Subluminal and Superluminal Electromagnetic Waves and the Lepton Mass Spectrum

Maxwell equation \dirac F = 0 for F \in \sec \bwe^2 M \subset \sec \clif (M), where \clif (M) is the Clifford bundle of differential forms, have subluminal and superluminal solutions characterized by $F^2 \neq 0$. We can write $F = \psi \gamma_{21} \tilde \psi$ where \psi \in \sec \clif^+(M). We can show that $\psi$ satisfies a non linear Dirac-Hestenes Equation (NLDHE). Under reasonable assumptions we can reduce the NLDHE to the linear Dirac-Hestenes Equation (DHE). This happens for constant values of the Takabayasi angle ($0$ or $\pi$). The massless Dirac equation \dirac \psi =0, \psi \in \sec \clif^+ (M), is equivalent to a generalized Maxwell equation \dirac F = J_{e} - \gamma_5 J_{m} = {\cal J}. For $\psi = \psi^\uparrow$ a positive parity eigenstate, $j_e = 0$. Calling $\psi_e$ the solution corresponding to the electron, coming from \dirac F_e =0, we show that the NLDHE for $\psi$ such that $\psi \gamma_{21} \tilde{\psi} = F_e + F^{\uparrow}$ gives a linear DHE for Takabayasi angles $\pi/2$ and $3\pi/2$ with the muon mass. The Tau mass can also be obtained with additional hypothesis.Comment: 24 pages, KAPPROC style (Kluwer Ac. Pub. Proceedings) with named references. The Abstract to appear in the e-print archive list has been corrected. The main text is the sam

On the Equation rotA = K A

We show that when correctly formulated the equation \nabla \times \mbox{\boldmath a} = \kappa \mbox{\boldmath a} does not exhibit some inconsistencies atributed to it, so that its solutions can represent physical fields.Comment: 8 pages, documentstyle [preprint,aps]{revtex} with special macro climacr

Subluminal and superluminal solutions in vacuum of the Maxwell equations and the massless Dirac equation

We show that Maxwell equations and Dirac equation (with zero mass term) have both subluminal and superluminal solutions in vacuum. We also discuss the possible fundamental physical consequences of our results.Comment: REVTeX, 8 pages, talk given at the International Conference on the Theory of the Electron, Sept.95, Mexico City. To appear in the proceeding

Equivalence Principle and the Principle of Local Lorentz Invariance

In this paper we scrutinize the so called Principle of Local Lorentz Invariance (\emph{PLLI}) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics we introduce in the General Theory of Relativity two classes of reference frames (\emph{PIRFs} and \emph{LLRF}$\gamma$\emph{s}) which natural generalizations of the concept of the inertial reference frames of the Special Relativity Theroy. We show that it is the class of the \emph{LLRF}$\gamma$\emph{s} that is associated with the \emph{PLLI.} Next we give a defintion of physically equivalent referefrence frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the \emph{PLLI}is false. However our find is not in contradiction with the many experimental claims vindicating the \emph{PLLI}, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that \emph{PIRFs}are not physically equivalent.Comment: This is a version of a paper originally published in Found. Phys.(2001) which includes a corrigenda published in Found. Phys. 32, 811-812 (2002

Spacetime model with superluminal phenomena

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.Comment: 12 pages, uses amstex, amsppt documentstyl

Rotating Frames in SRT: Sagnac's Effect and Related Issues

After recalling the rigorous mathematical representations in Relativity Theory (\emph{RT}) of (i): observers, (ii): reference frames fields, (iii): their classifications, (iv) naturally adapted coordinate systems (\emph{nacs}%) to a given reference frame, (v): synchronization procedure and some other key concepts, we analyze three problems concerning experiments on rotating frames which even now (after almost a century from the birth of \emph{RT}) are sources of misunderstandings and misconceptions. The first problem, which serves to illustrate the power of rigorous mathematical methods in \emph{RT}is the explanation of the Sagnac effect (\emph{SE}). This presentation is opportune because recently there are many non sequitur claims in the literature stating that the \emph{SE} cannot be explained by \emph{SRT}, even disproving this theory or that the explanation of the effect requires a new theory of electrodynamics. The second example has to do with the measurement of the one way velocity of light in rotating reference frames, a problem for which many wrong statements appear in recent literature. The third problem has to do with claims that only Lorentz like type transformations can be used between the \emph{nacs}associated to a reference frame mathematically moddeling of a rotating platform and the \emph{nacs} associated with a inertial frame (the laboratory). Whe show that these claims are equivocated

The geometry of spacetime with superluminal phenomena

Recent theoretical results show the existence of arbitrary speeds (0 <= v < \infty) solutions of all relativistic wave equations. Some recent experiments confirm the results for sound waves. The question arises naturally: What is the appropriate geometry of spacetime 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.Comment: 16 pages, Amstex, amsppt styl

Launching of Non-Dispersive Superluminal Beams

In this paper we analyze the physical meaning of sub- and superluminal soliton-like solutions (as the X-waves) of the relativistic wave equations and of some non-trivial solutions of the free Schr\"odinger equation for which the concepts of phase and group velocities have a different meaning than in the case of plane wave solutions. If we accept the strict validity of the principle of relativity, such solutions describe objects of two essentially different natures: carrying energy wave packets and inertia-free properly phase vibrations. Speeds of the first-type objects can exceed the plane wave velocity $c_*$ only inside media and are always less than the vacuum light speed $c$. Particularly, very fast sound pulses with speeds $c_* < v < c$ have already been launched. The second-type objects are incapable of carrying energy and information but have superluminal speed. If we admit the possibility of a breakdown of Lorentz invariance, pulses described, for example, by superluminal solutions of the Maxwell equations can be generated. Only experiment will give the final answer.Comment: 12 pages, standard Latex articl

Faster Than Light ?

In this paper we present a pedestrian review of the theoretical fact that all relativistic wave equations possess solutions of arbitrary velocities $0 \leq v < \infty$. We discuss some experimental evidences of $v \geq c$ transmission of electromagnetic field configurations and the importance of these facts with regard to the principle of relativity.Comment: 12 pages, Latex2e article, with figures. Requires packages epsfig and graphicx. Figure 2 has been correcte

The Hyperbolic Clifford Algebra of Multivecfors

In this paper we give a thoughtful exposition of the hyperbolic Clifford algebra of multivecfors which is naturally associated with a hyperbolic space, whose elements are called vecfors. Geometrical interpretation of vecfors and multivecfors are given. Poincare automorphism (Hodge dual operator) is introduced and several useful formulas derived. The role of a particular ideal in the hyperbolic Clifford algebra whose elements are representatives of spinors and resume the algebraic properties of Witten superfields is discussed.Comment: a few misprints and typos have been correcte