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With the mass-energy \(m=E(v=0)/c^{2}\) relation, all pivotal properties of special relativity have been now derived and we consider the related status of SR tests. 1) There are direct tests exploring i) the speed of light in different context, ii) the time dilation, iii) the body contraction, and iv) mass-energy relation. 2) The Michelson-Morley experiment tests indirectly body-contraction and more generally the relativity principle and aether properties. 3) Another family of tests addresses the verification of the Lorentz coordinate transformation. 4) We describe the Doppler effect tests which test relativity per se. We close with a discussion of time and how it is different from space.

The Special Theory of Relativity applies where gravitation is insignificant. There are many observations that remain poorly explained by the standard models of either the big of cosmology or the small of Quantum mechanics. The strength of the Scalar Theory Of Everything (STOE) is its ability to describe an extremely wide range of observations and to predict observations. Each of the STOE axioms has been used in the development of models of observations in the big and the small. The axioms that replace Special Relativity are: (1) Time is an abstraction of the duration between events causing events. (2) The diameter of the hods is the same throughout the universe. (3) The distance between hods is related to plenum density. Higher reduces the distance between hods. (4) The speed of photons and hods (light) is the greatest of any matter in a given environment. (5) The speed of the plenum wave is much faster than the speed of the hods. The STOE passes the tests of Special Relativity and does much more. The STOE is a major paradigm shift.

By means of the Lorentz Transformation, Einstein’s Special Theory of Relativity purports invariance of the standard wave equation. Counter-examples, satisfying the Lorentz Transformation, and hence Lorentz Invariance, prove that the Lorentz Transformation does not in fact produce invariance of the standard wave equation. Systems of clock-synchronised stationary observers are Galilean and necessarily transform by the Galilean Transformation. Einstein’s insistence that inertial (i.e. Galilean) systems of clock-synchronised stationary observers transform, not by the Galilean Transformation, but by the non-Galilean Lorentz Transformation, is logically inconsistent. The Special Theory of Relativity is therefore logically inconsistent. Therefore, it is false. The Lorentz Transformation is meaningless.

Relativity theory formulation is proposed, based not on the axiomatic postulation of its main principles but on their inference out of a thought experiment. With this approach, the experimentally observed independence of the speed of light from the motion of source and observer is a necessary consequence of the finiteness of propagation speed of all kinds of information. The mechanism of relativistic effects origination is described; the formulas of Lorentz transformations, Doppler quadratic effect, electromagnetic interaction and centrifugal force of inertia are derived.

It is shown that Ohm’s law is not only the main electrical engineering law, but also a generally scientific worldview law of the extreme significance, as in the interpretation of Steinmetz it proves physical reality of imaginary numbers theoretically and experimentally in the most indisputable way. Thus, it refutes the principle of light speed non-exceedance, which is fundamental in the special theory of relativity. Moreover, unlike the MINOS and OPERA experiments recognized by physical com-munity as not enough reliable, which were conducted for the same purpose, alternative experiments were performed during the research of oscillation processes in linear electric circuits. Therefore, they are absolutely reliable and conclusive as can be repeated and verified in any electrical engineering laboratory. The principle of phy-sical reality of imaginary numbers proven by the electrical engineering experiments is generally scientific, since mathematics is the universal language of the exact sciences. Therefore, all scientific theories and hypotheses in quantum mechanics, relativity theory, geo-physics, cosmology, optics, radio electronics and other sciences should be adjusted accordingly, given the principle of physical reality of imaginary numbers. There is an example of how this can be done in the special theory of relativity and astrophysics. This approach allowed explanation of dark matter and dark energy, which correspond to the invisible parallel universes existing in extra dimensions.

The Special Theory of Relativity applies where gravitation is insignificant. There are many observations that remain poorly explained by the standard models of either the big of cosmology or the small of Quantum mechanics. Each of the STOE axioms has been used in the development of models of observations in the big and the small. The strength of the Scalar Theory Of Everything (STOE) is its ability to describe an extremely wide range of observations and to predict observations. The axioms that replace Special Relativity are: (1) Time progression (d$t$) is a constant in the universe rather than the speed of light. (2) The diameter of the hods is the same throughout the universe. (3) The distance between hods is related to plenum density$\rho$. Higher $\rho$ reduces the distance between hods. (4) The speed of photons and hods is the greatest of any matter in a given environment. And (5) The speed of the plenum wave is much faster than the speed of the hods. The STOE passes the tests of Special Relativity and does much more. The STOE is a major paradigm shift.

