Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, special relativity uses the assumption about the Euclidean structures of gravity-free space and time in the usual inertial coordinate system. Introducing the so-called primed inertial coordinate system, in addition to the usual inertial coordinate system, for each inertial frame of reference, we assume the Euclidean structures of gravity-free space and time in the primed inertial coordinate system and their generalized Finslerian structures in the usual inertial coordinate system. We combine this assumption with the two postulates (i) and (ii) to modify special relativity.
The generalized Finsler geometry, as well as Finsler geometry, is a generalization of Riemann geometry. The generalized Finsler geometry can be endowed with the Cartan connection. The generalized Finsler geometry and its Cartan connection are, as the necessary mathematical tools, involved in our modification of special relativity, which is made by assuming the generalized Finslerian structures of gravity-free space and time in the usual inertial coordinate system and combining this assumption with two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed o…
The speed of light is usually taken as one of the fundamental constants. String, and field, theories appear to require the altercation of this constant into a functional form $E(m,c)$ which is not $E=mc^2$. The analysis requires the re-interpretation of the renormalization group flow equations. There are quantum corrections to the mass-energy relation generically for particles of any sort. A breakdown of special relativity follows. Cosmological data might be one of the best testbeds to analyze the computable functional forms of the mass energy relations.
Transformation equations for the kinetic energy of the same bullet in Galileo's and Einstein's special relativity are derived. The special relativity result is extended to the case of a photon.
The third modification of the space-time geometry is considered. (The first modification is the spacial relativity, the second one is the general relativity.) After the third modification of the space-time geometry the motion of free particles become to be primordially stochastic (multivariant). This circumstance forces one to construct a multivariant dynamics. The multivariant dynamics is the classical dynamics in the non-Riemannian space-time geometry. The multivariant dynamics explains quantum effects without a reference to the quantum principles. Elimination of quantum principles admits on…
The root of the divergence problem in the current quantum field theory seems to be in the special theory of relativity. Here we propose a modified special relativity theory by introducing the primed inertial coordinate system, in addition to the usual inertial coordinate system, for each inertial frame of reference, assuming the flat structures of gravity-free space and time in the primed inertial coordinate system and their generalized Finslerian structures in the usual inertial coordinate system, and combining this assumption with the two fundamental postulates, (i) the principle of relativi…
An orbiting `photon clock' is proposed to test directly the relativity of simultaneity of special relativity. This is done by comparison of the arrival times at a ground station of three microwave signals transmitted by two satellites following the same low Earth orbit.
Different formulations of special relativity are theoretically discussed. First an invariant formulation, i.e., the ''true transformations (TT) relativity,'' is exposed. There a physical quantity is represented by a true tensor which comprises both components and a basis. Also the usual covariant formulation and the ''apparent transformations (AT) relativity'' are considered. It is shown that all the experiments are in agreement with the ''TT relativity'' but not always with the ''AT relativity.''
A new approach to special relativity is presented which introduces coordinate systems with imaginary time axes, observation systems, and coordinate bases.
We present an introduction to special relativity kinematics stressing the part played by clocks synchronized following a procedure proposed by Einstein.
The most general form of transformations of spacetime coordinates in Special Theory of Relativity based solely on physical assumptions are described. Only the linearity of spacetime transformations and the constancy of the speed of light are used as assumptions. The application to tachyonic motion is indicated.
The correction to Maxwell-Boltzmann's velocity distribution law is obtained in the framework of the modified special relativity theory. The detection of velocity and velocity rate distributions for thermal molecules or atoms or other particles can serve as a test of the modified special relativity theory.
Fractional calculus represents a natural tool for describing relativistic phenomena in pseudo-Euclidean space-time. In this study, Fractional modified special relativity is presented. We obtain fractional generalized relation for the time dilation.
Handling substance-like physical quantities in the limits of special relativity theory we should make a net distinction between those which present a proper (rest) magnitude and those which have not. We show how the theory relates them via relativistic transformation equations.
Within an axiomatic framework of kinematics, we prove that the existence of faster than light particles is logically independent of Einstein's special theory of relativity. Consequently, it is consistent with the kinematics of special relativity that there might be faster than light particles.
A modest aim of this pedagogical presentation is to analyze, critically, certain fundamental physical concepts to illustrate the physical principles behind the special theory of relativity and, hence, to also illustrate the limitations of its applicability.
In Special Relativity there are infinitely many equivalence classes of frames of reference. In each such class every two frames of reference move uniformly with respect to one another. It appears that the following questions have never been asked : 1) In which of such equivalence classes of frames of reference is Special Relativity supposed to hold ? 2) How can we identify such a class, and do so theoretically or empirically ?
Controversies arise when specialists disagree on some particular issue. This normally occurs in any scientific brunch. We analyze some controversies, which have a good cause in Special Relativity. The paper does not question Special Relativity Theory but it challenges changing deeply held academic beliefs about imaginary experiments in Special Relativity Theory. PACS 03.30.+p
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, f…
We investigate the conditions under which computer programs represent correctly, in polar coordinates, the relativistic transformation equations for the space-time coordinates of the same event.
