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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The role of preferred frames for light propagation and time dilation in the region of a massive, spherical, gravitating bodies, where according to general relativity, space–time curvature is described by the Schwarzschild metric equation, is discussed in the context of the Sagnac effect (for light propagation) and the Hafele–Keating experiment (for time dilation). Predictions for both translational and rotational motion relative to the preferred frame are calculated up to order (v / c) 3 . Different published theoretical calculations of the Sagnac effect are critically reviewed. The conflation in the literature of measured time differences in Sagnac experiments (a classical order v / c effect) and time dilation (a relativistic order (v / c) 2 effect) are also discussed. [ABSTRACT FROM AUTHOR]

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 10 Gyr, 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. [ABSTRACT FROM AUTHOR]

A central idea in general relativity is that physics should not depend on the spacetime coordinates in use [A. Einstein, The Meaning of Relativity (Princeton University Press, 1945)]. But the qualitative description of various phenomena can appear superficially quite different. Here, we consider falling into a classical black hole using four distinct but equivalent metrics. First is the Schwarzschild case, with extreme time dilation at the horizon. Second, rescaling the dilation allows falling into the hole in finite proper time. Third, time and space are rescaled into a Penrose motivated picture where light trajectories all have unit slope. Fourth, a white hole variation of the second metric allows passage out through the horizon, with reentry forbidden. [ABSTRACT FROM AUTHOR]

The results of two space experiments, around the world clocks and gravity probe B, are analyzed theoretically using a field theory. The field equations of this theory are reduced to those of general relativity outside material distribution, while its equations of motion are not a geodesic one. This equation violates the weak equivalence principle because of the non-vanishing torsion in the geometry used. The predictions of the theory give rise to the time dilation measured by the first experiment and to the geodetic and frame drag effects measured by the second experiment. Furthermore, we show that these predictions are affected by the torsion of space-time. The torsion term, in the equation of motion, is connected to other effects through a coupling parameter. This parameter is called the "spin-torsion" coupling if the moving test particle is elementary one with non-vanishing quantum spin. We call this parameter "rotation-torsion" coupling if the moving test particle is a gyroscope. In the first case, the coupling parameter is well defined and confirmed by terrestrial experiment, while in the second case the parameter still needs further investigation and discussion. [ABSTRACT FROM AUTHOR]

Rotational transformations describe relativistic effects in rotating frames. There are four major kinematic rotational transformations: the Langevin metric; Post transformation; Franklin transformation; and the rotational form of the absolute Lorentz transformation. The four transformations exhibit different combinations of relativistic effects and simultaneity frameworks, and generate different predictions for relativistic phenomena. Here, the predictions of the four rotational transformations are compared with recent optical data that has sufficient resolution to distinguish the transformations. We show that the rotational absolute Lorentz transformation matches diverse relativistic optical and nonoptical rotational data. These include experimental observations of length contraction, directional time dilation, anisotropic one-way speed of light, isotropic two-way speed of light, and the conventional Sagnac effect. In contrast, the other three transformations do not match the full range of rotating-frame relativistic observations. [ABSTRACT FROM AUTHOR]

Statements about relativistic effects are often subtle. In this essay we will demonstrate that the three classical tests of general relativity, namely perihelion precession, deflection of light and gravitational redshift, are passed perfectly by an extension of Newtonian gravity that includes gravitational time dilation effects while retaining a non-relativistic causal structure. This non-relativistic gravity theory arises from a covariant large speed of light expansion of Einstein's theory of gravity that does not assume weak fields and which admits an action principle. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study the variability properties of the prompt emission of Gamma-Ray Bursts in the gamma-ray energy range. We use the power spectrum analysis in the time domain as developed by [Margutti, in preparation]; this technique is suitable to study the rms variations at different time scales. The timing analysis of 252 Swift light-curves in the 15-150 keV energy range reveals the existence of different variability classes. Moreover, after accounting for the cosmological time dilation, the distribution of the GRB characteristic variability time scales is found to cluster around 0.6-1 s we identify this time scale as a characteristic variability time scale of long GRBs in the source rest frame. [ABSTRACT FROM AUTHOR]

In this paper, we explore the effect of gravity on the flow of proper time near static spherically symmetric black hole possessing an electric charge. We use the Reissner–Nordström metric. In the first case, the traveling twin travels away from the black hole and in the second it travels toward it. We then compare it with the case of relativistic kinematics where the static twin ages faster than the traveling twin. [ABSTRACT FROM AUTHOR]

