Implementing Poincaré’s geometric conventionalism a scalar Lorentz-covariant gravity model is obtained based on gravitationally modified Lorentz transformations (or GMLT). The modification essentially consists of an appropriate space-time and momentum-energy scaling (“normalization”) relative to a nondynamical flat background geometry according to an isotropic, nonsingular gravitational affecting function Φ(r). Elimination of the gravitationally unaffected S 0 perspective by local composition of space–time GMLT recovers the local Minkowskian metric and thus preserves the invariance of the locally observed velocity of (...) light. The associated energy-momentum GMLT provides a covariant Hamiltonian description for test particles and photons which, in a static gravitational field configuration, endorses the four ‘basic’ experiments for testing General Relativity Theory: gravitational (i) deflection of light, (ii) precession of perihelia, (iii) delay of radar echo, (iv) shift of spectral lines. The model recovers the Lagrangian of the Lorentz–Poincaré gravity model by Torgny Sjödin and integrates elements of the precursor gravitational theories, with spatially Variable Speed of Light (VSL) by Einstein and Abraham, and gravitationally variable mass by Nordström. (shrink)

In the static field configuration, a spatially-Variable Speed of Light (VSL) scalar gravity model with Lorentz-Poincaré interpretation was shown to reproduce the phenomenology implied by the Schwarzschild metric. In the present development, we effectively cover configurations with source kinematics due to an induced sweep velocity field w. The scalar-vector model now provides a Hamiltonian description for particles and photons in full accordance with the first Post-Newtonian (1-PN) approximation of General Relativity Theory (GRT). This result requires the validity of Poincaré’s (...) Principle of Relativity, i.e. the unobservability of ‘preferred’ frame movement. Poincaré’s principle fixes the amplitude of the sweep velocity field of the moving source, or equivalently the ‘vector potential’ ξ of GRT (e.g.; S. Weinberg, Gravitation and cosmology, [1972]), and provides the correct 1-PN limit of GRT. The implementation of this principle requires acceleration transformations derived from gravitationally modified Lorentz transformations. A comparison with the acceleration transformation in GRT is done. The present scope of the model is limited to weak-field gravitation without retardation and with gravitating test particles. In conclusion the model’s merits in terms of a simpler space, time and gravitation ontology—in terms of a Lorentz-Poincaré-type interpretation—are explained (e.g. for ‘frame dragging’, ‘harmonic coordinate condition’). (shrink)

Inertial frames and Lorentz transformations have a preferred status in the special theory of relativity (STR). Lorentz transformations, in turn, embody Einstein's convention that the velocity of light is isotropic, a convention that is necessary for the establishment of a standard signal synchrony. If the preferred status of Lorentz transformations in STR is not due to some particular bias introduced by a convention on signal synchronism, but to the fact that the Lorentz transformation (...) group is the symmetry group of the theory, then the signal synchronism is not a matter of convention but rather a matter of fact. In order to explore the conventionalist thesis, that within the frame of STR isotropy in the velocity of light and, hence, signal synchronism is a matter of convention, we need a generalized Lorentz transformation group that does not embody Einstein's isotropy convention, and upon which STR can be based. We present here a new approach to the resulting search for a generalized STR, which is well suited for establishing some well-known results of Winnie as well as some new results. (shrink)

The Lorentz transformation of space and time between two reference frames is one of the pillars of the special relativity theory. As a result of the Lorentz transformation, space and time are only relative and are entangled, while the Minkowski metric is Lorentz invariant. For this reason, the Lorentz transformation is one of the major obstructions in the development of physical theories with quantized space and time. Here is described the Lorentz transformation of a physical (...) system with a discrete dynamical time and a continuous space that fulfills Lorentz invariance while approximating the Lorentz transformation at the time continuous limit and the Galilei transformation at the classical limit. Furthermore, the discreteness of time is not mixed with the continuous nature of space, making time distinct from space. (shrink)

