The Modification of Special Relativity

called the special theory of relativity, no doubt one of the boldest and most interesting theories ever designed.' Generations of physicists, mathematicians and philosophers were inspired by it. Bitter battles were fought over its principles and deductions which clashed with many an honourable idea backed up by honourable philosophical and scientific traditions. Yet all the knocks and bites from left and right seem to have left Einstein's theory unshaken. Today the battle-grounds of yesterday look rather deserted. The critic is likely to be silenced in the face of the theory's spectacular success. In the following I shall try to throw some new light on one or two old problems which Einstein's theory gives rise to. Section z is concerned with the obstacles we are faced with when we try to combine Einstein's special theory of relativity with a causal account of relativistic phenomena. The argument does not show, of course, that Einstein's theory is false, but it points to a possible incompleteness and to certain limitations inherent in the special theory of relativity. In section 3 a substratum theory of relativity is outlined which seems to be as simple and coherent as Einstein's special theory of relativity; the Lorentz transformations are deduced from two basic principles without making use of the principle of relativity. Finally, in section 4, the two theories are compared and some general conclusions are drawn. But let us first have a short look at the ideas underlying Einstein's theory. To begin with, the special theory of relativity is a transformation theory. This is its most fundamental aspect. Suppose we know the space and time co-ordinates of an event particle e (event with negligible spatiotemporal extension) in an inertial frame of reference F; then the theory

Science sets itself apart from other paths to truth by recognizing that even its greate practitioners sometimes err.

Maxwell unified the disparate concepts of electric and magnetic fields with one theory (electromagnetism) and Einstein then unified the disparate theories of electromagnetism and mechanics with one kinematics (Minkowski space of special relativity). In this talk, we will briefly explain how the disparate kinematics of quantum mechanics (finite-dimensional Hilbert space) and special relativity can be unified with one principle (relativity principle). This result follows from the axiomatic reconstruction of quantum mechanics via information-theoretic principles, which has successfully recast quantum mechanics as a principle theory a la Einstein, i.e., the formalism of the theory follows from an empirically discovered fact, just like special relativity. According to the quantum reconstruction program, the empirically discovered fact whence the Hilbert space formalism of quantum mechanics is Information Invariance & Continuity. Of course, the empirically discovered fact whence the Lorentz transformations of special relativity is the light postulate, i.e., everyone measures the same value for the speed of light c, regardless of their relative motions. Obviously, the light postulate can be justified by the relativity principle—the laws of physics are the same in all inertial reference frames—because c is a constant of Nature per Maxwell’s electromagnetism. [We label this “NPRF + c” for short, where NPRF stands for “no preferred reference frame.”] As we will show, Information Invariance & Continuity can also be justified by the relativity principle by first spatializing the quantum reconstruction program’s operational notion of measurement. In that case, Information Invariance & Continuity entails the empirically discovered fact that everyone measures the same value for Planck’s constant h, regardless of their relative spatial orientations or locations (Planck postulate). Since Poincar’e transformations relate inertial reference frames via spatial rotations and translations as well as boosts, and h is a constant of Nature per Planck’s radiation law, the relativity principle justifies the Planck postulate (NPRF + h) just like it justifies the light postulate (NPRF + c). Thus, the kinematics of quantum mechanics and special relativity are unified in that both follow most fundamentally from the relativity principle in the adynamical global constraints NPRF + h and NPRF + c. This approach provides a principle solution to the mystery of quantum entanglement that does not violate locality, statistical independence, intersubjective agreement, or the uniqueness of experimental outcomes and it does not alter quantum mechanics as a principle theory. An ontology consistent with this unification is introduced and we deflate both the ‘big’ and ‘small’measurement problems.

