190 research outputs found
Testing Einstein's time dilation under acceleration using M\"ossbauer spectroscopy
The Einstein time dilation formula was tested in several experiments. Many
trials have been made to measure the transverse second order Doppler shift by
M\"{o}ssbauer spectroscopy using a rotating absorber, to test the validity of
this formula. Such experiments are also able to test if the time dilation
depends only on the velocity of the absorber, as assumed by Einstein's clock
hypothesis, or the present centripetal acceleration contributes to the time
dilation. We show here that the fact that the experiment requires -ray
emission and detection slits of finite size, the absorption line is broadened;
by geometric longitudinal first order Doppler shifts immensely. Moreover, the
absorption line is non-Lorenzian. We obtain an explicit expression for the
absorption line for any angular velocity of the absorber.
The analysis of the experimental results, in all previous experiments which
did not observe the full absorption line itself, were wrong and the conclusions
doubtful. The only proper experiment was done by K\"{u}ndig (Phys. Rev. 129
(1963) 2371), who observed the broadening, but associated it to random
vibrations of the absorber. We establish necessary conditions for the
successful measurement of a transverse second order Doppler shift by
M\"{o}ssbauer spectroscopy. We indicate how the results of such an experiment
can be used to verify the existence of a Doppler shift due to acceleration and
to test the validity of Einstein's clock hypothesis.Comment: 11 pages, 4 figure
Unusual Response to a Localized Perturbation in a Generalized Elastic Model
The generalized elastic model encompasses several physical systems such as
polymers, membranes, single file systems, fluctuating surfaces and rough
interfaces. We consider the case of an applied localized potential, namely an
external force acting only on a single (tagged) probe, leaving the rest of the
system unaffected. We derive the fractional Langevin equation for the tagged
probe, as well as for a generic (untagged) probe, where the force is not
directly applied. Within the framework of the fluctuation-dissipation
relations, we discuss the unexpected physical scenarios arising when the force
is constant and time periodic, whether or not the hydrodynamic interactions are
included in the model. For short times, in case of the constant force, we show
that the average drift is linear in time for long range hydrodynamic
interactions and behaves ballistically or exponentially for local hydrodynamic
interactions. Moreover, it can be opposite to the direction of external
disturbance for some values of the model's parameters. When the force is time
periodic, the effects are macroscopic: the system splits into two distinct
spatial regions whose size is proportional to the value of the applied
frequency. These two regions are characterized by different amplitudes and
phase shifts in the response dynamics
On the theory of astronomical maser. I. Statistics of maser radiation
In this paper we re-analyse the amplification process of broadband continuum
radiation by astronomical masers in one-dimensional case. The basic equations
appropriate for the scalar maser and the random nature of the maser radiation
field are derived from basic physical principles. Comparision with the standard
radiation transfer equation allows us to examine the underlying assumptions
involved in the current theory of astronomical masers. Simulations are carried
out to follow the amplification of different realisations of the broadband
background radiation by the maser. The observable quantities such as intensity,
spectral line profile are obtained by averaging over an ensemble of the
emerging radiation corresponding to the amplified background radiation field.
Our simulations show that the fluctuations of the radiation field inside the
astronomical maser deviates significantly from Gaussian statistics even when
the maser is only partially saturated. Coupling between different frequency
modes and the population pulsing are shown to have increasing importance in the
transport of maser radiation as the maser approaches saturation. Our results
suggest that the standard formulation of radiation transfer provides a
satisfactory description of the intensity and the line narrowing effect in the
unsaturated and partially saturated masers within the framework of
one-dimensional model. Howerver, the application of the same formulation to the
strong saturation regime should be considered with caution.Comment: 16 pages, 4 figures, to appear on MNRA
Correlations in a Generalized Elastic Model: Fractional Langevin Equation Approach
The Generalized Elastic Model (GEM) provides the evolution equation which
governs the stochastic motion of several many-body systems in nature, such as
polymers, membranes, growing interfaces. On the other hand a probe
(\emph{tracer}) particle in these systems performs a fractional Brownian motion
due to the spatial interactions with the other system's components. The
tracer's anomalous dynamics can be described by a Fractional Langevin Equation
(FLE) with a space-time correlated noise. We demonstrate that the description
given in terms of GEM coincides with that furnished by the relative FLE, by
showing that the correlation functions of the stochastic field obtained within
the FLE framework agree to the corresponding quantities calculated from the
GEM. Furthermore we show that the Fox -function formalism appears to be very
convenient to describe the correlation properties within the FLE approach
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Spectral filtering as a method of visualising and removing striped artefacts in digital elevation data
Spectral filtering was compared with traditional mean spatial filters to assess their ability to identify and remove striped artefacts in digital elevation data. The techniques were applied to two datasets: a 100 m contour derived digital elevation model (DEM) of southern Norway and a 2 m LiDAR DSM of the Lake District, UK. Both datasets contained diagonal data artefacts that were found to propagate into subsequent terrain analysis. Spectral filtering used fast Fourier transformation (FFT) frequency data to identify these data artefacts in both datasets. These were removed from the data by applying a cut filter, prior to the inverse transform. Spectral filtering showed considerable advantages over mean spatial filters, when both the absolute and spatial distribution of elevation changes made were examined. Elevation changes from the spectral filtering were restricted to frequencies removed by the cut filter, were small in magnitude and consequently avoided any global smoothing. Spectral filtering was found to avoid the smoothing of kernel based data editing, and provided a more informative measure of data artefacts present in the FFT frequency domain. Artefacts were found to be heterogeneous through the surfaces, a result of their strong correlations with spatially autocorrelated variables: landcover and landsurface geometry. Spectral filtering performed better on the 100 m DEM, where signal and artefact were clearly distinguishable in the frequency data. Spectrally filtered digital elevation datasets were found to provide a superior and more precise representation of the landsurface and be a more appropriate dataset for any subsequent geomorphological applications
Modification of special relativity and local structures of gravity-free space and time
Besides two fundamental postulates, (i) the principle of relativity and (ii)
the constancy of the speed of light in all inertial frames of reference,
special relativity uses the assumption about the Euclidean structures of
gravity-free space and time in the usual inertial coordinate system.