Within the general theory of relativity, the curvature of spacetime is related to the energy and momentum of the present matter and radiation. One of the more specific predictions of general relativity is the deflection of light and particle trajectories in the gravitational field of massive objects. Bending angles for electromagnetic waves and light in particular were measured with a high precision. However, the effect of gravity on relativistic massive particles was never studied experimentally. Here we propose and analyze experiments devoted to that purpose. We demonstrate a high sensitivity of the laser Compton scattering at high energy accelerators to the effects of gravity. The main observable -- maximal energy of the scattered photons -- would experience a significant shift in the ambient gravitational field even for otherwise negligible violation of the equivalence principle. We confirm predictions of general relativity for ultrarelativistic electrons of energy of tens of GeV at a current level of resolution and expect our work to be a starting point of further high-precision studies on current and future accelerators, such as PETRA, European XFEL and ILC., Comment: 5+ pages. Published version. Description of experimental setup is drawn from arXiv:1401.3720 by another author

International audience; We present several experiments in fundamental physics that use atomic clocks and sensors together with high performance time/frequency transfer methods. Our account is far from being exhaustive and instead concentrates on a chosen subset of present and future experiments, whilst providing some theoretical background. We only give very brief overviews of the experiments and theories, but provide ample references for the interested reader.; Nous présentons plusieurs expériences en physique fondamentale qui utilisent les horloges et les capteurs atomiques en combinaison avec des méthodes de transfert en temps/fréquence de haute performance. Notre revue est loin d'être exhaustive et se concentre plutôt sur un sous-ensemble choisi d'expériences actuelles et futures, tout en fournissant un certain background théorique. Nous nous bornons à donner de brefs survols des expériences et des théories, mais fournissons d'amples références bibliographiques pour le lecteur intéressé par le sujet.

Some of the novel physical consequences of the Extended Relativity Theory in C-spaces (Clifford spaces) are presented. In particular, generalized photon dispersion relations which allow for energy-dependent speeds of propagation while still retaining the Lorentz symmetry in ordinary spacetimes, while breaking the extended Lorentz symmetry in C-spaces. We analyze in further detail the extended Lorentz transformations in Clifford Space and their physical implications. Based on the notion of “extended events” one finds a very different physical explanation of the phenomenon of “relativity of locality” than the one described by the doubly special relativity framework. We finalize with a discussion of the modified dispersion relations, rainbow metrics and generalized uncertainty relations in C-spaces which are extensions of the stringy uncertainty relations.

Some novel physical consequences of the Extended Relativity Theory in C-spaces (Clifford spaces) were explored recently. In particular, generalized photon dispersion relations allowed for energy-dependent speeds of propagation while still retaining the Lorentz symmetry in ordinary spacetimes, but breaking the extended Lorentz symmetry in C-spaces. In this work we analyze in further detail the extended Lorentz transformations in Clifford Space and their physical implications. Based on the notion of “extended events” one finds a very different physical explanation of the phenomenon of “relativity of locality” than the one described by the Doubly Special Relativity (DSR) framework. A generalized Weyl-Heisenberg algebra, involving polyvector-valued coordinates and momenta operators, furnishes a realization of an extended Poincare algebra in C-spaces. In addition to the Planck constant ħ, one finds that the commutator of the Clifford scalar components of the Weyl-Heisenberg algebra requires the introduction of a dimensionless parameter which is expressed in terms of the ratio of two length scales : the Planck and Hubble scales. We finalize by discussing the concept of “photons”, null intervals, effective temporal variables and the addition/subtraction laws of generalized velocities in C-space.

After the formulation of Special Relativity in 1905, Albert Einstein began looking for an extension of the theory, since Special Relativity has two limits: it favors a particular class of reference frames, the inertial frames (reference frames without acceleration, for which the law of inertia holds) and it cannot describe gravitational effects.

