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The standard analysis for type Ia supernovae uses a set of templates to overcome the intrinsic variation of the supernova light curves with wavelength. This paper shows that standard templates contain an anomaly in that the width of the template light curve is proportional to the emitted wavelength. Furthermore this anomaly is exactly what would be produced if epoch differences were not subject to time dilation and yet time dilation corrections were applied. It is the specific nature of this anomaly that is evidence for a static universe. The lack of time dilation is verified by direct analysis of the original supernovae data., Comment: 3 pages, 1 figures with major corrections

Two different forms of time dilation, namely, the kinematical time dilation of special relativity and gravitational red shift are coupled during observations of systems moving through a gravitational field. In the particular situation of free fall in a Schwarzschild geometry these two effects are decoupled and in consequence the time dilation, as observed by a distant observer, factorises. Such a factorization is not a universal feature. We define here a necessary and sufficient criterion for time dilation and gravitational red-shift decoupling. This property is manifested in a particular form of the Doppler shift in Schwarzschild geometry., Comment: 4 pages

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 $\gamma$-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 figures

We examine the effects of time dilation on the temporal profiles of gamma-ray burst (GRB) pulses. By using prescriptions for the shape and evolution of prompt gamma-ray spectra, we can generate a simulated population of single pulsed GRBs at a variety of redshifts and observe how their light curves would appear to a gamma-ray detector here on Earth. We find that the observer frame duration of individual pulses does not increase as a function of redshift as one would expect from the cosmological expansion of a Friedman-Lemaitre-Robertson-Walker Universe. In fact, the duration of individual pulses is seen to decrease as their signal-to-noise decreases with increasing redshift, as only the brightest portion of a high redshift GRB's light curve is accessible to the detector. The results of our simulation are consistent with the fact that a systematic broadening of GRB durations as a function of redshift has not materialized in either the Swift or Fermi detected GRBs with known redshift. We show that this fundamental duration bias implies that the measured durations and associated Eiso estimates for GRBs detected near an instrument's detection threshold should be considered lower limits to their true values. We conclude by predicting that the average peak-to-peak time for a large number of multi-pulsed GRBs as a function of redshift may eventually provide the evidence for time dilation that has so far eluded detection., Comment: 6 pages, 8 figures, submitted to ApJ

We study the orbits of two interacting particles described by a fully relativistic classical mechanical Hamiltonian. We use two sets of initial conditions. In the first set (dynamics 1) the system's center of mass is at rest. In the second set (dynamics 2) the center of mass evolves with velocity V. If dynamics 1 is observed from a reference frame moving with velocity -V, the principle of relativity requires that all observables must be identical to those of dynamics 2 seen from the lab frame. Our numerical simulations demonstrate that kinematic Lorentz space-time transformations fail to transform particle observables between the two frames. This is explained as a result of the inevitable interaction-dependence of the boost generator in the instant form of relativistic dynamics. In spite of general inaccuracies of Lorentz formulas, the orbital periods are correctly predicted by the Einstein's time dilation factor for all interaction strengths., Comment: 14 pages, 1 figure

In this paper we set out to measure time dilation in quasar light curves. In order to detect the effects of time dilation, sets of light curves from two monitoring programmes are used to construct Fourier power spectra covering timescales from 50 days to 28 years. Data from high and low redshift samples are compared to look for the changes expected from time dilation. The main result of the paper is that quasar light curves do not show the effects of time dilation. Several explanations are discussed, including the possibility that time dilation effects are exactly offset by an increase in timescale of variation associated with black hole growth, or that the variations are caused by microlensing in which case time dilation would not be expected., Comment: 8 pages, 5 figures. Accepted for publication in MNRAS. Published online 9 April 2010.

