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Tachyon kinematics and causality: A systematic thorough analysis of the tachyon causal paradoxes

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Abstract

The chronological order of the events along a spacelike path is not invariant under Lorentz transformations, as is well known. This led to an early conviction that tachyons would give rise to causal anomalies. A relativistic version of the Stückelberg-Feynman “switching procedure” (SWP) has been invoked as the suitable tool to eliminate those anomalies. The application of the SWP does eliminate the motions backwards in time, but interchanges the roles ofsource anddetector. This fact triggered the proposal of a host of causal “paradoxes.” Till now, however, it has not been recognized that such paradoxes can be sensibly discussed (and completely solved, at least “in microphysics”)only after the tachyon relativistic mechanics has been properly developed. We start by showing how to apply the SWP, both in the case ofordinary special relativity and in the case with tachyons. Then we carefully exploit the kinematics of the tachyon exchange between to (ordinary) bodies. Being finally able to tackle the tachyon causality problem, we successively solve the paradoxes of : (i) Tolman-Regge, (ii) Pirani, (iii) Edmonds, and (iv) Bell. Finally, we discuss a further, new paradox associated with the transmission of signals by modulated tachyon beams.

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  1. Erasmo Recami

    Present address: Department of Applied Mathematics, State University of Campinas, Campinas, S.P., Brazil

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  1. Dipartimento di Fisica, Università Statale di Catania, Catania, Italy

    Erasmo Recami

  2. I.N.F.N., Sezione di Catania, Catania, Italy

    Erasmo Recami

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Work partially supported by MPI and by FAP-UNICAMP.

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Recami, E. Tachyon kinematics and causality: A systematic thorough analysis of the tachyon causal paradoxes. Found Phys 17, 239–296 (1987). https://doi.org/10.1007/BF00733092

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