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Resumo O Princípio da Relatividade de Galileu (PRG) estabelece que as leis da mecânica são as mesmas em qualquer referencial inercial. Ao determinar que todos os referenciais inerciais são equivalentes, esse princípio implica em uma relatividade do movimento. Por outro lado, mesmo considerando o PRG como basilar para a mecânica, Isaac Newton introduz os conceitos de tempo e espaço absolutos e apresenta argumentos, de natureza dinâmica, em defesa do movimento absoluto, justificado na diferenciação entre referenciais inerciais e não-inerciais. A Teoria da Relatividade Restrita (TRR) critica as noções de tempo e espaço absolutos, mas preserva o papel privilegiado dos referenciais inerciais na descrição das leis da natureza. Apenas com a Teoria da Relatividade Geral (TRG) é estabelecida a equivalência entre todos os referenciais, independentemente do seu estado de movimento e, assim, é derrubada a noção de movimento absoluto. Este trabalho tem por objetivo discutir as principais dúvidas e questões que surgem ao se estudar os conceitos supramencionados, bem como investigar a aparente dubiedade entre o PRG e o movimento absoluto. Abstract Galileo’s Principle of Relativity (GPR) states that the laws of mechanics are the same in any inertial frame of reference. By determining that all inertial reference frames are equivalent, this principle implies a relativity of motion. On the other hand, even considering the GPR as fundamental for mechanics, Isaac Newton introduces the concepts of absolute time and space and presents arguments, of a dynamic nature, in defense of absolute motion, justified by the differentiation between inertial and non-inertial reference frames. The Special Relativity Theory (SRT) criticizes the notions of absolute time and space, but preserves the privileged role of inertial reference frames in the description of the laws of nature. Only with the General Relativity Theory (GRT) is equivalence established between all references, regardless of their state of motion and, thus, the notion of absolute motion is overthrown. This work aims to discuss the main doubts and issues that arise when studying the aforementioned concepts, as well as to investigate the apparent dubiousness between the PRG and the absolutemovement.

We present a comprehensive discussion of the formulation of the kinematics of special relativity, i.e., the Lorentz transformation. We begin with a concise new proof that the principle of relativity implies that the transformation of event coordinates between inertial reference frames is linear. We then give a clear derivation of the pre-Lorentz transformation, which follows from the principle of relativity. We then show that the pre-Lorentz transformation and the inertial invariance of the speed of light together result in the Lorentz transformation. This, of course, is essentially the traditional formulation. We next present two additional formulations, one using Lorentz–Fitzgerald contraction and one using time dilation, instead of inertial invariance. This is reasonable since Lorentz–Fitzgerald contraction and time dilation are about as well established as and are arguably less abstract than inertial invariance, and thus may profitably be used instead of inertial invariance to complete the formulation. We then present a complete proof that the pre-Lorentz transformation and the requirement of closure upon composition together imply that the transformation is either a Galilean transformation or a generalized Lorentz transformation. This is noteworthy in that it gets ever so close to the Lorentz transformation without invoking light. In the course of this, we obtain a generalized velocity addition rule, which reduces to the velocity addition rule of special relativity. We next show that the generalized Lorentz transformation, together with inertial invariance, Lorentz–Fitzgerald contraction, and time dilation, used one at a time, yields three more formulations. We then show that the unspecified, nonzero, constant speed in the generalized Lorentz transformation can be determined without any reference to light, thereby obtaining a seventh formulation. Light plays no explicit role in the four formulations employing Lorentz–Fitzgerald contraction and time dilation and plays no role whatsoever in the seventh formulation. Thus, and this is a fact which should be strongly emphasized, the formulation of special relativity in no way depends upon the nature of electromagnetic radiation. We conclude by briefly discussing these seven formulations of the kinematics of special relativity and some associated implications.

