings Volume 8121, The Nature of Light: What are Photons? IV; 812108 (2011) https://doi.org/10.1117/12.894342
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

The reciprocity principle requests that if an observer, say in the laboratory, sees an event with a given velocity, another observer at rest with the event must see the laboratory observer with minus the same velocity. The composition of velocities in the Lorentz-Einstein scheme does not fulfill the reciprocity principle because the composition rule is neither commutative nor associative. In other words, the composition of two non-collinear Lorentz boosts cannot be expressed as a single Lorentz boost but requires in addition a rotation. The Thomas precession is a consequence of this composition procedure. Different proposals such as gyro-groups have been made to fulfill the reciprocity principle. An alternative velocity addition scheme is proposed consistent with the invariance of the speed of light and the relativity of inertial frames. An important feature of the present proposal is that the addition of velocities is commutative and associative. The velocity reciprocity principle is then immediately fulfilled. This representation is based on a transformation of a hyperbolic scator algebra. The proposed rules become identical with the special relativity addition of velocities in one dimension. They also reduce to the Galilean transformations in the low velocity limit. The Thomas gyration needs to be revised in this nonlinear realization of the special relativity postulates. The deformed Minkowski metric presented here is compared with other deformed relativity representations.

Citation Download Citation

M. Fernández-Guasti "Alternative realization for the composition of relativistic velocities", Proc. SPIE 8121, The Nature of Light: What are Photons? IV, 812108 (28 September 2011); https://doi.org/10.1117/12.894342

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