We employed high-density microelectrode arrays to investigate spontaneous firing patterns of neurons in brain circuits of the primary somatosensory cortex (S1) in mice. We recorded from over 150 neurons for 10 min in each of eight different experiments, identified their location in S1, sorted their action potentials (spikes), and computed their power spectra and inter-spike interval (ISI) statistics. Of all persistently active neurons, 92% fired with a single dominant frequency — regularly firing neurons (RNs) — from 1 to 8 Hz while 8% fired in burst with two dominant frequencies — bursting neurons (BNs) — corresponding to the inter-burst (2–6 Hz) and intra-burst intervals (20–160 Hz). RNs were predominantly located in layers 2/3 and 5/6 while BNs localized to layers 4 and 5. Across neurons, the standard deviation of ISI was a power law of its mean, a property known as fluctuation scaling, with a power law exponent of 1 for RNs and 1.25 for BNs. The power law implies that firing and bursting patterns are scale invariant: the firing pattern of a given RN or BN resembles that of another RN or BN, respectively, after a time contraction or dilation. An explanation for this scale invariance is discussed in the context of previous computational studies as well as its potential role in information processing. [ABSTRACT FROM AUTHOR]

Mini superspace cosmology treats the scale factor a(t), the lapse function n(t) and an optional dilation field ϕ(t) as canonical variables. While pre-fixing n(t) means losing the Hamiltonian constraint, pre-fixing a(t) is serendipitously harmless at this level. This suggests an alternative to the Hartle-Hawking approach, where the pre-fixed a(t) and its derivatives are treated as explicit functions of time, leaving n(t) and a now mandatory ϕ(t) to serve as canonical variables. The naive gauge pre-fix a(t) = . is clearly forbidden, causing evolution to freeze altogether; so pre-fixing the scale factor, say a(t) = t, necessarily introduces explicit time dependence into the Lagrangian. Invoking Dirac's prescription for dealing with constraints, we construct the corresponding mini superspace time-dependent total Hamiltonian and calculate the Dirac brackets, characterized by {n, ϕ}D ≠ 0, which are promoted to commutation relations in the quantum theory. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

100 years after the invention of General Relativity (GR) and 110 years after the development of Special Relativity (SR) we have to state that until now no single experiment or observation allows any doubt about the validity of these theories within the accuracy of the available data. Tests of GR can be divided into three categories: (i) test of the foundations of GR, (ii) tests of the consequences of GR, and (iii) test of the interplay between GR and quantum mechanics. In the first category, we have tests of the Einstein Equivalence Principle and the structure of the Newton axioms, in the second category we have effects like the gravitational redshift, light defection, gravitational time delay, the perihelion shift, the gravitomagnetic effects as the Lense-Thirring and Schiff effect, and gravitational waves. Tests of the effects of gravity on quantum systems are a first step towards experiments searching for a quantum gravity theory. In this paper, we also highlight practical applications in positioning, geodesy, and the International Atomic Time. After 100 years, GR can now definitely be regarded also as practical and applied science. [ABSTRACT FROM AUTHOR]

Simultaneous nonlinear realizations of spontaneously broken supersymmetry in conjunction with other spontaneous and/or explicitly broken symmetries including R symmetry, global chiral symmetry, dilatations and the superconformal symmetries is reviewed. [ABSTRACT FROM AUTHOR]

The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR that may, by complementing the standard works, aid the understanding of SR and its fundamental principles in a more intuitive way. From the axiom that the velocity of light remains constant to any inertial observer, the geodesic is presented as a line of constant angle on the complex plane across a set of diverging reference frames. The resultant curve is a logarithmic spiral, and this view of the geodesic is extended to illustrate the relativistic Doppler effect, time dilation, length contraction, the twin paradox, and relativistic radar distance in an original way, whilst retaining the essential mathematical relationships of SR. Using a computer-generated graphical representation of photon trajectories allows a visual comparison between the relativistic relationships and their classical counterparts, to visualize the consequences of SR as velocities become relativistic. The model may readily be extended to other situations, and may be found useful in presenting a fresh understanding of SR through geometric visualization. [ABSTRACT FROM AUTHOR]

We received an Honorable Mention at the Gravity Research Foundation 2018 Awards for Essays on Gravitation by showing that a correct general relativistic interpretation of the Mössbauer rotor experiment represents a new, strong and independent proof of Einstein's general theory of relativity (GTR). Here, we correct a mistake which was present in our previous computations on this important issue by deriving a rigorous computation of the additional effect of clock synchronization. Finally, we show that some recent criticisms on our general relativistic approach to the Mössbauer rotor experiment are incorrect, by ultimately confirming our important result. [ABSTRACT FROM AUTHOR]