The special theory of relativity demands, by Einstein's two postulates (i) the principle of relativity and (ii) the constancy of the speed of light in vacuum, that a spherical wave of light in one inertial system transforms, via the Lorentz transformation, into a spherical wave of light (the Lorentz sphere) in another inertial system when the systems are in constant relative rectilinear motion. However, the Lorentz transformation in fact transforms a spherical wave of light into a translated ellipsoidal wave of light even though the speed of light in vacuum is invariant. The special theory of relativity is logically inconsistent and therefore invalid.

When Einstein developed the special theory of relativity (STR), he assumed the principle of relativity, i.e. that all inertial frames are equivalent. Einstein thought it was impossible to differentiate inertial frames into classically stationary frames where light propagates isotropically, and classically moving frames where light propagates anisotropically. However, the author has previously pointed out that classically moving frames have a velocity vector attached, and presented a thought experiment for determining the size of that velocity vector. The author has already shown a violation of the STR, but this paper presents a violation of the STR using different reasoning. More specifically, this paper searches for a coordinate system where light propagates anisotropically. This is done by using the correlation of two photons pair-generated from a photon pair generator. If the existence of such a coordinate system can be ascertained, it will constitute a violation of the STR.

An instantaneous velocity where clock at a moment only correponds to any arbitrary distance or position of space can not be indicated in axiom 1, but it indicates that there is only one dimensional existence,space or time, where a certain moment of clock only corresponds to a specific given length of space,not to any other distance.Further,each quantity of space and time correponds only to itself. Instead of Relavity, A velocity definition that consists of two dimensions representing relationship between space and time is not valid and there is only one dimensional space or time that is independent each other in axiom 1 .As an result,the principle of relativity and Principle of constant velocity of light are replaced by the principle of inertial system of axiom 1 and principle of universal invariant velocity of axiom 1. Unlike two dimensions whose magnutide is determined by the ratio,the magnutide of single dimension is determined by the unit values of one dimension,which indicates that an infinitely great velocity is meaningless,instead of ,there is only infinitely great space of one dimension and infinitely long time of one dimension. Further,The extensions of finite quantities of two inertial system in axiom 3 must only stay in the finite range,and do not reach infinite distance. If two such inertial systems are infinite versus finite,then it is known from axiom 3 that the change of direction means infinite great and this extension of infinite great can be defined to be inextensible.

The problem of covariance of physical quantities has not been solved fundamentally in the theory of relativity, which has caused a lot of confusion in the community; a typical example is the Gordon metric tensor, which was developed almost a century ago, and has been widely used to describe the equivalent gravitational effect of moving media on light propagation, predicting a novel physics of optical black hole. In this paper, it is shown that under Lorentz transformation, a covariant tensor satisfies three rules: (1) the tensor keeps invariant in mathematical form in all inertial frames; (2) all elements of the tensor have the same physical definitions in all frames; (3) the tensor expression in one inertial frame does not include any physical quantities defined in other frames. The three rules constitute a criterion for testing the covariance of physical laws, required by Einstein's principle of relativity. Gordon metric does not satisfy Rule (3), and its covariance cannot be identified before a general refractive index is defined. Finally, it is also shown as well that in the relativistic quantum mechanics, the Lorentz covariance of Dirac wave equation is not compatible with Einstein's mass-energy equivalence., A minor-revised version published in Optik. 4 pages, no figures. To help reading, Impact Statement is attached. arXiv admin note: substantial text overlap with arXiv:1702.03200

Einstein's famous explanation of the photoelectric effect is addressed using the Minkowski four-vector formalism. This formalism deals with energy and linear momentum simultaneously and it is Lorentz covariant. The energy and momentum equations for both electron emission and electron braking are obtained in the lab frame S. It is then shown that the energy and momentum equations for electron emission and electron braking in a second inertial frame S ′ are linear combinations of the corresponding equations in the original frame S, according to the principle of relativity. Although the photoelectric effect is basically a non-relativistic phenomenon, the approach presented here may provide new insights for both instructors and students.