Local Lorentz invariance is an important component of General Relativity. Testing for Local Lorentz invariance can not only probe the foundation stone of General Relativity but also help to explore the unified theory for General Relativity and quantum mechanics. In this paper, we search the Local Lorentz invariance violation associated with operators of mass dimension d = 6 in the pure-gravity sector with short-range gravitational experiments. To enlarge the Local Lorentz invariance violation signal effectively, we design a new experiment in which the constraints of all fourteen violation coefficients may be improved by about one order of magnitude.

Fizeau experiment actually proves not partial, as the special relativity asserts, but complete dragging of the light by moving medium. The decrease of the fringe shift in the Fizeau's two-beam interferometer is explained not with wrong Fresnel's aether drag hypothesis but with the phase deviations arising in the interfering beams because of Doppler shift of the frequencies. Fizeau experiment does not prove but, on the contrary, refutes Einstein's theory of relativity.

we pointed out the idea of Einstein, light speed is independent of the observer i.e. The principle of light speed invariance is incorrect. Instead of Lorentz Transformation we suggested a new time-space transformation, this revision of the Relativity will deeply effect the development of Science and Technology.

Novel physical consequences of the Extended Relativity Theory in C-spaces (Clifford spaces) are explored. The latter theory provides a very different physical explanation of the phenomenon of “relativity of locality” than the one described by the Doubly Special Relativity (DSR) framework. Furthermore, an elegant nonlinear momentum-addition law is derived in order to tackle the “soccer-ball” problem in DSR. Neither derivation in C-spaces requires a curved momentum space nor a deformation of the Lorentz algebra. While the constant (energy-independent) speed of photon propagation is always compatible with the generalized photon dispersion relations in C-spaces, another important consequence is that these generalized photon dispersion relations allow also for energy-dependent speeds of propagation while still retaining the Lorentz symmetry in ordinary spacetimes, while breaking the extended Lorentz symmetry in C-spaces. This does not occur in DSR nor in other approaches, like the presence of quantum spacetime foam. We conclude with some comments on the quantization program and the key role that quantum Clifford-Hopf algebras might have in the future developments since the latter q-Clifford algebras naturally contain the κ-deformed Poincare algebras which are essential ingredients in the formulation of DSR.

is a difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravita -tional fields [1], [2]. It means that astro-nauts return from space having aged less than those who remained on Earth; to the traveling party, those staying at home are living faster, while to those who stood still, their counterparts in motion lived at a slower rate. The theory predicts such behavior, and experiments have dem-onstrated it beyond doubt. The phenom-enon is due to differences in velocity and in gravity (and it is called time dilation because the moving clock ticks slower). The effect would be greater if the astro-nauts were traveling nearer to the speed of light (approximately 300,000 km/s). Both factors—gravity and relative veloc-ity—are the culprits and actually opposed one another.Albert Eintein’s theory briefly states [3], [4]:1) In special relativity (hypothetically, far from all gravitational masses), clocks that are moving with respect to an inertial system of observation run slower. This effect is described by the Lorentz transformation.2) In general relativity, clocks within a gravitational field (as in closer prox-imity to a planet) are also found to run slower.The first paper by Einstein, published in 1905, introduced the special relativity theory (SRT), and the second one, pub-lished in 1916, dealt with the much more difficult general relativity theory (GRT).The Lorentz transformation (named for Hendrik Antoon Lorentz, 1853–1928) explains how the speed of light is indepen-dent of the reference frame. Lorentz shared the 1902 Nobel Prize in Physics with Pieter Zeeman (1865–1943) for the discovery and theoretical explanation of the Zeeman effect (the splitting of a spectral line into several components in the presence of a static magnetic field). The transformation describes how measurements of space and time by two observers are related, reflect-ing the fact that observers moving at dif-ferent velocities may measure different distances and elapsed times. It was derived well before special relativity.The first postulate of the TR, or prin -ciple of relativity, states that the laws of physics are the same in all inertial frames of reference. The speed of light

Throughout the violation of momentum-velocity parallelism and deformation of the Einstein equivalence principle, the model of faster- than-light motion, wherein both the Minkowski energy-momentum space and the Lorentz invariance, laying the foundations of Special Relativity and Standard Model, is constructed. Recently announced and denounced CERN's superluminal neutrinos are confronted.