This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e.g. isotope Na 2 5 ) is a thermometer for an ultracold gas like the dipolar gas Na 2 3 K 4 0 . So, according to a Deformed Special Relativity (DSR) so-called Symmetrical Special Relativity (SSR), where there emerges an invariant minimum speed V in the subatomic world, one expects that the proper time of such a clock moving close to V in thermal equilibrium with the ultracold gas is dilated with respect to the improper time given in lab, i.e. the proper time at ultracold systems elapses faster than the improper one for an observer in the lab, thus leading to the so-called proper time dilation so that the atomic decay rate of an ultracold radioactive sample (e.g. Na 2 5 ) becomes larger than the decay rate of the same sample at room temperature. This means a suppression of the half-life time of a radioactive sample thermalized with an ultracold cloud of dipolar gas to be investigated by NASA in the Cold Atom Lab (CAL). [ABSTRACT FROM AUTHOR]

The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler–Lagrange equation, and relativistic Hamiltonian mechanics. We also formulate a modified local Lorentz transformation, such that the metric at a point is invariant only under the transformation defined at that point, and derive the formulae for time-dilation, length contraction, and gravitational redshift. Then we compare our formulation under non-relativistic approximations to the conventional ad hoc formulation, and we briefly analyze the relativistic Liénard oscillator and the spacetime it implies. [ABSTRACT FROM AUTHOR]

There are discernible and fundamental differences between clocks, waves and physical states in classical physics. These fundamental concepts find a common expression in the context of quantum physics in gravitational fields; matter and light waves, quantum states and oscillator clocks become quantum synonymous through the Planck-Einstein-de Broglie relations and the equivalence principle. With this insight, gravitational effects on quantum systems can be simply and accurately analyzed. Apart from providing a transparent framework for conceptual and quantitative thinking on matter waves and quantum states in a gravitational field, we address and resolve with clarity the recent controversial discussions on the important issue of the relation and the crucial difference between gravimetery using atom interferometers and the measurement of gravitational time dilation. [ABSTRACT FROM AUTHOR]

The gravitomagnetic field is the force exerted by a moving body on the basis of the intriguing interplay between geometry and dynamics which is the analog to the magnetic field of a moving charged body in electromagnetism. The existence of such a field has been demonstrated based on special relativity approach and also by special relativity plus the gravitational time dilation for two different cases, a moving infinite line and a uniformly moving point mass, respectively. We treat these two approaches when the applied cases are switched while appropriate key points are employed. Thus, we demonstrate that the strength of the resulted gravitomagnetic field in the latter approach is twice the former. Then, we also discuss the full linearized general relativity and show that it should give the same strength for gravitomagnetic field as the latter approach. Hence, through an exact analogy with the electrodynamic equations, we present an argument in order to indicate the best definition amongst those considered in this issue in the literature. Finally, we investigate the gravitomagnetic effects and consequences of different definitions on the geodesic equation including the second order approximation terms. [ABSTRACT FROM AUTHOR]

Selecting a system or a subset of systems that have the best performance among many alternative systems is an important area of research. All efforts are paid to do this selection with a high probability of correct selection P (C S). In this paper, we compare the performance of two popular procedures used to select the best systems, namely, the method of Kim and Nelson () which is considered as a ranking and selection procedure, and the Optimal Computing Budget Allocation ( ℬ) procedure. Both of these procedures determine the number of samples for each system that are needed to achieve the maximum P (C S). Recently, the ℬ has been developed in order to be able to approximate the value of P (C S) , so both procedures approximate the value of P (C S). To do the comparison, we implement the two methods on two examples; one is a generic example and the other one involves a management of inventory model. The two examples assure that the ℬ method always outperforms the method. [ABSTRACT FROM AUTHOR]

Quantum-gravitational pressure can stop gravitational collapse and cause a bounce. We observe that: (i) due to the huge time dilation, the process can last micro-seconds in local proper time and billions of years observed from the outside; (ii) the bounce volume can be much larger than planckian, because the onset of quantum-gravity effects is governed by density, not size; (iii) the emerging object can then be bigger than planckian by a factor (m/mP)n, where m is the initial mass, mP is the Planck mass, and n positive; (iv) the interior of an evaporating hole can keep memory of the initial mass, providing an independent scale for the physics of the final explosion. If so, primordial black holes could produce a detectable signal of quantum gravitational origin, which we estimate, under some hypotheses, around the wavelength 10-14 cm. [ABSTRACT FROM AUTHOR]