Recent experiments with high-speed ions have investigated potential deviations from the time-dilation predicted by special relativity (SR). The main contribution of this article is to show that the SR predictions are matched by the experimental results only when the transverse Doppler effect in the observed emissions from the ions are neglected in the analysis. However, the Doppler effect in the emission cannot be neglected because it is similar to the time dilation effect. Thus, the article highlights the need to consider Doppler emission effects when validating SR time dilation using high-speed ion experiments., Comment: 3 pages, 3 figures

Gamma-Ray Bursts have been observed out to very high redshifts and provide time measures that are directly related to intrinsic time scales of the burst. Einstein's theory of relativity is quite definite that if the universe is expanding then the observed duration of these measures will increase with redshift. Thus gamma-ray burst measures should show a time dilation proportional to redshift. An analysis of gamma-ray burst data shows that the hypothesis of time dilation is rejected with a probability of 4.4$\times10^{-6}$ for redshifts out to z=6.6. Traditionally the lack of an apparent time dilation has been explained by an inverse correlation between luminosity and time measures together with strong luminosity selection as a function of redshift. It is shown that the inverse correlation between luminosity and some time measures is confirmed, but using concordance cosmology strong luminosity selection cannot be achieved. It may be possible to explain the apparent lack of time dilation with a combination of gamma-ray burst selection, some luminosity evolution and some time measure evolution. But this requires a remarkable coincidence in order to produce the apparent lack of time dilation. However the data are consistent with a static cosmology in a non-expanding universe., Comment: 17 pages 4 Figures Correction to reference

The rates of chemical reactions are not absolute but their magnitude depends upon the relative speeds of the moving observers. This has been proved by unifying theories of chemical kinetics, which are transition state theory, collision theory, RRKM and Marcus theory, with the special theory of relativity. Boltzmann constant and energy spacing between permitted quantum levels of molecules are quantum mechanically proved to be Lorentz variant. The relativistic statistical thermodynamics has been developed to explain quasiequilibrium existing between reactants and activated complex. The newly formulated Lorentz transformation of the rate constant from Arrhenius Equation, of the collision frequency and of the Eyring and Marcus equations renders the rate law also Lorentz variant. For a moving observer moving at fractions of the speed of light along the reaction coordinate the transition state possess less kinetic energy to sweep translation over it. This results in the slower transformation of reactants into products and in a stretched time frame for the chemical reaction. Lorentz transformation of the half-life equation explains time dilation of the half life period of chemical reactions and proves special theory of relativity and presents theory of relativistic chemical kinetics in accord with each other. To demonstrate the effectiveness of the present theory, the enzymatic reaction of methylamine dehydrogenase and radioactive disintegration of Astatine are considered as numerical examples., Comment: 34 pages, 1 figures, 2 tables

We introduce what we call a locally inertial Godunov method with dynamical time dilation, and use it to simulate a new one parameter family of general relativistic shock wave solutions of the Einstein equations for a perfect fluid. The forward time solutions resolve the secondary reflected wave (an incoming shock wave) in the Smoller-Temple shock wave model for an explosion into a static singular isothermal sphere. The backward time solutions indicate black hole formation from a smooth underlying solution via collapse associated with an incoming rarefaction wave. As far as we know, this is the first numerical simulation of a fluid dynamical shock wave in general relativity.

We present a gravitationally rigorous and clear answer, in the negative, to the question whether gravimetry with atom interferometers is equivalent to the the measurement of the relative gravitational time dilation of two clocks separated in space. Though matter and light waves, quantum states and oscillator clocks are quantum synonymous through the Planck-Einstein-de Broglie relations and the equivalence principle, there are crucial differences in the context of tests of gravitation theories., Comment: 10 pages, 1 figure

In an article "Missing Transverse-Doppler Effect in Time-Dilation Experiments with High-Speed Ions" by S. Devasia [arXiv:1003.2970v1], our recent Doppler shift experiments on fast ion beams are reanalyzed. Contrary to our analysis, Devasia concludes that our results provide an "indication of Lorentz violation". We argue that this conclusion is based on a fundamental misunderstanding of our experimental scheme and reiterate that our results are in excellent agreement with Special Relativity.

