Narrow Results

A review of experimental tests of time dilation in special relativity is given, with an emphasis on the recent heavy-ion storage-ring work, currently the most sensitive method. The experimental results are evaluated in the context of the kinematic test theories of Robertson and Mansouri and Sexl, which assume the existence of a preferred inertial reference frame. Prospects for future improvements and the sensitivity of time dilation experiments to Lorentz and CPT violating extensions of the standard model are discussed.

The common opinion that the Lorentz transformation distorts the Minkowski spacetime arises from a mathematically incorrect neglect of its non-diagonal terms. When the non-diagonal Lorentz transformation is properly treated, the time dilation and the space distortion disappear. Consequently, the Lorentz metric produced by the Lorentz transformation is identical to the Minkowski metric. The spacetime distortion in moving inertial frames is properly described by the so-called Doppler metric produced by the Doppler transformation. This transformation assumes the existence of a preferred frame and depicts the Doppler shift of light for a moving light source and/or observer. The Doppler metric is Lorentz invariant and leaves the Maxwell’s equations unchanged from their form in the Minkowski spacetime. Moreover, the Doppler metric is experimentally confirmed because it yields the null result in the Michelson–Morley experiment and other interferometric experiments. The suitability of the Doppler metric for describing light properties in Special and General Relativity is supported by recent cosmological observations of the cosmic microwave background.

We consider the grand canonical ensemble of the static and extremal black holes, when the equivalence of the electric charge and mass of individual black hole is postulated. Assuming uniform distribution of black holes in space, we are finding the effective mass of test particle and mean time dilation at the admissible points of space, taking into account the gravitational action of surrounding black holes. Having specified the statistics that governs extremal black holes, we study its effect on those quantities. Here, the role of statistics is to assign a statistical weight to the configurations of certain fixed number of black holes. We borrow these weights from Bose–Einstein, Fermi–Dirac, classical and infinite statistics. Using mean field approximation, the aforementioned characteristics are calculated and visualized, which permits us to draw the conclusions on visible effect of each statistics.

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 basic 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 quasi-equilibrium 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 of reaction to be 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 to complete. 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 in accord with each other. To demonstrate the effectiveness of the present theory, the enzymatic reaction of methylamine dehydrogenase and radioactive disintegration of Astatine into Bismuth are considered as numerical examples.

We investigate decoherence of quantum superpositions induced by gravitational time dilation and spontaneous emission between two atomic levels. It has been shown that gravitational time dilation can be a universal decoherence source by Pikovski et al. Here, we consider the decoherence induced by the gravitational time dilation only in the situation of spontaneous emission. We obtain the analytical results of the coherence of particle’s position state. Then, we obtain that the coherence of particle’s position state depends on reference frame because the time dilation changes the distinguishability of emitted photons from two positions of particle in different reference frames. For observing the decoherence effect induced by the gravitational time dilation, time-delayed feedback can be utilized to increase the decoherence of particle’s superposition state.

According to a new tired-light cosmological model, where $H(z)=H_0(1+z)$, the number density of galaxies has been nearly constant over the last 10Gyr, at least, meaning that, as far as galaxy counts are concerned, the Universe has been stationary. In this context, an analysis of the luminosity distances of quasars and supernovae Ia shows that the Universe is far from being as transparent as assumed nowadays, the photon lifetime along the line-of-sight being one third of the Hubble time. Such a “low” value could mean that there are huge amounts of grey dust in the inter galactic medium, that have so far escaped detection. It could also be a signature of “new physics,” namely, a consequence of the decay of photons into lighter particles.

The tired-light model advocated in this study would be falsified if, for instance, the time-dilation of remote events was shown to have a general character, that is, if it were definitely observed for phenomena other than the light curves of supernovae Ia. On the other hand, further developments are needed in order to turn this model into an actual cosmology. In particular, the physical origin of the current stability of the Universe on galactic scales remains to be identified.

A new penalization method is proposed for implementing the rigid bodies on the solution of the vorticity-stream function formulation of the incompressible Navier–Stokes equations. The method is based upon an active transformation of dependent variables. The transformation may be interpreted as time dilation. In this interpretation, the rigid body is considered as a region where the time is dilated infinitely, that is, time is stopped. The transformation is introduced in the vorticity and stream function equations to achieve a set of modified equations. The, in the modified equations, the time dilation of the solid region is approached to infinity. The mathematical and physical properties of the modified equations are investigated and implementation of the no-slip and no-penetration conditions are justified. Moreover, a suitable numerical method is presented for the solution of the modified equations. In the proposed numerical method, time integration is performed via the Crank–Nicolson method, and the semi-discrete equations are spatially discretized via second-order finite differencing on a uniform Cartesian grid. The method is applied to the fluid flow around a square obstacle placed in a channel, a sudden flow perpendicular to a thin flat plate, and the flow around a circular cylinder. The accuracy of the numerical solutions is evaluated.

