Abstract
A rigorous extension of the full Lorentz group is found which is parameterized by interframe velocities v(t) and which reduces to Special Relativity for acceleration-free cases and to Galilean relativity for low velocity cases. Full group properties are exhibited. Four-momentum is defined and particle masses are shown to be invariants. Four-force is introduced and pseudoforces are shown to enter the equations of particle dynamics. Maxwell's equations are shown to take on pseudocurrent terms in accelerating frames. A four-vector Green function solution to the modified Maxwell equations is presented. Finally, a discussion is offered concerning philosophical questions such as the operational definition of time.
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Urani, J., Gale, G. An extension of special relativity to accelerating frames and some of its philosophical implications. Synthese 50, 301–323 (1982). https://doi.org/10.1007/BF00413887
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DOI: https://doi.org/10.1007/BF00413887