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 the universality of the (two-way) speed of light. The synthesis of such seemingly incompatible concepts as the existence of preferred frame and the relativity principle is possible at the expense of the freedom in assigning the one-way speeds of light that exists in special relativity. In the framework developed, a degree of anisotropy of the one-way speed acquires meaning of a characteristic of the really existing anisotropy caused by motion of an inertial frame relative to the preferred frame. The anisotropic special relativity kinematics is developed based on the symmetry principles: 1) Space-time transformations between inertial frames leave the equation of anisotropic light propagation invariant and 2) a set of the transformations possesses a group structure. The Lie group theory apparatus is applied to define groups of transformations between inertial frames. Applying the transformations to the problem of calculating the CMB temperature distribution yields a relation in which the angular dependence coincides with that obtained on the basis of the standard relativity theory but the mean temperature is corrected by the terms second order in the observer velocity.

The subject of this study is the special theory of relativity (SRT) by A. Einstein, the debate about which has been going on for more than a hundred years. The aim of the study is to evaluate SRT from the side of whether everything that is discussed in this theory and thus in the new, relativistic physics is possible in nature itself. At the same time, the author pays special attention to three issues: the principle of relativity, the necessary condition for the objectivity of the content of scientific theories and the Einstein style of scientific thinking, which predetermined the ideological component of SRT and all relativistic physics. But such issues as relativistic reductions of lengths and durations, the relativity of simultaneity and a single space-time do not remain without attention. The study revealed the fallacy of a long-standing and widespread opinion about the relativity of properties. The necessary condition for the objectivity of scientific theories is revealed. The natural form of expression of quantities is revealed and the non-relative nature of all natural quantities is shown. The hidden form of relativity inherent in the SRT postulate about the constancy of the speed of light in all inertial reference frames and extended in SRT to the magnitude of all lengths and durations considered in it is revealed. It is shown that such relativity is based on the dependence of the quantities on the choice of their reflection systems. It is shown that such dependence is impossible in nature itself. It is concluded that the SRT is erroneous. At the same time, the factors that served as favorable ground for the emergence and spread of this erroneous theory are listed.

Einstein assumed the “principle of relativity” when constructing the special theory of relativity (STR). He claimed that all inertial frames are equivalent, and that it is impossible to discriminate between inertial frames. However, among the coordinate systems regarded by Einstein as inertial frames, there are some in which light propagates isotropically, and some in which light propagates anisotropically. A method has been found which discriminates between these. This paper discusses the “triplet thought experiment” in which accelerated motion is eliminated from the famous twin paradox thought experiment of the STR. Here the inertial frames regarded as equivalent by the STR are identified as “classically stationary frames SCl” and “classically moving frames (S'Cl) ” First, an observer M in frame performs the triplet thought experiment, and it is confirmed that the delay in time which elapses in the moving frame agrees with the predictions of the STR. Next, an observer in rocket A (S'Cl) performs the triplet thought experiment, and observes the same time delay. Before starting movement at constant velocity, rocket A experiences accelerated motion. The coordinate system of rocket A cannot be regarded physically as a stationary frame. Even so, observer A observes the delay predicted by the STR. If it can be accepted that frames SCl are included in inertial frames, then the problem of the twin paradox will no longer be a paradox.

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.

In the perspective to guiding undergraduate students on advanced topics in theoretical physics, this article approaches a brief study about some aspects of the Lorentz transformations. The two fundamental postulates of Einstein's Theory of Special Relativity (or special relativity) are explained. The detailed process of constructing the Lorentz transformations and in particular the transformations performed considering the rectilinear and uniform motion of a frame of reference in relation to the other along the x-axis direction are presented. Some consequences resulting from Lorentz transformations such as Length contraction, Time dilation and the Relativity of simultaneity are highlighted.

