Research Reports

In the last years, two types of superluminal wave motion have been predicted theoretically and verified experimentally:{i} superluminal group velocities, observed in the propagation of electromagnetic waves in dispersive media, in tunneling of electrons and microwaves and in the propagation of microwaves in air;(ii} superluminal motion of finite aperture approximations (FAA) to superluminal solutions in vacuum of the Maxwell equations. In this work we try to clarify the meaning of such phenomena and their implications for the foundations of Quantum Theory and Relativity. For what concerns Quantum Theory, we show that when the main relativistic equations (the homogeneous wave equation and the Maxwell, Dirac, Weyl, Klein-Gordon equations) are expressed in the Clifford bundle formalism (which is developed with enough details), there are unsuspected relationships, between, e.g., Maxwelland Dirac equations, a fact that naturally suggests a de Broglie-Bohm interpretation of the theory. This suggests a common origin and interpretation for the `superluminal' tunneling of microwaves and of electrons in tunneling experiments. In both cases, despite superluminal group velocities being observable (under certain conditions), it happens that electrons have always subluminal velocities and the energy flow of any given microwave is such that its energy always travels with subluminal or luminal velocity. The origin of the superluminal group velocities in these two cases is a phenomenon called pulse reshaping, which is analyzed in detail in this work, and which also explains naturally almost all superluminal group velocities found (under appropriate conditions) also in wave propagation in dispersive media. Fundamental for the understanding of the meaning of the experiments showing superluminal group velocities is to understand deeply the concept of signal. It is shown, from the theoretical point of view, that limited frequency band waves have no beginning and no ending in the temporal domain, being in a certain precise sense non causal. For these waves (under appropriate conditions) genuine superluminal velocities may be associated, because they have no fronts, contrary to broad (i.e., infinite) frequency band waves that are limited in the time domain (Brillouin-Sommerfeld signals) and whose fronts propagate, at least in dispersive media, with the velocity of light in vacuum. The paper presents also a complete mathematical theory of how to generate arbitrary velocities solutions ($0 \leq v < \infty$) for all relativistic wave equations mentioned above and also discuss how to generate FAA for, e.g., superluminal electromagnetic $X$-waves (SEXWs). The meaning of superluminality associated with FAA to waves like SEXWs is also discussed. It is shown that it is due to a process analogous (but not identical) to the reshaping phenomena that occur in the case of, e.g., the tunneling of microwaves. A rigorous mathematical presentation of the Principle of Relativity (PR) is also given. We show that the existence of genuine superluminal electromagnetic wave motion (i.e., that cannot be atributed to pulse reshaping (or analogous) phenomena) violates the PR. However, we must say that none of the experiences analyzed in this paper implies in any violation of the PR.}

rp-1999-59.pdf