Lorentz transformation relations of special relativity are generally derived for light like intervals in almost all texts. The procedure assumes invariance of spherical wave front equation in all inertial frames. This paper deals with the derivation of the transformation relations of event coordinates together with Doppler formula from a single treatment by constructing identical length and time standard under identical conditions in compared frames. To meet this end critical review of the postulates of Special Relativity in the perspective of equivalence of length, time and mass standard followed by the meaning of phase of clock in any inertial frame is presented. It has been shown that special relativity is in reality a supreme creation of human mind where identical length and time standards being independent of the perspective are not naturally given but had been constructed under identical experimental condition in a scientific way so that observations from different frames can be compared using same system of units.

Employing Minkowski’s program for regarding physics as geometry of the real spacetime produces spectacular results – it explained the principle of inertia, the principle of relativity (including the constancy of the speed of light), why acceleration is absolute in both special and general relativity, that absolute acceleration is a manifestation of an absolute geometric feature (the curvature of the worldline of the accelerating body) and does not imply the existence of absolute space.

We explore the role of symmetry in the theory of Special Relativity. Using the symmetry of the principle of relativity and eliminating the Galilean transformations, we obtain a universally preserved speed and an invariant metric, without assuming the constancy of the speed of light. We also obtain the spacetime transformations between inertial frames depending on this speed. From experimental evidence, this universally preserved speed is c, the speed of light, and the transformations are the usual Lorentz transformations. The ball of relativistically admissible velocities is a bounded symmetric domain with respect to the group of affine automorphisms. The generators of velocity addition lead to a relativistic dynamics equation. To obtain explicit solutions for the important case of the motion of a charged particle in constant, uniform, and perpendicular electric and magnetic fields, one can take advantage of an additional symmetry&mdash, the symmetric velocities. The corresponding bounded domain is symmetric with respect to the conformal maps. This leads to explicit analytic solutions for the motion of the charged particle.

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.

I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein’s historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space–time has a discrete spectrum, relative to classical observers in space–time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.

Until now, we have seen that the structure of our space-time provides the same picture in each inertial system. The principle of relativity now requires more. Also, the physical laws should stay the same in each inertial system. This physical experience was made at first in mechanics. This is now our subject. Electrodynamics will be studied in Chap. 9, Sect. 3.

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.

This paper describes method to measure and calculate speed, time dilation, and length contraction of the source through using the observed differences in the vector of a ray compared to the vector of a solid projectile emanating from the same source, aimed in the same direction. This method can be used to measure motion even in absence of a reference body and has identified an inertial reference frame that has properties unlike any others. This contradicts the principle of relativity.

Before starting the presentation on the conceptual evolution of the extension of the Principle of Relativity to all frames of reference, and mechanics (along with all other physical phenomena) is freed from the shackles of inertial frames, a brief note on the titles of the two theories propounded by Einstein can be very useful.

The basic concepts and laws of classical dynamics are analyzed from the standpoint of their adequacy to the physical nature of material bodies and to the dynamical processes. What Newton called absolute immovable space is the world ether that generates any forces, including the inertial forces imposing constraints on the magnitude of the acceleration. Inertial reference frames are frames moving translationally, rectilinearly, and uniformly relative to the ether. The physical nature of the principle of relativity is that the acceleration of a material point in all inertial reference frames coincides with its acceleration relative to the ether, and, therefore, Newton's dynamical equation retains the same form in any inertial reference frame. The principle of relativity is valid as long as Newton's dynamical equation is valid. In new formulations, the four laws of dynamics contain the concepts of ether and inertial forces. These laws are independent between themselves, and each of them expresses only one elementary truth.

The perception of events in two inertial reference frames in relative motion was analyzed from the perspective of the Special Relativity postulates, leading to the Lorentz transformation equations for the time and space coordinate in the relative motion direction. Yet, straightforward inconsistencies were identified upon examining the conversion of the time interval between two co-local events in the traveling reference frame. The approach used in the Special Relativity formulation to get around the identified inconsistencies was revealed. Subsequent mathematical contradictions in the Lorentz transformation equations, disproving the Special Relativity predictions, were shown.