We give a mathematical interpretation for a previously investigated model, which is based on a set of axioms incorporating fundamental aspects from both Galilei and special relativity (SR). The model considers two time variables, one of them identified with absolute time [characteristic of Galilei relativity (GR)] and the other identified with the local time of SR. Its main characteristics rely on two classes of transformations. One is what we call generalized Lorentz transformation, which includes the standard Lorentz transformations as a particular case. The other is the h-map, which essentially relates absolute and local times. The h-map also determines the basic kinematics of SR from the corresponding kinematics of GR. This allows us to express a Lorentz transformation in terms of a Galilei transformation. It suggests us to see the h-map as a natural transformation between two functors \(\overline{G}\) and \(\overline{L}\), representing the notions of Galilei and Lorentz transformations in functorial language. The categorical framework we develop not only elucidates the structure of Galilei and Lorentz transformations but also provides a unified model for Galilei and special relativity, where the former acquires a distinguished role in itself, not being a mere low speed limit of the latter.

The present work calls attention to an undeclared assumption made by Einstein in his landmark paper [Ann. Physik 322 (10), 891 (1905)] in which he introduced the Special Theory of Relativity (STR). The emphasis in textbooks and periodicals is always on his two postulates of relativity [the Relativity Principle (RP) and the constancy of the speed of light in free space]. Yet, the well-known results of his theory such as Fitzgerald-Lorentz length contraction (FLC) and the symmetry of time dilation (two clocks in motion each running slower than the other) are based exclusively on this third postulate. It is shown that an alternative assumption of clock-rate proportionality (Newtonian Simultaneity) is also consistent with Einstein’s first two postulates and with the Relativistic Velocity Transformation (RVT), but that it leads to a fundamentally different space-time transformation than the Lorentz Transformation (LT) of STR. It is referred to as the Newton-Voigt Transformation (NVT). Its predictions regarding length and time measurements by moving observers differ sharply from those of the LT. A “clock riddle,” distinct from the well-known “clock paradox,” is presented to underscore the differences between these two versions of the relativistic space-time transformation. It is shown that the NVT is consistent with remote simultaneity and the impossibility of time inversion, and therefore does not rule out the existence of faster-than-c particles under the condition that they have null proper mass

This paper presents an instrument made up of Excel spreadsheets used to study the relativistic transformation of the electromagnetic field. Knowing the electric and magnetic components of an electromagnetic field in an inertial reference frame, we can determine the components of the same electromagnetic field in another inertial reference frame. Two sets of input data are utilized. The former is made up of the components of the electric and magnetic field in the reference frame considered to be fixed. The latter is made up of the components of the velocity of the reference frame considered to be mobile in relation to the fixed reference frame. The results are expressed both numerically and graphically through charts in the main spreadsheet. The charts comparatively present the components of the electric, respectively magnetic, field in the two reference frames. The instrument can contribute to the fixation and consolidation of students' knowledge regarding the structure of the electromagnetic field. Thus it is verified that the orthogonality property of the electric and magnetic field vectors is one invariantly relativistic. Moreover, it is verified that we cannot transform a purely electric field in a purely magnetic one and the other way around through any Lorentz transformation. Exploring the facilities of spreadsheets, we can elaborate with them new instruments to help us in the teaching and learning of fundamental concepts of Physics. The presented instrument represents a good example of rendering, in an interactive way, certain aspects of the connection between Electromagnetism and the Special Theory of Relativity. With its help, a series of particular cases can be analyzed so that students gain a new learning experience and be motivated in the study of Physics.

It is often claimed that the special theory of relativity (STR) necessitates the block universe view, according to which all the events spread out in space-time are determinate, ‘fixed’ once and for all. After having briefly recalled the basic notions of STR (principle of relativity, constancy of the speed of light, relativity of simultaneity) (Sect. 6.2), I will distinguish and discuss the different arguments taken from STR in favor of the block universe view: the ‘geometric argument’ (the spatialization of time) (Sect. 6.3), the ‘becoming-argument’ (the loss of the becoming) (Sect. 6.4), and the ‘determinateness-argument’ (the determinateness of the future) (Sect. 6.5). Among these, I will focus in particular on the last argument, which can be summarized as follows: STR entails this puzzling consequence that any future event in a given inertial reference frame is already present or past in another inertial reference frame. Any future event is therefore already determinate. I will show that this argument contains a fallacy, and present several replies to it. My conclusion is that the notion of time in STR does not necessarily imply the block universe view; rather, it gives rise to a new ontology that is more complex but nevertheless consistent.

