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Tachyon mechanics and classical tunnel effect

1971; Springer Science+Business Media; Volume: 2; Issue: 7 Linguagem: Inglês

10.1007/bf02772821

1827-613X

H. K. Wimmel,

Relativity and Gravitational Theory

I t is uncertain whether classical point-particle theory of tachyons would describe any tachyon phenomena, provided tachyous exist. The reason for this uncer ta inty is an apparent disagreement between classical point-particle theory and classical or quantized field theories of taehyons, the main points of disagreement being the nonlocalizability of tachyon fields and the impossibility of propagating supraluminal signals by tachyon fields (1.3). On the other hand, it is found in this paper that classical tachyon mechanics determines the Lorentz-covariance properties of the tachyon observables correctly. I t also yields a peculiar effect, the classical tunneling of tachyons, which seems interesting in itself. I t is known that the coupling of classical point tachyons with electromagnetic or gravitational fields leads to divergent Cerenkov fields (4-v). Hence, in this paper charged tachyons in external electromagnetic fields are considered, with omission of Cerenkov radiation and Ccrenkov self-force. From this starting point a self-consistent theory of the Vlasov type (s) could be established, but is not i~Lvestigated in this paper. The main point in setting up any formalisin of taehyon mechanics is to realize tha t in the case of tachyons the principle of relativity provides that several observables, e.g. charge, momentum and energy, do not possess the usual Lorentz-covariance properties. This is important as it completely eliminates the problem of interpreting negative kinetic energies (s~). In tardon physics the proper time r is used as a real-valued orbit parameter of worldlines. I t is a perfectly well-determined, i.e. observable, quant i ty because of the definition dr 2 = dt 2 dr ~, dr~dr > 0. Such is not the case for tachyons and the real-valued, scalar proper path s, with ds 2 = dr 2 d r : , because sign (dt/ds) is not Lorentz inva-