This paper has pedagogical motivation. It is not uncommon that students have great difficulty in accepting the new concepts of standard special relativity, since these seem contrary to common sense. Experience shows that geometrical or graphically exposition of the basic ideas of relativity theory improves student understanding of the algebraic expressions of the theory. What we suggest here may complement standard textbook approaches.
In the framework of special relativity, all particles are point-like or string-like. This nature of particles has caused the divergence difficulties in quantum field, string and superstring theories. In the framework of special relativity, due to the non-uniformity of the m-space and phase space in the usual inertial coordinate system, Boltzmann's hypothesis of the equality of the probability of equal volume element is no longer appropriate. That makes it very difficult to construct Lorentz-invariant statistical mechanics and thermodynamics for many-particle systems. Besides, some observations…
It is proved that local Lorentz transformations for different systems cannot derive varying speed of light. Based on the special relativity principle, an invariant speed is necessarily obtained. Therefore, the exact basic principles of the special relativity should be redefined as: I. The special relativity principle, which derives necessarily an invariant speed. II. Suppose that the invariant speed in the theory is the speed of light in the vacuum c. If the second principle does not hold, for example, the superluminal motions exist, the theory will be still the extensive special relativity, i…
We take Co-Operative Phenomena as a common physical conceptual base to speculate on the existence of a medium and the properties that it must have to physically understand some of the problems in Special Relativity, Gravitation and Quantum Mechanics.
Evaluation of the additive constants in the space-time Lorentz transformation equations required, according to Einstein, to correctly describe synchronised clocks at different spatial locations, reveals the spurious and unphysical nature of the 'relativity of simultaneity' and 'length contraction' effects of conventional special relativity. Unlike time dilation, there is no experimental evidence for these putative effects. Only a universal (position independent) time dilation effect for different inertial frames distinguishes special from Galilean relativity.
The Special Theory of Relativity and the Theory of the Electron have had an interesting history together. Originally the electron was studied in a non relativistic context and this opened up the interesting possibility that lead to the conclusion that the mass of the electron could be thought of entirely in electromagnetic terms without introducing inertial considerations. However the application of Special Relativity lead to several problems, both for an extended electron and the point electron. These inconsistencies have, contrary to popular belief not been resolved satisfactorily today, eve…
The special theory of relativity is the foundation of modern physics, but its unusual postulate of invariant vacuum speed of light results in a number of plausible paradoxes. This situation leads to radical criticisms and suspicions against the theory of relativity. In this paper, from the perspective that the relativity is nothing but a geometry, we give a uniform resolution to some famous and typical paradoxes such as the ladder paradox, the Ehrenfest's rotational disc paradox. The discussion shows that all the paradoxes are caused by misinterpretation of concepts. We misused the global simu…
We show the compatibility of the theory of special relativity with the absolute reference frame with a longitudinal Doppler shift. Using two absolute velocities vA and vS, the relative velocity u is derived. Thereafter the Doppler frequency is derived using the relative velocity u. We also show the method for detecting the absolute reference frame. The representation of the theory of special relativity using the absolute reference frame appears more intuitive than an orthodox interpretation.
Transverse redshift effects are sometimes presented as being unique to special relativity (the "transverse Doppler effect"). We argue that if the detector is aimed at 90 degrees in the laboratory frame, most theories will predict a redshifted frequency at the detector, although these predictions can be concealed by specifying that angles should be defined in a frame /other/ than the laboratory frame. These redshifts are often stronger than special relativity's predictions. We list some of the situations in which lab-transverse redshifts would be expected.
Einstein's argument on the relativity of simultaneity itself is the first result of the special theory of relativity. The nature of this result is explored, and implications of this result for the structure and functioning of the physical world found in the special theory are discussed.
Based on two previous papers, the physical meaning of synchronization and simultaneity as is presented in Einstein's Special Relativity paper of 1905 is reconsidered. We follow Einstein's argumentation to introduce a criterium of synchronization and for the same arguments we arrive at a different criterium for synchronization. From that we conclude that simultaneity is absolute.
An orbiting `photon clock' is proposed to test directly the relativity of simultaneity effect of special relativity. This is done by exchanging microwave signals between two satellites in low Earth orbit carrying clocks that have previously been synchronised in the Earth-centered inertial system. A similar experiment using synchronised signals from two GPS satellites with the receiver on a single satellite in low Earth orbit, is also proposed.