We re-examined the four-dimensional spacetime formulation of invariance of electromagnetic fields between two inertial frames under Lorentz transformation, which predicts a pure electric (magnetic) field in one inertial frame is composed the Cartesian components of a pure both electric and magnetic fields in another inertial frame. This contradicts the Lorentz invariance condition which requires that the vector quantities in one inertial frame must have the same form in another inertial frame. In this work, we introduce a three-dimensional quasi-time vector to modify the classical four-dimensional spacetime (3+1) to a new six-dimensional spacetime (3+3) and derive spacetime metric equation and relativistic velocity. We use the classical vector transformation theory to derive expressions for Cartesian components of relativistic velocity and net electromagnetic force vectors. Considering two massive inertial frames form a closed system, we integrated the transformed relativistic velocity with the law of conservation of energy to prove that contrary to the common belief, the electromagnetic field that appears as a purely electric (magnetic) field in one massive inertial frame, it also appears as a pure electric (magnetic) field in another massive inertial frame under Lorentz transformation. As an application of the proposed six-dimensional spacetime theory, we prove Lorentz invariance of Maxwell’s equations with and without charge and current source. We also prove the scalar electromagnetic wave equations with and without charge and current source and the conservation laws of the continuity equations of current and densities of electromagnetic energy and linear and angular momentums between two massive inertial frames under Lorentz transformation.

It has been critically argued by V. A. Leus (Sobolev Institute of Mathematics, Novosibirsk, Russia) that in my proof that Einstein’s Special Theory of Relativity is logically inconsistent and therefore false, I violated the basic tenets of Special Relativity and foisted an alternative theory upon Einstein’s. A careful study of the critical analysis reveals however a failure to address the key arguments I adduced to prove Special Relativity logically inconsistent, and a concomitant invocation of Einstein’s theory to try to argue that my analysis is incorrect because it does not concur with Einstein. There is therefore no proof advanced of any alleged error in my analysis. In my paper I did not introduce an alternative theory. The aforementioned critical paper affords opportunity in rebuttal to amplify the invalidity of A. Einstein’s tacit assumption, in constructing the Special Theory of Relativity, that systems of clock-synchronised stationary observers consistent with Lorentz Transformation can be mathematically constructed. Since such systems of observers have in fact no mathematical existence the Special Theory of Relativity is logically inconsistent. It is therefore invalid. The consequences for physics, astronomy, and cosmology, are significant.

One of the most basic principles in science is the objectivity of measurement of physical properties. According to the special theory of relativity (STR), this ancient principle is violated for observers in relative motion since it predicts that they generally will disagree on the ratios of the lengths of two objects and also on whose clock is running slower at any given time. Both predictions stem from the Lorentz transformation (LT), which is the centerpiece of Einstein's STR. It has recently been pointed out that two of the claims of this theory are mutually contradictory; it is impossible that the rates of two clocks in motion are strictly proportional to one another (time dilation) while one of them finds that two events are simultaneous whereas the other does not (remote nonsimultaneity). This recognition proves that the LT is not a valid component of the relativistic theory of motion, including its well-known thesis that space and time are not distinct quantities. Instead, it has always been found experimentally that the rates of clocks in motion are governed by a Universal Timedilation Law (UTDL), whereby the speed of the clock relative to a specific rest system is the sole determining factor. A simple way of describing this state of affairs is to say that the standard unit of time in each rest frame is different and increases with its relative speed to the above rest system by a definite factor. The measurement process is thereby rendered to be completely objective in nature. A key goal of relativity theory is therefore to develop a quantitatively valid method for determining this factor. It will be shown that the same factor appears in the true relativistic space-time transformation and that it also plays a key role in the uniform scaling of all other physical properties