In support of their contention that it is the absence of a subsisting medium that imbues the speed of light with fundamentality, Bryan Cheng and James Read discuss certain “fishbowl universes” in which physical influences evolve, not at the speed of light, but that of sound. The Lorentz transformation simulated in these sonic universes, which the authors cite from the literature of analogue gravity, is not that of Einstein, for whom an aether was “superfluous”, but that of the earlier (...) relativity of Lorentz and Poincaré, which did suppose such a medium. The authors’ intention is not to argue analogically, but simply to contrast the situation of light with that of sound. However, I argue that these universes are too successful as analogues to support the authors’ case. By reducing Lorentzian relativity to its bare essentials, they provide a compelling demonstration of the viability and explanatory strengths of the earlier theory. They show how a thoroughly wave-theoretic treatment of the elementary particles would explain why all aspects of matter transform in like manner, thereby avoiding a difficulty that was a significant reason for the demise of Lorentzian relativity after 1905. Importantly, these sonic universes suggest a unifying explanation, not only of the Lorentz transformation and de Broglie wave, but of the principle of relativity, which was merely postulated, rather than explained, by Einstein in 1905. (shrink)

A velocity-orientation formalism to deal with compositions of successive Lorentz transformations, emphasizing analogies shared by Lorentz and Galilean transformations, has recently been developed. The emphasis in the present article is on the convenience of using the velocity-orientation formalism by resolving a paradox in the study of successive Lorentz transformations of the electromagnetic field that was recently raised by Mocanu. The paradox encountered by Mocanu results from the omission of the Thomas rotation (or, precession) which (...) is involved in the composition of two Lorentz transformations with corresponding noncollinear velocity parameters. By resolving this paradox, we expose (i) the central role that the Thomas rotation plays in special relativity, (ii) the need to consider in special relativity orientations in addition to velocities between inertial frames, and (iii) the power and elegance of the novel velocity-orientation formalism. A similar paradox in STR that Mocanu pointed out, also resulting from the omission of the Thomas rotation, has been resolved in a previous communication. (shrink)

We consider a space with Generalized Uncertainty Principle which can be obtained in the frame of the deformed commutation relations. In the space with GUP we have found transformations relating coordinates and times of moving and rest frames of reference in the first order over the parameter of deformation. In the non-relativistic case we find the deformed Galilean transformation which is rotation in Euclidian space–time. This transformation is similar to the Lorentz one but written for Euclidean space–time where (...) the speed of light is replaced by some velocity related to the parameter of deformation. We show that for relativistic particle in the space with GUP the coordinates of the rest and moving frames of reference satisfy the Lorentz transformation with some effective speed of light. (shrink)

In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B, respectively, are examined using both the geometric algebra and tensor formalisms. Different 4D algebraic objects are used to represent the usual observer dependent and the new observer independent electric and magnetic fields. It is found that the ST of the ME differ from their LT and (...) consequently that the ME with the 3D E and B are not covariant upon the LT but upon the ST. The obtained results do not depend on the character of the 4D algebraic objects used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors EHv and BHv and the abstract tensors, the 4-vectors Ea and Ba. All these quantities are defined without reference frames, i.e., as absolute quantities. When some basis has been introduced, they are represented as coordinate-based geometric quantities comprising both components and a basis. It is explicitly shown that this geometric approach agrees with experiments, e.g., the Faraday disk, in all relatively moving inertial frames of reference, which is not the case with the usual approach with the 3D bf E and B and their ST. (shrink)

A new vectorial representation for the successive Lorentz transformations has recently been proved very convenient to achieve a straightforward treatment of the Thomas rotation effect. Such a representation rests on equivalent forms for the pure Lorentz transformation and SLT whose physical meaning escaped us. The present paper fills this gap in by showing that those equivalent forms could represent appropriate world lines, lines and planes of simultaneity. Those geometric elements are particularly convenient to build up two new (...) graphical representations for the SLT: the first rests on that equivalent form for the SLT, while the second takes the SLT as a PLT preceded or followed by a Thomas rotation and uses the equivalent form for the PLT. As an application, the SLT Lorentz contraction formulas are derived for the first time. The dependence of the SLTLC on the Thomas rotation is put in evidence. The SLTLC along directions transverse and parallel to the composite velocity is studied. Original SLT Minkowski diagrams are given for the first time. (shrink)

On the Linearity of the Lorentz transformations. U. Hoyer's argument for the linearity is discussed and a modification of the argument is proposed.