Modification of special theory of relativity is proposed to describe the propagation of signals with superluminal velocity. Modified kinematics and Lorentz transformations of Maxwell's equations are described. A possible experiment on measuring the speed of light for verification of the theory is discussed. It is shown that replacing the maximum speed in special theory of relativity by the neutrino superluminal velocity measured by the OPERA collaboration leads to lower value of the muon mass reconstructed from the muon decay products with the modified relativistic kinematics. This value is in…
In order to respect the Principle of Relativity, the analysis of the behavior of the longitudinal light clock reveals the necessity to extend the Doppler effect also to space and time. As a consequence, the bodies in inertial motion must dilate along the direction of their movement.
A phenomenological explanation is presented for the physics of aberration, which is in contrast with special relativity physics. The effect of relativity is identified with an effect due to the velocity of observation being affected by the velocity of a moving particle. In contrast with the currently accepted view, it is demonstrated that the classical concepts of time and simultaneity are natural for describing relativistic phenomena.
The modern view, that there exists a preferred frame of reference related to the cosmic microwave background (CMB), is in apparent contradiction with the principles of special relativity. The purpose of the present study is to develop a counterpart of the special relativity theory that is consistent with the existence of a preferred frame but, like the standard relativity theory, is based on the relativity principle and universality of the (\textit{two-way}) speed of light. In the framework developed, a degree of anisotropy of the one-way velocity acquires meaning of a characteristic of the re…
We compare the results obtained by interpreting some fundamental relativistic experiments from the point of view of two alternative theories: Einstein's special relativity theory and the Lorentz-Poincare theory admitting the existence of a special reference frame relative to which we can measure absolute velocities. The experiments that we consider here are the time dilation, the radar echo, the Doppler Effect and the radar detection. The most important result is that both theories lead to the Lorentz-Einstein transformations for the space-time coordinates of the same event. This conclusion en…
We look afresh at the deduction of the "Lorentz contraction" of a "rod" from the Lorentz transformation equations of the special theory of relativity. We show that under special conditions, which include acceleration of the "rod", length "expansion" and "invariance" are possible, and thus these are purely kinematical phenomena. We then take a closer look at Einstein's two famous papers on the special theory of relativity and point out a flaw in his argument. It seems that it is possible to have the times of the clocks of two, and indeed all, inertial systems to agree with each other.
The properties of the light, the Lorentz transformations and the relation mass-energy are introduced using the wave picture of the light and of the massive particles.
Invariance of the counted number of photons and the Lorentz-Einstein transformations enable us to derive transformation equations for the physical quantities introduced in order to characterize energy emission and transport in a plane and in a spherical electromagnetic wave propagating in vacuum.
The relativistic time dilatation effect and Einstein's second postulate of special relativity are used to analyse train/embankment thought expriments, both Einstein's original one, and an extension where observers on two trains moving at different speeds, as well as on the embankment, are considered. Whereas the relativistic analysis of Einstein's experiment shows, in contradiction to Einstein's interpretation, no `relativity of simultaneity' effect, the latter is apparent for certain events in the two-train experiment. The importance of relativistic kinematics --embodied for photons in Einste…
In this paper the transport phenomena in On-Chip-Transmission Line are investigated . The transport equation are developed and solved. The near light speed phenomena in OCTL are investigated Key words: On-chip transmission line, transport phenomena, near light speed phenomena
The special theory of relativity is constructed demanding the retention of the rectilinear form of a trajectory and invariance of the wave equation under linear transformations of space and time coordinates. The usual approach to relativity based on manipulations with the impulse of light is shown to be owing to that the symmetry of the particular solution of the wave equation coincides with the symmetry of the very wave equation. Thereof instead of the equation in partial derivatives we may deal with the algebraic form referred to as the interval.
We show that a topology can be defined in the four dimensional space-time of special relativity so as to obtain a topological semigroup for time. The Minkowski 4-vector character of space-time elements as well as the key properties of special relativity are still the same as in the standard theory. However, the new topological structure allows the possibility of an intrinsic asymmetry in the time evolution of physical systems.
We present a solution for the apparent paradox regarding an incompatibility between the Lorentz force law and special relativity presented by Mansuripur [Phys. Rev. Lett. 108, 193901 (2012)]. A connection between the apparent paradox and the Abraham-Minkowski debate about the momentum of electromagnetic waves in material media is also presented.
In the special relativity, a rigid rod slides upon itself, with one extremity oscillating harmonically. We discovered restrictions in the amplitude of the motion and in the length of the rod, essential to eliminate unphysical solutions. ------- Cxe la speciala relativeco, rigida stango movigxas sur si mem, kun unu fino oscilante harmonie. Ni malkovris limigajn kondicxojn pri la amplitudo de movado kaj pri la longo de stango, necesegaj por elimini ne-fizikajn solvojn.
This is a write-up of two lectures delivered at COST CA18108 First Training School. They cover the motivations and some basic technical results in the field of Doubly Special Relativity and Relative Locality. The energy-dependent speed of light is a recurring theme here. The soccer ball problem is also briefly described. The video recording of these and other lectures can be found at https://www.youtube.com/channel/UChRfzgjTkO9sOkwq358kHZw/videos.