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.

Homogeneity of space and time, spatial isotropy, principle of relativity and the existence of a finite speed limit (or its variants) are commonly believed to be the only axioms required for developing the special theory of relativity (Lorentz transformations). In this paper it is shown, however, that Lorentz transformation cannot actually be derived without the explicit assumption of time isotropy (time-reversal symmetry) which is logically independent of the other postulates of relativity. Postulating time isotropy also restores the symmetry between space and time in the postulates of relativity. Inertial frames are defined in influential texts as frames having space-time homogeneity and spatial isotropy only. Inclusion of time isotropy in that definition is also suggested., Comment: Changes/Updates in v2: Revision of an endnote. Addition to references. Abstract and introduction rewritten for clearer presentation. All results, analysis and conclusion however remain the same as in v1. Critiques, queries, comments and suggestions are welcome at author's email ids

This paper discusses a thought experiment whose result contradict the predictions of the special theory of relativity. The reason why this contradiction appears is a velocity vector attached to an inertial frame. Since this sort of inertial frame exists in the natural world, the “principle of relativity” that regards all inertial frames as equivalent, cannot be regarded as a true principle. This paper concludes that the special theory of relativity, which assumes the “principle of relativity” in its development, is a theory with a built-in contradiction.

The chapter has as main objective to clarify some important concepts appearing in relativistic spacetime theories and which are necessary of a clear understanding of our view concerning the formulation and understanding of Maxwell, Dirac and Einstein theories. Using the definition of a Lorentzian spacetime structure \((M,\boldsymbol{g},D,\tau _{\boldsymbol{g}},\uparrow )\) presented in Chap. 4 we introduce the concept of a reference frame in that structure which is an object represented by a given unit timelike vector field \(\boldsymbol{Z} \in \sec TU\) (\(U \subseteq M\)). We give two classification schemes for these objects, one according to the decomposition of \(D\boldsymbol{Z}\) and other according to the concept of synchronizability of ideal clocks (at rest in \(\boldsymbol{Z}\)). The concept of a coordinate chart covering U and naturally adapted to the reference frame \(\boldsymbol{Z}\) is also introduced. We emphasize that the concept of a reference frame is different (but related) from the concept of a frame which is a section of the frame bundle. The concept of Fermi derivative is introduced and the physical meaning of Fermi transport is elucidated, in particular we show the relation between the Darboux biform \(\Omega \) of the theory of Frenet frames and its decomposition as an invariant sum of a Frenet biform \(\Omega _{F}\) (describing Fermi transport) and a rotation biform \(\Omega _{\mathbf{S}}\) such that the contraction of \(\star \Omega _{\mathbf{S}}\) with the velocity field v of the spinning particle is directly associated with the so-called Pauli-Lubanski spin 1-form. We scrutinize the concept of diffeomorphism invariance of general spacetime theories and of General Relativity in particular, discuss what meaning can be given to the concept of physically equivalent reference frames and what one can understand by a principle of relativity. Examples are given and in particular, it is proved that in a general Lorentzian spacetime (modelling a gravitational field according to General Relativity) there is in general no reference frame with the properties (according to the scheme classifications) of the inertial referenced frames of special relativity theories. However there are in such a case reference frames called pseudo inertial reference frames (PIRFs) that have most of the properties of the inertial references frames of special relativity theories. We also discuss a formulation (that one can find in the literature) of a so-called principle of local Lorentz invariance and show that if it is interpreted as physical equivalence of PIRFs then it is not valid. The Chapter ends with a brief discussion of diffeormorphism invariance applied to Schwarzschild original solution and the Droste-Hilbert solution of Einstein equation which are shown to be not equivalent (the underlying manifolds have different topologies) and what these solutions have to do with the existence of blackholes in the “orthodox”interpretation of General Relativity.