A covariant theory of gravitation in flat space-time is stated and compared with general relativity. The results of the theory of gravitation in flat space-time and of general relativity agree for weak gravitational fields to low approximations. For strong fields the results of the two theories deviate from one another. Flat space-time theory of gravitation gives under some natural assumptions non-singular cosmological models with a flat space. The universe contracts to a positive minimum and then it expands for all times. Shortly, after the minimum is reached, the cosmological models of two theories approximately agree with one another if models in general relativity with zero curvature are considered. A flat space is proved by experiments.

An alternative presentation of a relativistic theory of gravitation, equivalent to general relativity, is given. It is based upon the restriction of the Lorentz invariance of special relativity from a global invariance to a local one. The resulting expressions appear rather simple as we consider the transformations of a local set of pseudo-orthonormal coordinates and not the geometry of a 4-dimension hyper-surface described by a set of curvilinear coordinates. This is the major difference with the usual presentations of general relativity but that difference is purely formal. The usual approach is most adequate for describing the universe on a large scale in astrophysics and cosmology. The approach of this paper, derived from particle physics and focused on local reference frames, underlines the formal similarity between gravitation and the other interactions inasmuch as they are associated to the restriction of gauge symmetries from a global invariance to a local one.

It is generally believed that special relativistic effects are important only when studying objects moving at speeds close to that of light. This belief leaves many practicing scientists and engineers with the impression that an understanding of relativity is not necessary for their day jobs. Our aim is to show that the ideas and mathematics of the special theory of relativity are used in practical applications involving objects moving much slower than the speed of light. In particular, we show how the Doppler shift for sound and light can be calculated from the postulates of relativity.

As shown earlier, a linear transformation with the same form for the spatial coordinates as the Lorentz transformation (LT), and that allows for time dilation, but leaves simultaneity invariant instead of the one-way speed of light, predicts the same results as the LT for the usual tests of special relativity. Such a transformation is allowed by general covariance. A complementarity between the invariance of the one-way speed of light and the invariance of simultaneity is discussed. Using this transformation, interpreted as involving external synchronization, it is shown that two frames moving uniformly with equal and opposite velocities, v and –v relative to a third inertial frame, in which clocks are synchronized so that the one-way speed of light is c, can be related by a Galilean-like transformation with a relative velocity 2v/(1-(v/c)2).These transformations do not form a group, hence the term “pseudo-Galilean” is used to distinguish them from the Galilean transformations. An analogy with the Sagnac effect is discussed, and consistency with the LT for stellar aberration, and the Doppler effect is shown. Implication of the above complementarity for the possible unification of quantum theory and gravitation is briefly discussed, as well as the inferred physical significance of general covariance.

In this paper, we present an explanation of several fundamental tests of special relativity from the perspective of the frame co-moving with a rotating observer. The solution is of great interest for real-time applications because Earth-bound laboratories are inertial only in approximation. We present the derivation of the Sagnac, Michelson–Morley, Kennedy–Thorndike and the Hammar experiments as viewed from the Earth-bound uniformly rotating frame or, as in the case of the Mossbauer rotor experiments, from the perspective of the rotating device. An entire section is dedicated to length/time measurement and to clock synchronization and another one to the Doppler effect and aberration on uniformly rotating platforms. This paper brings new information in the following areas: – new approach for clock synchronization on a rotating platform – new approach for length measurement in rotating frames – new explanation of the Doppler effect and of the Mossbauer rotor experiment – new explanation of the Kennedy–Thorndike experiment. The main thrust of this paper is to give a consistent explanation of various tests of special relativity as judged from the perspective of the rotating frame of the experimental setup. In addition, we correct certain misconceptions relative to clock synchronization and length measurement that have survived a long time in the specialty literature. A special chapter is dedicated to the derivation of the Doppler effect and of aberration in rotating frames. It is shown that such derivation is far from being trivial.