Introducing the so-called primed inertial coordinate system, in addition to the
usual inertial coordinate system, for each inertial frame of reference, we
assume the Euclidean structures of gravity-free space and time in the primed
inertial coordinate system and their generalized Finslerian structures in the
usual inertial coordinate system. We combine this assumption with the two
postulates (i) and (ii) to modify special relativity.Comment: 7 pages, no figur
Space-Time Approach to Scattering from Many Body Systems
We present scattering from many body systems in a new light. In place of the
usual van Hove treatment, (applicable to a wide range of scattering processes
using both photons and massive particles) based on plane waves, we calculate
the scattering amplitude as a space-time integral over the scattering sample
for an incident wave characterized by its correlation function which results
from the shaping of the wave field by the apparatus. Instrument resolution
effects - seen as due to the loss of correlation caused by the path differences
in the different arms of the instrument are automatically included and analytic
forms of the resolution function for different instruments are obtained. The
intersection of the moving correlation volumes (those regions where the
correlation functions are significant) associated with the different elements
of the apparatus determines the maximum correlation lengths (times) that can be
observed in a sample, and hence, the momentum (energy) resolution of the
measurement. This geometrical picture of moving correlation volumes derived by
our technique shows how the interaction of the scatterer with the wave field
shaped by the apparatus proceeds in space and time. Matching of the correlation
volumes so as to maximize the intersection region yields a transparent,
graphical method of instrument design. PACS: 03.65.Nk, 3.80 +r, 03.75, 61.12.BComment: Latex document with 6 fig
A Derivation of Three-Dimensional Inertial Transformations
The derivation of the transformations between inertial frames made by
Mansouri and Sexl is generalised to three dimensions for an arbitrary direction
of the velocity. Assuming lenght contraction and time dilation to have their
relativistic values, a set of transformations kinematically equivalent to
special relativity is obtained. The ``clock hypothesis'' allows the derivation
to be extended to accelerated systems. A theory of inertial transformations
maintaining an absolute simultaneity is shown to be the only one logically
consistent with accelerated movements. Algebraic properties of these
transformations are discussed. Keywords: special relativity, synchronization,
one-way velocity of light, ether, clock hypothesis.Comment: 16 pages (A5), Latex, one figure, to be published in Found. Phys.
Lett. (1997
Was Einstein Right? Testing Relativity at the Centenary
We review the experimental evidence for Einstein's special and general
relativity. A variety of high precision null experiments verify the weak
equivalence principle and local Lorentz invariance, while gravitational
redshift and other clock experiments support local position invariance.
Together these results confirm the Einstein Equivalence Principle which
underlies the concept that gravitation is synonymous with spacetime geometry,
and must be described by a metric theory. Solar system experiments that test
the weak-field, post-Newtonian limit of metric theories strongly favor general
relativity. The Binary Pulsar provides tests of gravitational-wave damping and
of strong-field general relativity. Recently discovered binary pulsar systems
may provide additional tests. Future and ongoing experiments, such as the
Gravity Probe B Gyroscope Experiment, satellite tests of the Equivalence
principle, and tests of gravity at short distance to look for extra spatial
dimensions could constrain extensions of general relativity. Laser
interferometric gravitational-wave observatories on Earth and in space may
provide new tests of gravitational theory via detailed measurements of the
properties of gravitational waves.Comment: 21 pages, 3 figures, to be published in "100 Years of Relativity:
Spacetime Structure - Einstein and Beyond", ed. Abhay Ashtekar (World
Scientific, Singapore
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