82 research outputs found
Generalized composition law from 2x2 matrices
Many results that are difficult can be found more easily by using a
generalization in the complex plane of Einstein's addition law of parallel
velocities. Such a generalization is a natural way to add quantities that are
limited to bounded values. We show how this generalization directly provides
phase factors such as the Wigner angle in special relativity and how this
generalization is connected in the simplest case with the composition of 2x2 S
matrices.Comment: Accepted for publication in Am. J. Phy
Composition law for polarizers
The polarization process when polarizers act on an optical field is studied.
We give examples for two kinds of polarizers. The first kind presents an
anisotropic absorption - as in a polaroid film - and the second one is based on
total reflection at the interface with a birefringent medium. Using the Stokes
vector representation, we determine explicitly the trajectories of the wave
light polarization during the polarization process. We find that such
trajectories are not always geodesics of the Poincar\'e sphere as it is usually
thought. Using the analogy between light polarization and special relativity,
we find that the action of successive polarizers on the light wave polarization
is equivalent to the action of a single resulting polarizer followed by a
rotation achieved for example by a device with optical activity. We find a
composition law for polarizers similar to the composition law for noncollinear
velocities in special relativity. We define an angle equivalent to the
relativistic Wigner angle which can be used to quantify the quality of two
composed polarizers.Comment: 23 pages, 9 figures, accepted for publication in Physical Review
The cosmological constant and the coincidence problem in a new cosmological interpretation of the universal constant c
In a recent paper (Vigoureux et al. Int. J. Theor. Phys. 47:928, 2007) it has
been suggested that the velocity of light and the expansion of the universe are
two aspects of one single concept connecting space and time in the expanding
universe. It has then be shown that solving Friedmann's equations with that
interpretation (and keeping c = constant) can explain number of unnatural
features of the standard cosmology (for example: the flatness problem, the
problem of the observed uniformity in term of temperature and density of the
cosmological background radiation, the small-scale inhomogeneity problem...)
and leads to reconsider the Hubble diagram of distance moduli and redshifts as
obtained from recent observations of type Ia supernovae without having to need
an accelerating universe. In the present work we examine the problem of the
cosmological constant. We show that our model can exactly generate
(equation of state with ) contrarily to the standard model which cannot generate it exactly. We
also show how it can solve the so-called cosmic coincidence problem
Constructing Fresnel reflection coefficients by ruler and compass
A simple and intuitive geometical method to analyze Fresnel formulas is
presented. It applies to transparent media and is valid for perpendicular and
parallel polarizations. The approach gives a graphical characterization
particularly simple of the critical and Brewster angles. It also provides an
interpretation of the relation between the reflection coefficients for both
basic polarizations as a symmetry in the plane
Fresnel coefficients as hyperbolic rotations
We describe the action of a plane interface between two semi-infinite media
in terms of a transfer matrix. We find a remarkably simple factorization of
this matrix, which enables us to express the Fresnel coefficients as a
hyperbolic rotation.Comment: 6 pages, 3 figure
Weakness of accelerator bounds on electron superluminality without a preferred frame
The reference laboratory bounds on superluminality of the electron are
obtained from the absence of in-vacuo Cherenkov processes and the
determinations of synchrotron radiated power for LEP electrons. It is usually
assumed that these analyses establish the validity of a standard
special-relativistic description of the electron with accuracy of at least a
few parts in , and in particular this is used to exclude electron
superluminality with such an accuracy. We observe that these bounds rely
crucially on the availability of a preferred frame. In-vacuo-Cherenkov
processes are automatically forbidden in any theory with "deformed Lorentz
symmetry", relativistic theories that, while different from Special Relativity,
preserve the relativity of inertial frames. Determinations of the synchrotron
radiated power can be used to constrain the possibility of Lorentz-symmetry
deformation, but provide rather weak bounds, which in particular for electron
superluminality we establish to afford us no more constraining power than for
an accuracy of a few parts in . We argue that this observation can have
only a limited role in the ongoing effort of analysis of the anomaly
tentatively reported by the OPERA collaboration, but we stress that it could
provide a valuable case study for assessing the limitations of "indirect" tests
of fundamental laws of physics.Comment: LaTex, 6 page
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