This article gives a brief summary on recently obtained classical lagrangians for the nonminimal fermion sector of the Standard-Model Extension (SME). Such lagrangians are adequate descriptions of classical particles that are subject to a Lorentz-violating background field based on the SME. Explicitly, lagrangians were obtained for the leading nonminimal contributions of the m, a, c, e, and f coefficients. These results were then used to interpret classical, kinematic tests of Special Relativity in the framework of the nonminimal SME. This led to new constraints on certain nonminimal controlling coefficients. Although the experiments were very sophisticated in the era when they were carried out, their sensitivities for detecting Lorentz violation were still far away from the Planck scale. Obtaining the novel constraints can be considered as a proof-of-principle demonstrating the applicability of the classical lagrangians computed., Comment: Presented at the Seventh Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 20-24, 2016

Superconducting-gravimeter measurements are used to test the local Lorentz invariance of the gravitational interaction and of matter-gravity couplings. The best laboratory sensitivities to date are achieved via a maximum-reach analysis for 13 Lorentz-violating operators, with some improvements exceeding an order of magnitude., Comment: 5 pages, 1 figure, published version

This Letter, i.e. for the first time, proves that a general invariant velocity is originated from the principle of special relativity, namely, discovers the origin of the general invariant velocity, and when the general invariant velocity is taken as the invariant light velocity in current theories, we get the corresponding special theory of relativity. Further, this Letter deduces triple special theories of relativity in cosmology, and cancels the invariant presumption of light velocity, it is proved that there exists a general constant velocity K determined by the experiments in cosmology, for K > 0, = 0 and < 0, they correspond to three kinds of possible relativistic theories in which the special theory of relativity is naturally contained for the special case of K > 0, and this Letter gives a prediction that, for K < 0, there is another likely case satisfying the principle of special relativity for some special physical systems in cosmology, in which the relativistic effects observed would be that the moving body would be lengthened, moving clock would be quickened. And the point of K = 0 is a bifurcation point, through which it gives out three types of possible universes in the cosmology (or multiverse). When a kind of matter with the maximally invariant velocity that may be superluminal or equal to light velocity is determined by experiments, then the invariant velocity can be taken as one of the general invariant velocity achieved in this Letter, then all results of current physical theories are consistent by utilizing this Letter's theory., 12 pages, 6 figures

We explore some novel consequences of Born's reciprocal relativity theory in flat phase-space and generalize the theory to the curved space–time scenario. We provide, in particular, six specific results resulting from Born's reciprocal relativity and which are not present in special relativity. These are: momentum-dependent time delay in the emission and detection of photons; energy-dependent notion of locality; superluminal behavior; relative rotation of photon trajectories due to the aberration of light; invariance of areas-cells in phase-space and modified dispersion relations. We finalize by constructing a Born reciprocal general relativity theory in curved space–time which requires the introduction of a complex Hermitian metric, torsion and nonmetricity. The latter procedure can be extended to the curved phase-space scenario.

It is now widely acknowledged that cosmic rays experiments can test possible new physics directly generated at the Planck scale or at some other fundamental scale. By studying particle properties at energies far beyond the reach of any man-made accelerator, they can yield unique checks of basic principles. A well-known example is provided by possible tests of special relativity at the highest cosmic-ray energies. But other essential ingredients of standard theories can in principle be tested: quantum mechanics, uncertainty principle, energy and momentum conservation, effective space-time dimensions, hamiltonian and lagrangian formalisms, postulates of cosmology, vacuum dynamics and particle propagation, quark and gluon confinement, elementariness of particles... Standard particle physics or string-like patterns may have a composite origin able to manifest itself through specific cosmic-ray signatures. Ultra-high energy cosmic rays, but also cosmic rays at lower energies, are probes of both "conventional" and new Physics. Status, prospects, new ideas, and open questions in the field are discussed. The Post Scriptum shows that several basic features of modern cosmology naturally appear in a SU(2) spinorial description of space-time without any need for matter, relativity or standard gravitation. New possible effects related to the spinorial space-time structure can also be foreseen. Similarly, the existence of spin-1/2 particles can be naturally related to physics beyond Planck scale and to a possible pre-Big Bang era., Talk given at the Cosmic Ray International Seminar - CRIS 2010, Catania, 13-17 September 2010. A Post Scriptum added to the version published by Nuclear Physics Proceedings. 13 pages