In 1905 Albert Einstein, in a paper entitled “On the Electrodynamics of Moving Bodies”, as a solution to the disagreement between classical mechanics and the results of the Michelson's experiment, who showed the invariance of the speed of light in vacuum measured in different inertial reference systems, developed the theory of special relativity. In this essay Einstein expounded a theory that, instead of introducing a privileged system, required the revision of the concepts of space and time of classical physics. Combining the principle of Galilean relativity, according to which the laws of physics are invariant in all inertial reference systems, with the physics of electromagnetism, according to which the speed of light in a vacuum is constant, Einstein concluded that time is no more than a relative measure, namely that whenever we have to do with speed equal to or close to that of light, time is no longer a variable absolute and independent of the reference system adopted, but depends on the variable position. This is what Einstein shows through the critical examination of the concept of simultaneity. The abandonment of the traditional conception of space and time based on the idea of a spatial continuum flowing through a temporal continuum coherently leads to the assumption of a space-time continuum (chronotope) in which distances and time intervals vary with the changing the reference system, and together vary, of course, all other sizes to those connected (speed, acceleration, mass).

In this section we discuss the principle of equivalence. We shall see that, besides allowing the extension of the principle of relativity to a generic, not necessarily inertial, frame of reference, it allows to define gravity, in a relativistic framework, as a property of the four-dimensional space-time geometry.

Assuming that the Universe consists of absolute space, or more properly aether-space, (as evidenced by several well-documented experiments, and supported by the DSSU* theory) the transformation of the coordinates from one moving inertial frame to another frame while retaining the information of their absolute motion (with respect to aether-space) requires the application of the Lorentz transformation, not once, but twice. The combined transformations are detailed. The resulting expressions for space-and-time coordinates are then used to redefine: absolute velocity, apparent velocity, length contraction, momentum, mass, and kinetic energy —all redefined in terms of absolute inertial motion. Each of the resulting expressions are validated by showing that each reduces, under the specified condition, to the Einstein Special Relativity form (as each must) and also reduces, under specified speed restrictions, to the familiar Newtonian-Galilean form (again, as each must). In effect, DSSU relativity (the relativity of absolute motion) encompasses both Special relativity and Classical relativity. * DSSU is the acronym for Dynamic Steady State Universe. It is a model based on the premise that all things are processes.

Based on the principle of relativity and the postulate on universal invariant constants (c,l), all possible kinematics can be set up with sub-symmetries of the Umov-Weyl-Fock transformations for the inertial motions. Further, in the combinatory approach, all these symmetries are intrinsically related to each other, e.g. to the very important dS kinematics for the cosmic scale physics., Comment: 11 pages

Machs principle and the principle of relativity have been discussed by H. I. Hartman and C. Nissim-Sabat in this journal. Several phenomena were said to violate the principle of relativity as applied to rotating motion. These claims have recently been contested. However, in neither of these articles have the general relativistic phenomenon of inertial dragging been invoked, and no calculation have been offered by either side to substantiate their claims. Here I discuss the possible validity of the principle of relativity for rotating motion within the context of the general theory of relativity, and point out the significance of inertial dragging in this connection. Although my main points are of a qualitative nature, I also provide the necessary calculations to demonstrate how these points come out as consequences of the general theory of relativity, 17 pages

This paper explores the possibility of detecting a difference in the Doppler Shift phenomenon when generated in different inertial frames, as a means of testing Einstein’s Principle of Relativity. Specifically, the Doppler shifts generated alternatively by movement of the observer and movement of the light source are examined and show an observable difference that is inconsistent with the Relativity Principle.

The theory of reference frames is a new theory of relativity that represents the scientific evolution of Einstein’s relativity. In this essay the following points are examined: considerations about the theory of relativity of Albert Einstein, general notes on the theory of reference frames, the Michelson–Morley experiment, the new equations of space-time transformation, the kinematic principles of the theory of reference frames, the transformations of Maxwell’s equations for inertial systems, the Doppler effect, and the mystery of supernovas. The new theory responds to numerous and recent experimental results that are not confirmed by previous theories. In particular, the interpretation of the luminous phenomenon that causes supernovas is at variance with theoretical predictions of Einstein’s relativity but is in accordance with those of the theory of reference frames. The most important theoretical concept in this essay is the inertial time, which is a common time valid for all inertial reference frames that replaces Newtonian– Galilean absolute time and Einstein’s relativistic time.