In this paper, we suppose that the universe has an information processing layer, which coveys the informational contents accompanying the physical events. In this manner, universe is considered to be composed of several associative layers such that one rises on the other layer. Preliminary, we present a method for the analytical treatment of the amount of information processed by universe itself, and then we try to show its correspondence with theories developed for the time dilation and gravitational forces., Comment: 14 pages, 6 figures

The relativistic addition of parallel velocities is derived involving relativity only via the time dilation formula, avoiding the length contraction used by many authors in conjunction with time dilation. The followed scenario involves a machine gun that fires successive bullets, considered from its rest frame and from the rest frame of the target, the bullets hit.

A rigorous quantum relativistic approach has been used to calculate the relationship between the decay laws of an unstable particle seen from two inertial frames moving with respect to each other. In agreement with experiment, it is found that the usual Einstein's time dilation formula is rather accurate in this case. However, small corrections to this formula were also obtained. Although the observation of these corrections is beyond the resolution of modern experiments, their presence indicates that special relativistic time dilation is not rigorously applicable to particle decays., Comment: 28 pages, 2 figures; v.2 fixed typos; v3 added reference

Time dilation $\frac{1}{\sqrt{1-v^2}}$ and relative velocity $v$ are observationally indistinguishable in the special theory of relativity, a duality that carries over into the general theory under Fermi coordinates along a curve (in coordinate-independent language, in the tangent Minkowski space along the curve). For example, on a clock stationary at radius $r$, a distant observer sees time dilation of $\frac{1}{\sqrt{1-v^2}}=\frac{1}{\sqrt{1-2M/r}}$ under the Schwarzschild metric and sees the clock receding with a relative velocity of $v=\sqrt{2M/r}$ under the Painlev{\'e}-Gullstrand free fall metric. Duality implies that during gravitational collapse, the intensifying time dilation observed at the star's center from a fixed radius $r>0$ is indistinguishable (along a curve) from an increasing relative velocity at which the center recedes as seen from any direction, implying a local inflation., Comment: 7 pages, Latex2e

We have obtained high-quality Keck optical spectra at three epochs of the Type Ia supernova 1997ex, whose redshift z is 0.361. The elapsed calendar time between the first two spectra was 24.88 d, and that between the first and third spectra was 30.95 d. In an expanding universe where 1 + z represents the factor by which space has expanded between the emission and detection of light, the amount of aging in the supernova rest frame should be a factor of 1 / (1 + z) smaller than the observed-frame aging; thus, we expect SN 1997ex to have aged 18.28 d and 22.74 d between the first epoch and the second and third epochs, respectively. The quantitative method for determining the spectral-feature age of a SN Ia, developed by Riess et al. (1997), reveals that the corresponding elapsed times in the supernova rest frame were 16.97 +/- 2.75 d and 18.01 +/- 3.14 d, respectively. This result is inconsistent with no time dilation with a significance level of 99.0%, providing evidence against "tired light" and other hypotheses in which no time dilation is expected. Moreover, the observed timescale of spectral evolution is inconsistent with that expected in the "variable mass theory." The result is within ~1 sigma of the aging expected from a universe in which redshift is produced by cosmic expansion., Comment: 15 pages, 3 figures, accepted for publication in ApJL

Einstein's famous 1938 experiment to test relativity of time is plagued by too many ambiguities and does not prove anything. Nevertheless, it is a landmark experiment at the foundation of the modern theory of time perception., Comment: 8 pages, 2 figures, prepared for the April issue of JEST

We predict a new class of excitations propagating along a Josephson vortex in two-dimensional Josephson junctions. These excitations are associated with the distortion of a Josephson vortex line and have an analogy with shear waves in solid mechanics. Their shapes can have an arbitrary profile, which is retained when propagating. We derive a universal analytical expression for the energy of arbitrary shape excitations, investigate their influence on the dynamics of a vortex line, and discuss conditions where such excitations can be created. Finally, we show that such excitations play the role of a clock for a relativistically-moving Josephson vortex and suggest an experiment to measure a time dilation effect analogous to that in special relativity., Comment: 10 pages, 2 figures