54 research outputs found
Elementary analysis of the special relativistic combination of velocities, Wigner rotation, and Thomas precession
The purpose of this paper is to provide an elementary introduction to the
qualitative and quantitative results of velocity combination in special
relativity, including the Wigner rotation and Thomas precession. We utilize
only the most familiar tools of special relativity, in arguments presented at
three differing levels: (1) utterly elementary, which will suit a first course
in relativity; (2) intermediate, to suit a second course; and (3) advanced, to
suit higher level students. We then give a summary of useful results, and
suggest further reading in this often obscure field.Comment: V1: 25 pages, 6 figures; V2: 22 pages, 5 figures. The revised version
is shortened and the arguments streamlined. Minor changes in notation and
figures. This version matches the published versio
Geometric phase via adiabatic manipulations of the environment
We show that geometric phases may be generated in a quantum system subject to
noise by adiabatic manipulations of the fluctuating fields, e.g., by variation
of the system-environment coupling. For a two-state quantum system we express
this phase in terms of the geometry of the path, traversed by the slowly
varying direction and amplitude of the fluctuations. We discuss the origin of
this phase and possibilities to separate it from the known environment-induced
modification of the Berry phase
Spectrometric method to detect exoplanets as another test to verify the invariance of the velocity of light
Hypothetical influences of variability of light velocity due to the
parameters of the source of radiation, for the results of spectral measurements
of stars to search for exoplanets are considered. Accounting accelerations of
stars relative to the barycenter of the star - a planet (the planets) was
carried out. The dependence of the velocity of light from the barycentric
radial velocity and barycentric radial acceleration component of the star
should lead to a substantial increase (up to degree of magnitude) semi-major
axes of orbits detected candidate to extrasolar planets. Consequently, the
correct comparison of the results of spectral method with results of other
well-known modern methods of detecting extrasolar planets can regard the
results obtained in this paper as a reliable test for testing the invariance of
the velocity of light.Comment: 11 pages, 5 figure
Triple Michelson Interferometer for a Third-Generation Gravitational Wave Detector
The upcoming European design study `Einstein gravitational-wave Telescope'
represents the first step towards a substantial, international effort for the
design of a third-generation interferometric gravitational wave detector. It is
generally believed that third-generation instruments might not be installed
into existing infrastructures but will provoke a new search for optimal
detector sites. Consequently, the detector design could be subject to fewer
constraints than the on-going design of the second generation instruments. In
particular, it will be prudent to investigate alternatives to the traditional
L-shaped Michelson interferometer. In this article, we review an old proposal
to use three Michelson interferometers in a triangular configuration. We use
this example of a triple Michelson interferometer to clarify the terminology
and will put this idea into the context of more recent research on
interferometer technologies. Furthermore the benefits of a triangular detector
will be used to motivate this design as a good starting point for a more
detailed research effort towards a third-generation gravitational wave
detector.Comment: Minor corrections to the main text and two additional appendices. 14
pages, 6 figure
The Sagnac Phase Shift suggested by the Aharonov-Bohm effect for relativistic matter beams
The phase shift due to the Sagnac Effect, for relativistic matter beams
counter-propagating in a rotating interferometer, is deduced on the bases of a
a formal analogy with the the Aharonov-Bohm effect. A procedure outlined by
Sakurai, in which non relativistic quantum mechanics and newtonian physics
appear together with some intrinsically relativistic elements, is generalized
to a fully relativistic context, using the Cattaneo's splitting technique. This
approach leads to an exact derivation, in a self-consistently relativistic way,
of the Sagnac effect. Sakurai's result is recovered in the first order
approximation.Comment: 18 pages, LaTeX, 2 EPS figures. To appear in General Relativity and
Gravitatio
The relativistic Sagnac Effect: two derivations
The phase shift due to the Sagnac Effect, for relativistic matter and
electromagnetic beams, counter-propagating in a rotating interferometer, is
deduced using two different approaches. From one hand, we show that the
relativistic law of velocity addition leads to the well known Sagnac time
difference, which is the same independently of the physical nature of the
interfering beams, evidencing in this way the universality of the effect.
Another derivation is based on a formal analogy with the phase shift induced by
the magnetic potential for charged particles travelling in a region where a
constant vector potential is present: this is the so called Aharonov-Bohm
effect. Both derivations are carried out in a fully relativistic context, using
a suitable 1+3 splitting that allows us to recognize and define the space where
electromagnetic and matter waves propagate: this is an extended 3-space, which
we call "relative space". It is recognized as the only space having an actual
physical meaning from an operational point of view, and it is identified as the
'physical space of the rotating platform': the geometry of this space turns out
to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor
corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and
M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also
http://digilander.libero.it/solciclo
Limiting degree of polarization of a nonmonochromatic radiation propagating in a fiber guide with random inhomogeneities
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