Nowadays, in any textbook of physics (in the part devoted to mechanics) one finds written that the laws of Newtonian mechanics are invariant under Galileo transformations, or, equivalently, that the equations of the mechanics are the same in all inertial reference systems.

The structure of the Lorentz transformations follows purely from the absence of privileged inertial reference frames and the group structure (closure under composition) of the transformations---two assumptions that are simple and physically necessary. The existence of an invariant speed is \textit{not} a necessary assumption, and in fact is a consequence of the principle of relativity (though the finite value of this speed must, of course, be obtained from experiment). Von Ignatowsky derived this result in 1911, but it is still not widely known and is absent from most textbooks. Here we present a completely elementary proof of the result, suitable for use in an introductory course in special relativity., 4 pages, 1 figure

The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for the continuum. Here we show how the clash can be overcome within a discrete quantum theory where the evolution of fields is described by a quantum cellular automaton. The reconciliation is achieved by defining the change of observer as a change of representation of the dynamics, without any reference to space-time. We use the relativity principle, i.e. the invariance of dynamics under change of inertial observer, to identify a change of inertial frame with a symmetry of the dynamics. We consider the full group of such symmetries, and recover the usual Lorentz group in the relativistic regime of low energies, while at the Planck scale the covariance is nonlinearly distorted., 5 pages, 3 figures + Supplemental Information (8 pages, 3 figures)

In a previous work, we have shown that the null result of the Michelson–Morley experiment in vacuum is deeply connected with the notion of time. The same is true for the postulate of constancy of the two-way speed of light in vacuum in all frames independently of the state of motion of the emitting body. The argumentation formerly given is very general and has to be true not only within Special Relativity and its “equivalence” of all inertial frames, but as well as in Lorentz-Poincare scenario of a preferred reference frame. This paper is the second of a trilogy intending to revisit the foundations of Special Relativity, and addresses the question of the constancy of the one-way speed of light and of the differences and similarities between both scenarios. Although they manifestly differ in philosophy, it is debated why and how the assumption of a “special system of reference experimentally inaccessible” is indeed compatible with Einstein’s Special Relativity, as beautifully outlined and discussed by Bell [Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1988)]. This rather trivial statement is still astonishing nowadays to a big majority of scientists. The purpose of this work is to bring such assertion into perspective, widening the somewhat narrow view of Special Relativity often presented in textbooks and scientific papers.

In the rod and hole paradox as described by Rindler (1961 Am. J. Phys. 29 365–6), a rigid rod moves at high speed over a table towards a hole of the same size. Observations from the inertial frames of the rod and slot are widely different. Rindler explains these differences by the concept of differing perceptions in rigidity. Gron and Johannesen (1993 Eur. J. Phys. 14 97–100) confirmed this aspect by computer simulation where the shapes of the rod are different as observed from the co-moving frames of the rod and slot. Lintel and Gruber (2005 Eur. J. Phys. 26 19–23) presented an approach based on retardation due to speed of stress propagation. In this paper, we consider the situation when two parallel rods collide while approaching each other along a line at an inclination with their axis. The collisions of the top and bottom ends are shown to be reversed in time order as seen from the two co-moving frames. This result is explained by the concept of 'extended present' derived from the principle of relativity of simultaneity.

This paper examines the possibility of detecting a difference in the stellar aberration phenomenon when generated in different inertial frames, as a means of testing Einstein’s principle of relativity. Specifically, stellar aberration resulting alternately from movement of Earth and movement of the light source are examined and show an observable difference that is inconsistent with the relativity principle.