Relativistic transformations and their application to electrodynamics of a weakly accelerated electron considered in [A. Einstein, Zur Elektrodynamik der bewegter Korper, Annalen der Physik, 17 (1905) 891-921] are further analyzed in their relation to the principle of relativity, the concept of mass, and the mass-energy equation. Alternative consideration in dynamics of weakly accelerated electrons demonstrates that the factors in longitudinal @[email protected]^3 and transverse @[email protected]^2 masses of an electron with the mass @m at rest naturally appear in observed accelerations as a result of relativistic transformations, without any deviation from the principle of relativity and the second Newton's law of motion. As concerns the special relativity in accelerated motion, this allows us to retain the concept of mass as scalar characteristic of an accelerated body. It is argued that ''the principle of equivalence of the mass and energy of rest'' (Einstein) depends on the speed of the information transmitting signal by which the observation (measurement) is made (synchronization of clocks is achieved), so that relativistic equation E=mc^2 appears as an image phenomenon which essentially depends on the propagation of light as a measuring signal and on its speed V=c as the critical parameter of Einstein's relativistic transformations. It is demonstrated that the spherical waves considered by Einstein are distorted in real time, and the fundamental Lorentz invariant is not crisp, but presents a soft interval whose diameter is in the range of 30,000 km for time delays of 0.1 s in transmission of information. The results open new avenues for further research in the theory of relativity and its applications.

The Mansouri–Sexl theory is a well-known test theory of relativity. In the following paper we demonstrate a novel way of detecting second-order effects in terms of both lab and ion speed for light speed anisotropy detection. Prior literature15,18–21 has shown the way of constraining the Mansouri–Sexl parameter "a" via the Ives–Stilwell experiment, however, the prior approaches have proven to be incomplete in managing to constrain only one parameter, the "a" parameter. In the current paper we will take the unprecedented step of reconstructing the Mansouri–Sexl formalism for the Ives–Stilwell experiment and by showing how to improve on the theoretical and experimental bases such as to constrain both the parameter "a" and the parameter "b". Our paper is organized as follows: in the first section we give a new and more complete derivation of the Mansouri–Sexl Doppler effect. In the second part, we apply the newly expanded Mansouri–Sexl Doppler formalism in order to revise the principles of the Ives–Stilwell experiment. We continue by showing how the revised experiment is to be used in order to constrain both the parameter "a" and the parameter "b" in a measurement of light speed isotropy. This turns the Mansouri–Sexl Ives–Stilwell experiment into a very powerful tool for constraining light speed anisotropy.

Classical optical experiments that confirm the validity of special relativity are considered. Transformations of spatial coordinates and time that were proposed at different times for the passage from one inertial reference frame (IRF) to another and that differ from the classical Lorentz transformations are critically analyzed. It is shown that, although some of these transformations are capable of explaining the results of single classical optical experiments, in particular, the Michelson-Morley experiments, neither of them, except for the Tangherlini transformations, can explain the results of the entire set of these experiments. The discrepancy between the predictions of incorrect transformations and the results of the well-known experiments is caused by the absence of a clearly formulated procedure for synchronizing spaced clocks in a rest IRF (where the observer is located) and a moving IRF, which should be consistent with the transformation of time. A number of relativistic and quantum effects are indicated, which have been predicted but not yet detected, to a search for which efforts of physicists are directed, and which are convenient to describe with the help of the formalism of the Tangherlini transformations.

The paper highlights a recent debate in the quantum gravity community on the status of Lorentz invariance in theories that introduce a fundamental length scale, and in particular in deformed special relativity. Two arguments marshaled against that theory are examined and found wanting.

We review the experimental evidence for Einstein’s general relativity. A variety of high precision null experiments 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. Binary pulsars test gravitational-wave damping and aspects of strong-field general relativity. During the coming decades, tests of general relativity in new regimes may be possible. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests via precise measurements of the properties of gravitational waves. Future efforts using X-ray, infrared, gamma-ray and gravitational-wave astronomy may one day test general relativity in the strong-field regime near black holes and neutron stars.