It is known that very distant galaxies, much like our own, show remarkably high receding velocities, the magnitude of which increases with distance. Therefore, in this study, a gravitational analog of the photoelectric effect was investigated by replacing the classical (wave) theory of gravity with a gravity quanta hypothesis. The significance of this concept regarding the motion of distant galaxies is evaluated by comparing the results obtained for a photon traveling through a Planck lattice model of spacetime to the observational data for both the cosmological redshift and time dilation effects of light from distant Type Ia supernovae. The photogravity effect does not necessarily invalidate the standard big bang cosmology and may in fact add a layer of fidelity to its conclusions concerning the evolution and age of the universe.

Four-vectors are defined analogously to three-vectors and provide a compact means of presenting mathematical results in relativity theory. However, the four-velocity vector does not have the same physical significance as the three-velocity vector, but assuming so has led to the declaration that there is motion through spacetime which explains special relativistic time dilation. It is shown that four-velocity cannot legitimately be employed in this manner and that the time dilation effect does not require any motion through spacetime nor any speed through time.

Einstein’s theory of special relativity is one of the topics taught in undergraduate university physics courses. As undergraduates rarely have the opportunity to collect data and verify the concepts of Special Relativity, namely time dilation and length contraction, this paper aims to serve as a detailed instructional manual (self-contained) as well as provide insights from the undergraduates’ point of view on how to use a muon detector to collect data at various locations and altitudes in order to experimentally verify the aforementioned concepts. This experimental element enhances and complements the understanding of Special Relativity. The desktop muon detector used — the CosmicWatch Desktop Muon Detector V2 — was developed by the Department of Physics at Massachusetts Institution of Technology.

The notion of observers’ and their measurements is closely tied to the Lorentzian metric geometry of spacetime, which in turn has its roots in the symmetries of Maxwell’s theory of electrodynamics. Modifying either the one, the other or both ingredients to our modern understanding of physics, requires also a reformulation of the observer model used. In this presentation we will consider a generalized theory of electrodynamics, so called local and linear premetric, or area metric, electrodynamics and its corresponding spacetime structure. On this basis we will describe an observer’s measurement of time and spatial length. A general algorithm how to determine observer measurements will be outlined and explicitly applied to a first order premetric perturbation of Maxwell electrodynamics. The latter contains for example the photon sector of the minimal standard model extension. Having understood an observer’s measurement of time and length we will derive the relativistic observables time dilation and length contraction. In the future a modern relativistic description of the classical test of special relativity shall be performed, including a consistent observer model.

Time dilation is not only one of the most intriguing effects of Special Relativity (SR) but also one of its early experimental pillars. Following a proposal of Einstein, Ives and Stilwell¹ used the relativistic Doppler shift of optical lines emitted from Hydrogen canal rays to experimentally confirm time dilation on the percent level. We report a modern version of this experiment using laser spectroscopy on a beam of lithium ions in a storage ring (see fig. 1)…

Laser spectroscopy on high quality ion beams allows to explore physical properties of atoms and molecules and to test fundamental theories. An experiment to measure time dilation shows the potential.

An analysis of the net proper time difference for a Twin Paradox scenario is shown to require an asymmetric construct such as a special physics frame and also shows that Special Relativity’s time dilation equation does not describe proper time. An analysis of GPS confirms the need for a special physics frame and is sharply at odds with Special Relativity despite claims that GPS uses it.

A review of the literature on the Lyman alpha forest gives direct evidence on the dynamics of the universe. In an expanding universe one would expect the average temperature of the universe to fall as it expands - but a review of the Doppler parameters of the Hydrogen clouds in Quasar spectra shows that contrary to this, they are increasing in temperature (or at least, becoming increasingly disturbed) as the universe ages. Additionally, the evidence is that Hydrogen clouds are, on average, evenly spaced up to a redshift of one - if not beyond. These results beg the question, how is it that the Hydrogen clouds can have differing redshifts and hence widely differing ‘velocities’ whilst, on average, remain equally spaced? Especially since this range of redshifts includes the supernovae data used to show ‘acceleration’ and so called ‘time dilation.’ Taking these results in isolation implies that the universe has been static for at least the last billion years or so and therefore a new model of redshift is needed to explain redshifts in a static universe. The model proposed here is that in a static universe, photons of light from distant galaxies are absorbed and reemitted by electrons in the plasma of intergalactic space and on each interaction the electron recoils. Energy is lost to the recoiling electron (New Tired Light theory) and thus the reemitted photon has less energy, a reduced frequency and therefore an increased wavelength. It has been redshifted. The Hubble relationship becomes 'photons of light from a galaxy twice as far away, make twice as many interactions with the electrons in the plasma of IG space, lose twice as much energy and undergo twice the redshift. A relationship between redshift and distance is found and, using published values of collision cross-sections and number density of electrons in IG space, a value for the Hubble constant is derived which is in good agreement with measured values. Assuming that the energy transferred to the recoiling electron is emitted as secondary radiation; the wavelength is calculated and found to be consistent with the wavelengths of the CMB. A further test is proposed whereby a high powered laser could be fired through sparse cold plasma and the theories predicted increase in emission of microwave radiation of a particular frequency determined.