Our recently proposed inertial transformations of the space and time variables based on absolute simultaneity imply the existence of a single isotropic inertial reference system (“privileged system”). We show, however, that aresynchronization of clocks in all inertial systems is possible leading to a different, arbitrarily chosen,isotropic “privileged” system. Such a resynchronization does not modify any one of the empirical consequences of the theory,which is thus compatible with a formulation of the relativity principle weaker than adopted in Einstein’s theory of special relativity.

The inertial transformations of the space and time variables have recently been shown to provide a viable alternative description of relativistic phenomena. In the present paper we find the inertial transformations of a force by starting from Newton’s law. This allows us to write also the inertial transformations of the electric and magnetic fields. Relative to a moving frame, the Maxwell equations assume a novel velocity-dependent form.

Newton’s Mathematical Principles of Natural Philosophy provided the foundation of classical physics. This paper reviews several of his critical definitions, his three axioms, key corollaries, and concept of inertial frames. Newton’s first axiom or law requires the vector addition of velocities by Corollary I to translate the equation of motion of a constantly moving body from one inertial frame to another inertial frame. His relativity principle in Corollary V is often expanded to mean that any equation retains the same form in all inertial frames. This is true if the equations involve only Newtonian forces, but equations that specify velocity need to include the mutual velocity between moving inertial frames to fully transform the results between all reference frames. The speed of light parameter must correctly incorporate the mutual velocity between moving inertial frames. It is assumed the speed of light is a constant in all directions only in absolutely stationary, nongravitated reference frames, which is less restrictive than the assumption of universal speed of light in all inertial frames. A test is outlined with suggested equipment to measure the one-way speed of light simultaneously in three dimensions. Equations are provided to convert the results into the instantaneous directional velocity of the laboratory frame. It may take a few years to collect data to separate the Earth’s rotation, precession, nutation, polar wobble, Earth’s orbital velocity around the Earth-Sun and Earth-Moon barycenters, and the solar system’s movement due to the Milky Way’s rotation and translational velocity within the universe.

In the previous reading selection from Part II of his book Relativity, Einstein introduced his general principle of relativity as a reasonable extension of special relativity. Whereas the special principle of relativity claims that all inertial (i.e. uniformly moving) observers are equivalent—meaning that none of them have a privileged perspective—the general principle claims that non-inertial observers are all equivalent too. For Einstein recognized that an observer who is in a state of uniform acceleration will witness precisely the same motion of nearby objects as if he or she were at rest in the presence of a gravitational field.

Many authors noted that the principle of relativity together with space–time homogeneity and isotropy restricts the form of the coordinate transformations from one inertial frame to another to being Lorentz-like. The equations contain a free parameter, k (equal to c−2 in special relativity), whose value is claimed to be merely an empirical matter, so that special relativity does not need the postulate of constancy of the speed of light. I analyze this claim and argue that the distinction between the cases k=0 and k ≠ 0 is on the level of a postulate and that until we assume one or the other, we have an incomplete structure that leaves many fundamental questions undecided, including basic prerequisites of experimentation. I examine an analogous case in which isotropy is the postulate dropped and use it to illustrate the problem. Finally I analyze two attempts by Sfarti, and Behera and Mukhopadhyay to derive the constancy of the speed of light from the principle of relativity. I show that these attempts make hidden assumptions that are equivalent to the second postulate.

In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFγs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory. We show that it is the class of the LLRFγs that is associated with the PLLI. Next we give a definition of physically equivalent reference frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false. However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that PIRFs are not physically equivalent.

