On the existence of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ

Foundations of Physics (Impact Factor: 1.03). 03/1997; 27(3):435-508. DOI: 10.1007/BF02550165


We present the theory, the experimental evidence and fundamental physical consequences concerning the existence of families
of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ<∞, which are solutions of the homogeneuous wave equation,
the Maxwell equations, and Dirac, Weyl, and Klein-Gordon equations.

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Available from: Waldyr Alves Rodrigues,
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    • "Historical details about the discovery of these solutions and other non referenced statements below may be found in [31] "
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    ABSTRACT: By analyzing the structure of the Weyl spinor field in the Clifford bundle formalism we show that in each spinorial frame it is represented by F\insec(\doublebarwedge^0 T^\starM + \doublebarwedge^2 T^\star M + \doublebarwedge^{4} T^\star M)\hookrightarrowsecC\ell(M,g) satisfying the equation \partialF=0, where \partial is the Dirac operator acting on sections of the Clifford bundle C\ell(M,g). With this result we show that introducing a generalized potential A=(A + \gamma_5 B)\insec(\doublebarwedge^{1}T^{\star}M + \doublebarwedge^3 T^\star M)\hookrightarrowsecC\ell(M,g) for the Weyl field such that F=\partialA it is possible to exhibit superluminal solutions (including one with a front moving at superluminal speed) for Weyl equation, which surprisingly describes the propagation of a massive tachyonic neutrino. We propose to interpret these extraordinary solutions in order that eventually they may serve as possible models for the emission process and propagation of the superluminal neutrinos observed at the OPERA experiment. Moreover, complementing this study we show that general local chiral invariance of Weyl equation implies that it describes for all solutions that are eigenstates of the parity operator a pair of `sub-particles' carrying opposite magnetic charges (thus possibly carrying a small magnetic moment) which thus interact with an external electromagnetic field. Even if at the Earth's electromagnetic field the effect may result negligible, eventually the idea may be a useful one to study neutrinos leaving the electromagnetic field of stars.
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    • "Viewed in this way the effect seems close to other cases where velocities larger than c can be obtained by interference. A particular case is the superluminal X-wave in free Maxwell theory, which is created by interference between monochromatic plane waves [18] [19]. "
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    ABSTRACT: We examine the effect of superluminal signal propagation through a birefringent crystal, where the effect is not due to absorption or reflection, but to the filtration of a special polarization component. We first examine the effect by a stationary phase analysis, with results consistent with those of an earlier analysis of the system. We supplement this analysis by considering the transit of a gaussian wave and find bounds for the validity of the stationary phase result. The propagation of the gaussian wave is illustrated by figures.
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    • "Recently it was found that wave equations admit solutions which describe waves propagating slower or faster than the velocity appearing in the equation in question ([1] [2] [3] [4] [5]), and there are experiments proving the existence of such waves in the case of sound (supersonic waves) [6]. As a particular case, the Maxwell equations, too, admit subluminal and superluminal wave solutions with arbitrary speed. "
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    ABSTRACT: recent theoretical results show the existence of arbitrary speeds ($0\leq v <\infty$) solutions of the wave equations of mathematical physics. Some recent experiments confirm the results for sound waves. The question arises naturally: What is the appropriate spacetime model to describe superluminal phenomena? In this paper we present a spacetime model that incorporates the valid results of Relativity Theory and yet describes coherently superluminal phenomena without paradoxes.
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