It is shown that if we can define a physical quantity with proper character in a given inertial reference frame (kinematic, dynamic, electromagnetic in its nature) which transforms when detected from a reference frame relative to which it moves with velocity $u_x$ as $F=\f{F^o}{\sqrt{1-\f{u_x^2}{c^2}}}$ then we can derive for it transformation equations following one and the same procedure, which involves the addition law of relativistic velocities which can be derived without using the Lorentz transformations. The transformation equation derived that way, generates the physical quantities $u_xF$ and $u_x'F'$, for which physicists invent names reflecting theirs physical meaning.
Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial solutions: Einstein special theory of relativity and Newton gravitation theory), quantum mechanics, and observations, too.
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.
A thought experiment first proposed by Sartori is analysed using the parallel velocity addition formula of special relativity. The distances and proper-time intervals between some similarly defined spatial coincidence events are found to be widely different in different inertial frames. This relativity of space and time intervals is quite distinct from the well-known time-dilatation and length contraction effects of special relativity. Sartori's claimed derivation of the parallel velocity addition formula, assuming relativistic time dilatation, based on the thought experiment, is shown to be f…
Let $r(φ)$ denote the orbit of Mercury. We compare the formulae obtained via general relativity for $r(φ)$ and for the corresponding perihelion precession angle $Δφ$, with the formulae obtained via the relativistic gravitational law, $F=GMmγ^6/r^2$. The latter law can be derived from Newton's gravitational law by employing the gravitational rather than the rest masses of the Sun and Mercury. Remarkably, it is found that the two expressions for the dominant part of $r(φ)$ are identical and that the two expressions for $Δφ$ are also identical.
After having shown that the corresponding components of a four vector transform via the same transformation factors as the space-time coordinates of the same event do, we design a relativistic diagram that displays in true values theirs components. One diagram works for events generated by tardyons whereas a second diagram works for events generated by light signals or photons. We consider both approaching and receding tardyons respectively photons in each case. We also show how the relativistic diagram for radar and photographic detections of moving profiles.
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.
In previous work, the author extended the Poincare Lie algebra to include a four position operator as a natural extension to a large fifteen parameter Lie algebra of operators. We here propose to generalize the metric contained in those structure constants to be the Riemann metric as determined by Einstein's equations from the energy momentum tensor. This gives a new type of "Lie" algebra whose structure constants are space-time dependent. One obtains a new type of uncertainty principle in strong gravitational fields and an altered spectra for the hydrogen atom.
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…
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.
Beside the rise of total cross sections or interaction radii of colliding high energetic particles and the shrinkage of mean-free-paths of ultra relativistic particles (nucleii) in material media (anomalons), which have been shown to be of special relativistic origin [1], still other phenomena in high energy physics may arise from relativistic kinematics. In particular this seems to be the case with the EMC-effect and the so called atmosperic neutrino anomaly.
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.
We first define the functions which ensure the transformation of momentum and energy of a tardyon, the transformation of the wave vector and the frequency of the associated wave. Having done this, we show that they ensure the relativistic invariance of the quotient between momentum and wave vector and between energy and frequency if the product between particle velocity u and phase velocity w is a relativistic invariant (uw=c^2), a condition which is a natural combination of special relativity theory and quantum mechanics.
By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear algebra are employed for the development of the present work.
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta of velocity. It is shown that the resulting space-time geometry is Gaussian and the four-vector calculus has its roots in the complex-number algebra, furthermore, that Einstein's "relativity of simultaneity" is based on a misinterpretation of the principle of relativity. Among others predictions of the experimentally verified rise of the interaction-radii o…
It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the kinetic energy operator which relation with the ususal one is consistent with corresponding relation of kinetic energies in special relativity theory. The Schrödinger equation with this operator gives new interesting possibilities for quantum phenomena description.
Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon equation by taking its square root in a bi-quaternionic formalism fully justified by the first principles of the scale relativity theory. This is no more true when an external electro-magnetic field comes into play. If one tries to derive the electro-magnetic Dirac equation in a manner analogous to the one used when this field is absent, one obtains an addi…
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.