In effort to investigate how quantum physics might modify Einstein's Theory of Relativity at speeds v→c, the relationship between space-time coordinates of different reference frames is revisited by introducing only one new parameter xo, a fundamental constant for the quantization of space. The starting point is three criteria: (a) real space-time data are conditioned by standard quantum effects on measurements; (b) since currently used apparatus are only capable of probing the aggregate behavior of these quanta the relevant model is one which maximizes the Entropy subject to certain defining constraints; and (c) the constraints simply involve fixed ensemble averages in the case of an inertial frame, or boundary conditions on running averages in the case of an accelerated frame. In this context it is found that both the Lorentz transformation and a simple scheme for the quantization of space-time which resembles identically Planck's photon picture of radiation are a direct consequence of the Principle of Relativity. Non-inertial behavior corresponds to local Entropy maxima, obtainable by solution of a diffusion equation which gives gradually varying ensemble averages across space-time, as demonstrated by the example of a profile which connects a central region of highly agitated quanta with an asymptotic ambient environment—the outcome is the Schwarzschild metric of General Relativity. Apart from the above, a new feature emerges from the theory: the space-time data of an observer, when referred to the frame of his moving partner, are subject to extra quantum fluctuations which increase indefinitely in severity as v→c, with the Lorentz transformation providing only the mean data values. Thus for fast moving bodies like cosmic rays or matter at the horizon of a black hole, physical processes which affect them may not always be perceived by us to occur at the expected length or time scales.

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., 7 pages, no figure

title SUMMARY /title The 1920 manuscript by Einstein entitled: Vorlesungen ber Relativittstheorie points out paradigmatically all the preparations of the Special Theory of Relativity, the importance and the role of this theory in the General Theory of Relativity, the passage from a "Special Theory of Relativity" to a "general" one, and the doubts and certainties of its inventor, all that from a point of view of one of the most important issues of the history modem science: the problem of Ether definition. Just the Ether Theory, filtered through H. A. Lorentz's Theory, becomes in Einstein an "Inertial case" of the Classical Principle of Relativity and then, losing all its mechanical qualities, becomes Gravitational Theory in H. Weyl's phenomenological point of view.

Although textbooks usually present the conservation laws of energy and momentum only in the laboratory frame of reference, it is important that an introductory physics course show that they are valid in any inertial frame. It can be useful to apply the conservation laws in more than one frame of reference so as to highlight that they are precise only in closed systems. This is of particular note if one of the interacting partners is of near-infinite mass, whose share of the redistributed energy cannot always be neglected. In this sense, the notion of “infinitely large mass” is frame dependent. Balancing the energy and momentum in more than one frame of reference can help resolve some common difficulties with regard to energy conservation. We show also that the energy-work theorem holds in noninertial frames where inertial forces are treated as external.

Foundations of special relativity The special theory of relativity has had a profound impact upon notions of time and space within the scientific and philosophic communities. This well-established model of local coordinate transformations in the universe is built upon two fundamental postulates: • The principle of relativity: the laws of physics apply in all inertial reference systems; • The universality of the speed of light: the speed of light in a vacuum is the same for all inertial observers, regardless of the motion of the source or observer. The principle of relativity is not unique to the special theory of relativity; indeed it is assumed within Galilean relativity. However, if the equations of electrodynamics described by Maxwell's equations describe laws of nature, then the second postulate immediately follows from the first, since Maxwell's equations predict a universal speed of propagation of electromagnetic waves in a vacuum. The consequences of these postulates will be developed briefly. Lorentz transformations One of the most direct routes towards developing the transformations satisfying the postulates of special relativity involves examining the distance traveled by a propagating light pulse: (Δ x ) 2 + (Δ y ) 2 + (Δ z ) 2 = (Δct) 2 .

We calculate the self-force of a constantly accelerating electric dipole, showing, in particular, that classical electromagnetism does not predict that an electric dipole could self-accelerate, nor could it levitate in a gravitational field. We also resolve a paradox concerning the inertial mass of a longitudinally accelerating dipole, showing that the combined system of dipole plus field can be assigned a well-defined energy-momentum four-vector, so that the Principle of Relativity is satisfied. We then present some general features of electromagnetic phenomena in a gravitational field described by the Rindler metric, showing in particular that an observer fixed in a gravitational field described by the Rindler metric will find any charged object supported in the gravitational field to possess an electromagnetic self-force equal to that observed by an inertial observer relative to which the body undergoes rigid hyperbolic motion. It follows that the Principle of Equivalence is satisfied by these systems., Comment: 10 pages, 4 figures; improved discussion of pressure; added remarks on simultaneity and Rindler frame