4,409 research outputs found
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 . We can
write where \psi \in \sec \clif^+(M). We
can show that 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 ( or ). 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 a
positive parity eigenstate, . Calling the solution
corresponding to the electron, coming from \dirac F_e =0, we show that the
NLDHE for such that
gives a linear DHE for Takabayasi angles and 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}\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}\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 () 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
only inside media and are always less than the vacuum light speed .
Particularly, very fast sound pulses with speeds 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 . We discuss some experimental evidences of 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
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