Special Relativity can be based on the whole proper group of both ortho- and antichronous Lorentz transformations, and a clear physical meaning can be given also to antichronous (i.e., nonorthochronous) Lorentz transformations. From the active point of view, the latter requires existence, for any particle, of its antiparticle within a purely relativistic, classical context. From the passive point of view, they give rise to frames “dual” to the ordinary ones, whose properties—here briefly discussed—are linked with the (...) fact that in relativity it is impossible to teach another, far observer (by transmitting only instructions, and no physical objects) our own conventions about the choices right/left, matter/antimatter, and positive/negative time direction. Interesting considerations follow, in particular, by considering—as it is the case—theCPT operation as an actual (even if antichronous) Lorentz transformation. (shrink)

We revisit the introduction of the Superluminal Lorentz transformations which carry from “bradyonic” inertial frames to “tachyonic” inertial frames, i.e., which transform time-like objects into space-like objects, andvice versa. It has long been known that special relativity can be extended to Superluminal observers only by increasing the number of dimensions of the space-time or—which is in a sense equivalent—by releasing the reality condition (i.e., introducing also imaginary quantities). In the past we always adopted the latter procedure. Here we (...) show the connection between that procedure and the former one. In other words, in order to clarify the physical meaning of the imaginary units entering the classical theory of tachyons, we have temporarily to call into play anauxiliary six-dimensional space-time M(3, 3); however, we are eventually able to go back to the four-dimensional Minkowski space-time. We revisit the introduction of the Superluminal Lorentz transformations also under another aspect. In fact, the generalized Lorentz transformations had been previously written down in a form suited only for the simple case of collinear boosts (e.g., they formed a group just for collinear boosts). We express now the Superluminal Lorentz transformations in a more general form, so that they constitute a group together with the ordinary—orthochronousand antichronous—Lorentz transformations, and reduce to the previous form in the case of collinear boosts. Our approach introduces either real or imaginary quantities, with exclusion of (generic) complex quantities. In the present context, a procedure—in two steps—for interpreting the imaginary quantities is put forth and discussed. In the case of a chain of generalized Lorentz transformations, such a procedure (when necessary) is to be applied only at the end of the chain. Finally, we justify why we call “transformations” also the Superluminal ones. (shrink)

U. Hoyer's argument for the linearity is discussed and a modification of the argument is proposed.

In this article we analyse the role of the principle of relativity and the generalisation of Lorentz transformations in Einstein's relativistic physics, whose philosophical ideal was the construction of an image of nature endowed with maximum unity and logical simplicity. In his critical-rationalist realism, Einstein aimed to develop a "conception of the world" that expressed the logical unity of nature. Throughout his scientific career, this philosophical programme led him to produce "great syntheses", seeking compatibility between different physical systems.

The use of the axial vector representing a three-dimensional rotation makes the rotation representation much more compact by extending the trigonometric functions to vectorial arguments. Similarly, the pure Lorentz transformations are compactly treated by generalizing a scalar rapidity to a vector quantity in spatial three-dimensional cases and extending hyperbolic functions to vectorial arguments. A calculation of the Wigner rotation simplified by using the extended functions illustrates the fact that the rapidity vector space obeys hyperbolic geometry. New representations bring (...) a Lorentz-invariant fundamental equation of motion corresponding to the Galilei-invariant equation of Newtonian mechanics. (shrink)

We present a derivation of the homogeneous Lorentz transformations that arrives immediately at the general form without the usual specialization in thex direction.

We present a mechanical model of a quasi-elastic body which reproduces Maxwell’s equations with charges and currents. Major criticism against mechanical models of electrodynamics is that any presence of charges in the known models appears to violate the continuity equation of the aether and it remains a mystery as to where the aether goes and whence it comes. We propose a solution to the mystery—in the present model the aether is always conserved. Interestingly it turns out that the charge velocity (...) coincides with the aether velocity. In other words, the charges appear to be part of the aether itself. We interpret the electric field as the flux of the aether and the magnetic field as the torque per unit volume. In addition we show that the model is consistent with the theory of relativity, provided that we use Lorentz–Poincare interpretation of relativity theory. We make a statistical-mechanical interpretation of the Lorentz transformations. It turns out that the length of a body is contracted by the electromagnetic field which the molecules of this same body produce. This self-interaction causes also delay of all the processes and clock-dilation results. We prove this by investigating the probability distribution for a gas of self-interacting particles. We can easily extend this analysis even to elementary particles. (shrink)

In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D space-time and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E a and B a , as well-defined (...) 4D quantities, are introduced instead of ill-defined 3D E and B. The proof is given in the tensor and the Clifford algebra formalisms. (shrink)

A complete treatment of the Thomas rotation involves algebraic manipulations of overwhelming complexity. In this paper, we show that a choice of convenient vectorial forms for the relativistic addition law of velocities and the successive Lorentz transformations allows us to obtain straightforwardly the Thomas rotation angle by three new methods: (a) direct computation as the angle between the composite vectors of the non-collinear velocities, (b) vectorial approach, and (c) matrix approach. The new expression of the Thomas rotation angle (...) permits us to simply obtain the Thomas precession. Original diagrams are given for the first time. (shrink)

As shown by Ramarkrishnan, the faithful mapping, in the sense of Lie groups, of the real line onto the finite segment−1Lorentz-Poincaré transformation formulas. Composition of translations is merely one application of this. Carmeli has shown that composition of rotations is another one. There may be still others.

Application of recently developed non-Archimedean algebra to a flat and finite universe of total mass M 0 and radius R 0 is described. In this universe, mass m of a body and distance R between two points are bounded from above, i.e., 0≤m≤M 0, 0≤R≤R 0. The universe is characterized by an event horizon at R 0 (there is nothing beyond it, not even space). The radial distance metric is compressed toward horizon, which is shown to cause the phenomenon of (...) red shift. The corresponding modified Minkowski's metric and Lorentz transforms are obtained. Applications to Newtonian gravity shows a weakening at large scales (R→R 0) and a regular behavior as R→0. (shrink)

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. (shrink)

One of the most debated problems in the foundations of the special relativity theory is the role of conventionality. A common belief is that the Lorentz transformation is correct but the Galilean transformation is wrong. It is another common belief that the Galilean transformation is incompatible with Maxwell equations. However, the “principle of general covariance” in general relativity makes any spacetime coordinate transformation equally valid. This includes the Galilean transformation as well. This renders a new paradox. This new paradox (...) is resolved with the argument that the Galilean transformation is equivalent to the Lorentz transformation. The resolution of this new paradox also provides the most straightforward resolution of an older paradox which is due to Selleri in. I also present a consistent electrodynamics formulation including Maxwell equations and electromagnetic wave equations under the Galilean transformation, in the exact form for any high speed, rather than in low speed approximation. Electrodynamics in rotating reference frames is rarely addressed in textbooks. The presented formulation of electrodynamics under the Galilean transformation even works well in rotating frames if we replace the constant velocity v\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {v}$$\end{document} with v=ω×r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {v}=\varvec{\omega }\times \mathbf {r}$$\end{document}. This provides a practical tool for applications of electrodynamics in rotating frames. When electrodynamics is concerned, between two inertial reference frames, both Galilean and Lorentz transformations are equally valid, but the Lorentz transformation is more convenient. In rotating frames, although the Galilean electrodynamics does not seem convenient, it could be the most convenient formulation compared with other transformations, due to the intrinsic complex nature of the problem. (shrink)

The behavior of Lyapunov exponents λ and dynamical entropies h, whose positivity characterizes chaotic motion, under Lorentz and Rindler transformations is studied. Under Lorentz transformations, λ and h are changed, but their positivity is preserved for chaotic systems. Under Rindler transformations, λ and h are changed in such a way..

The priorities of French policy regarding genetically modified (GM) food shifted in the late 1990s from aggressive promotion to strict regulation based on precaution and separation of GM food. This paradigmatic policy change coincided with a rapid shift in the dominant meanings of GM food in larger French public discourses. Using data from media coverage, organizational documents, and in-depth interviews, the study examines the relationship between policy developments and GM food’s symbolic transformation. I argue that the interpretive dimension interacted (...) with and co-evolved incrementally with formal policy developments, and that it cannot be understood as epiphenomenal to political processes, or as preceding and propelling a policy change. I identify three mechanisms of symbolic transformation: (1) multiplication of meanings; (2) association with other salient issues; and (3) coupling with national identity (boundary work). Conversely, this symbolic transformation influenced the terms of political debates and viable strategies, influencing policy developments. The study also demonstrates how certain longstanding elements of French political culture shaped, and were changed or reproduced through, these processes. (shrink)

The behavior of Lyapunov exponents λ and dynamical entropies h, whose positivity characterizes chaotic motion, under Lorentz and Rindler transformations is studied. Under Lorentz transformations, λ and h are changed, but their positivity is preserved..

When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is largely because of the emergence of quantum mechanics with wave-particle duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have to deal with Lorentz transformations of waves. We now have some nderstanding of plane waves or running waves in (...) the covariant picture, but we do not yet have a clear picture of standing waves. In this report, we show that there is one set of standing waves which can be Lorentz-transformed while being consistent with all physical principle of quantum mechanics and relativity. It is possible to construct a representation of the Poincaré group using harmonic oscillator wave functions satisfying space-time boundary conditions. This set of wave functions is capable of explaining the quantum bound state for both slow and fast hadrons. In particular it can explain the quark model for hadrons at rest, and Feynman’s parton model hadrons moving with a speed close to that of light. (shrink)

Although Maxwell theory is O(3,1)-covariant, electrodynamics only transforms invariantly between Lorentz frames for special forms of the field, and the generator of Lorentz transformations is not generally conserved. Bérard, Grandati, Lages, and Mohrbach have studied the O(3) subgroup, for which they found an extension of the rotation generator that satisfies the canonical angular momentum algebra in the presence of certain Maxwell fields, and is conserved by the classical motion. The extended generator depends on the field strength, but (...) not the potential, and so is manifestly gauge invariant. The conditions imposed on the Maxwell field by the algebra lead to a Dirac monopole solution.In this paper, we study the generalization of the Bérard, Grandati, Lages and Mohrbach construction to the full Lorentz group in N dimensions. The requirements can be maximally satisfied in a three-dimensional subspace of the full Minkowski space; this subspace can be chosen to describe either an O(3)-invariant space sector, or an O(2,1)-invariant restriction of spacetime. The field solution reduces to the Dirac monopole found in the nonrelativistic case when the O(3)-invariant subspace is selected. When an O(2,1)-invariant subspace is chosen, the field strength can be associated with a Coulomb-like potential of the type A μ(x) = n μ/ρ, where ρ = (x μ x μ)1/2, similar to that used by Horwitz and Arshansky to obtain a covariant generalization of the hydrogen-like bound state. In the presence of these fields, which are determined entirely by symmetry considerations, without reference to a source equation, the extended generator is conserved under classical relativistic system evolution. (shrink)

In 1992 M.W. Evans proposed the O(3) symmetry of electromagnetic fields by adding a constant longitudinal magnetic field to the well-known transverse electric and magnetic fields of circularly polarized plane waves, such that certain cyclic relations of a so-called O(3) symmetry are fulfilled. