449 research outputs found
Reference frames and rigid motions in relativity: Applications
The concept of rigid reference frame and of constricted spatial metric, given
in the previous work [\emph{Class. Quantum Grav.} {\bf 21}, 3067,(2004)] are
here applied to some specific space-times: In particular, the rigid rotating
disc with constant angular velocity in Minkowski space-time is analyzed, a new
approach to the Ehrenfest paradox is given as well as a new explanation of the
Sagnac effect. Finally the anisotropy of the speed of light and its measurable
consequences in a reference frame co-moving with the Earth are discussed.Comment: 13 pages, 1 figur
Relativistic contraction and related effects in noninertial frames
Although there is no relative motion among different points on a rotating
disc, each point belongs to a different noninertial frame. This fact, not
recognized in previous approaches to the Ehrenfest paradox and related
problems, is exploited to give a correct treatment of a rotating ring and a
rotating disc. Tensile stresses are recovered, but, contrary to the prediction
of the standard approach, it is found that an observer on the rim of the disc
will see equal lengths of other differently moving objects as an inertial
observer whose instantaneous position and velocity are equal to that of the
observer on the rim. The rate of clocks at various positions, as seen by
various observers, is also discussed. Some results are generalized for
observers arbitrarily moving in a flat or a curved spacetime. The generally
accepted formula for the space line element in a non-time-orthogonal frame is
found inappropriate in some cases. Use of Fermi coordinates leads to the result
that for any observer the velocity of light is isotropic and is equal to ,
providing that it is measured by propagating a light beam in a small
neighborhood of the observer.Comment: 15 pages, significantly revised version, title changed, to appear in
Phys. Rev.
On the relation of Thomas rotation and angular velocity of reference frames
In the extensive literature dealing with the relativistic phenomenon of
Thomas rotation several methods have been developed for calculating the Thomas
rotation angle of a gyroscope along a circular world line. One of the most
appealing concepts, introduced in \cite{rindler}, is to consider a rotating
reference frame co-moving with the gyroscope, and relate the precession of the
gyroscope to the angular velocity of the reference frame. A recent paper
\cite{herrera}, however, applies this principle to three different co-moving
rotating reference frames and arrives at three different Thomas rotation
angles. The reason for this apparent paradox is that the principle of
\cite{rindler} is used for a situation to which it does not apply. In this
paper we rigorously examine the theoretical background and limitations of
applicability of the principle of \cite{rindler}. Along the way we also
establish some general properties of {\it rotating reference frames}, which may
be of independent interest.Comment: 14 pages, 2 figure
The Relative Space: Space Measurements on a Rotating Platform
We introduce here the concept of relative space, an extended 3-space which is
recognized as the only space having an operational meaning in the study of the
space geometry of a rotating disk. Accordingly, we illustrate how space
measurements are performed in the relative space, and we show that an old-aged
puzzling problem, that is the Ehrenfest's paradox, is explained in this purely
relativistic context. Furthermore, we illustrate the kinematical origin of the
tangential dilation which is responsible for the solution of the Ehrenfest's
paradox.Comment: 14 pages, 2 EPS figures, LaTeX, to appear in the European Journal of
Physic
On the experimental determination of the one-way speed of light
In this contribution the question of the isotropy of the one-way speed of
light from an experimental perspective is addressed. In particular, we analyze
two experimental methods commonly used in its determination. The analysis is
aimed at clarifying the view that the one-way speed of light cannot be
determined by techniques in which physical entities close paths. The procedure
employed here will provide epistemological tools such that physicists
understand that a direct measurement of the speed not only of light but of any
physical entity is by no means trivial. Our results shed light on the physics
behind the experiments which may be of interest for both physicists with an
elemental knowledge in special relativity and philosophers of science.Comment: 8 pages, 5 figures. To appear in the European Journal of Physic
Locality hypothesis and the speed of light
The locality hypothesis is generally considered necessary for the study of
the kinematics of non-inertial systems in special relativity. In this paper we
discuss this hypothesis, showing the necessity of an improvement, in order to
get a more clear understanding of the various concepts involved, like
coordinate velocity and standard velocity of light. Concrete examples are
shown, where these concepts are discussed.Comment: 23 page
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
The Role of Calcineurin/NFAT in SFRP2 Induced Angiogenesis—A Rationale for Breast Cancer Treatment with the Calcineurin Inhibitor Tacrolimus
Tacrolimus (FK506) is an immunosuppressive drug that binds to the immunophilin FKBPB12. The FK506-FKBP12 complex associates with calcineurin and inhibits its phosphatase activity, resulting in inhibition of nuclear translocation of nuclear factor of activated T-cells (NFAT). There is increasing data supporting a critical role of NFAT in mediating angiogenic responses stimulated by both vascular endothelial growth factor (VEGF) and a novel angiogenesis factor, secreted frizzled-related protein 2 (SFRP2). Since both VEGF and SFRP2 are expressed in breast carcinomas, we hypothesized that tacrolimus would inhibit breast carcinoma growth. Using IHC (IHC) with antibodies to FKBP12 on breast carcinomas we found that FKBP12 localizes to breast tumor vasculature. Treatment of MMTV-neu transgenic mice with tacrolimus (3 mg/kg i.p. daily) (n = 19) resulted in a 73% reduction in the growth rate for tacrolimus treated mice compared to control (n = 15), p = 0.003; which was associated with an 82% reduction in tumor microvascular density (p<0.001) by IHC. Tacrolimus (1 µM) inhibited SFRP2 induced endothelial tube formation by 71% (p = 0.005) and inhibited VEGF induced endothelial tube formation by 67% (p = 0.004). To show that NFATc3 is required for SFRP2 stimulated angiogenesis, NFATc3 was silenced with shRNA in endothelial cells. Sham transfected cells responded to SFRP2 stimulation in a tube formation assay with an increase in the number of branch points (p<0.003), however, cells transfected with shRNA to NFATc3 showed no increase in tube formation in response to SFRP2. This demonstrates that NFATc3 is required for SFRP2 induced tube formation, and tacrolimus inhibits angiogenesis in vitro and breast carcinoma growth in vivo. This provides a rationale for examining the therapeutic potential of tacrolimus at inhibiting breast carcinoma growth in humans
Simultaneity and generalized connections in general relativity
Stationary extended frames in general relativity are considered. The
requirement of stationarity allows to treat the spacetime as a principal fiber
bundle over the one-dimensional group of time translations. Over this bundle a
connection form establishes the simultaneity between neighboring events
accordingly with the Einstein synchronization convention. The mathematics
involved is that of gauge theories where a gauge choice is interpreted as a
global simultaneity convention. Then simultaneity in non-stationary frames is
investigated: it turns to be described by a gauge theory in a fiber bundle
without structure group, the curvature being given by the Fr\"olicher-Nijenhuis
bracket of the connection. The Bianchi identity of this gauge theory is a
differential relation between the vorticity field and the acceleration field.
In order for the simultaneity connection to be principal, a necessary and
sufficient condition on the 4-velocity of the observers is given.Comment: RevTeX, 9 pages, 2 figures, 1 table. Previous title "The gauge nature
of simultaneity". Classical and Quantum Gravity
http://www.iop.org/EJ/journal/CQ
Performance bounds on compressed sensing with Poisson noise
This paper describes performance bounds for compressed sensing in the
presence of Poisson noise when the underlying signal, a vector of Poisson
intensities, is sparse or compressible (admits a sparse approximation). The
signal-independent and bounded noise models used in the literature to analyze
the performance of compressed sensing do not accurately model the effects of
Poisson noise. However, Poisson noise is an appropriate noise model for a
variety of applications, including low-light imaging, where sensing hardware is
large or expensive, and limiting the number of measurements collected is
important. In this paper, we describe how a feasible positivity-preserving
sensing matrix can be constructed, and then analyze the performance of a
compressed sensing reconstruction approach for Poisson data that minimizes an
objective function consisting of a negative Poisson log likelihood term and a
penalty term which could be used as a measure of signal sparsity.Comment: 5 pages; to appear in Proc. ISIT 200
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