We propose a new interpretation of doubly special relativity (DSR) based on the distinction between the momentum and the translation generators in its phase space realization. We also argue that the implementation of DSR theories does not necessarily require a deformation of the Lorentz symmetry, but only of the translation invariance., 10 pages, plain TeX

In his book, Physical Relativity, Harvey Brown challenges the orthodox view that special relativity is preferable to those parts of Lorentz’s classical ether theory it replaced because it revealed various phenomena that were given a dynamical explanation in Lorentz’s theory to be purely kinematical. I want to defend this orthodoxy. The phenomena most commonly discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other phenomena of this kind that played a role in the early reception of special relativity in the physics literature: the Fresnel drag eect in the Fizeau experiment, the velocity dependence of electron mass in -ray deflection experiments by Kaufmann and others, and the delicately balanced torques on a moving charged capacitor in the Trouton-Noble experiment. I oer historical sketches of how Lorentz’s dynamical explanations of

Like Euclid, Riemann and Lobachevski geometries are on an almost equal footing, based on the principle of relativity of maximum symmetry proposed by Professor Lu Qikeng and the postulate on invariant universal constants c and R, the de Sitter/anti-de Sitter (dS/AdS) special relativity on dS/AdS-space with radius R can be set up on an almost equal footing with Einstein’s special relativity on the Minkowski-space in the case of R→∞. Thus the dS-space is coin-like: a law of inertia in Beltrami atlas with Beltrami time simultaneity for the principle of relativity on one side, and the proper-time simultaneity and a Robertson-Walker-like dS-space with entropy and an accelerated expanding S 3 fitting the cosmological principle on another side. If our universe is asymptotic to the Robertson-Walker-like dS-space of R ≃ (3/Λ)1/2, it should be slightly closed in O(Λ) with entropy bound S ≃ 3πc 3 k B /ΛGħ. Contrarily, via its asymptotic behavior, it can fix on Beltrami inertial frames without ‘an argument in a circle’ and acts as the origin of inertia. There is a triality of conformal extensions of three kinds of special relativity and their null physics on the projective boundary of a 5-d AdS-space, a null cone modulo projective equivalence [ $$ \mathcal{N} $$ ] ≅ ∂ P (AdS 5). Thus there should be a dS-space on the boundary of S 5 × AdS 5 as a vacuum of supergravity. In the light of Einstein’s ‘Galilean regions’, gravity should be based on the localized principle of relativity of full maximum symmetry with a gauge-like dynamics. Thus, this may lead to the theory of gravity of corresponding local symmetry. A simple model of dS-gravity characterized by a dimensionless constant g ≃(ΛGħ/3c 3)1/2 ∼ 10−61 shows the features on umbilical manifolds of local dS-invariance. Some gravitational effects out of general relativity may play a role as dark matter. The dark universe and its asymptotic behavior may already indicate that the dS special relativity and dS-gravity be the foundation of large scale physics.

Special relativity derives directly from the principle of relativity and from Newton's laws of motion with a single undetermined parameter, which is found from Faraday's and Ampère's experimental work and from Maxwell's own introduction of the displacement current to be the − c −2 term in the Lorentz transformations. The axiom of the constancy of the speed of light is quite unnecessary. The behaviour and the mechanism of the propagation of light are not at the foundations of special relativity.

An experiment to directly test the second postulate of special relativity is described. The speed of photons, resulting from the annihilation of either thermal positrons or in-flight positrons (moving with relativistic velocity), is measured using two complementary variations of the same basic experiment. For both at rest and moving positrons the constancy of the speed of light was confirmed to an accuracy of approximately 1%. This apparatus can be used in an advanced undergraduate laboratory and also used to place limits on alternative theories to special relativity that have transformations other than the Lorentz transformation.

The Eotvos experiment on the verification of equivalence between inertial mass and gravitational mass of a body is famous for its accuracy. A question is, however, can these experimental results be applied to the case of a physical space in general relativity, where the space coordinates could be arbitrary? It is pointed out that it can be validly applied because it has been proven that Einstein's equivalence principle for a physical space must have a frame of reference with the Euclidean-like structure. Will claimed further that such an overall accuracy can be translated into an accuracy of the equivalence between inertial mass and each type of energy. It is shown that, according to general relativity, such a claim is incorrect. The root of this problem is due to an inadequate understanding of special relativity that produced the famous equation E = mc2, which must be understood in terms of energy conservation. Concurrently, it is pointed out that this error is a problem in Will's book, `Theory and Experiment in Gravitational Physics'.

This article is an overview of the contributions numerical relativity has made to our understanding of strong field gravity, to be published in the book "General Relativity and Gravitation: A Centennial Perspective", commemorating the 100th anniversary of general relativity.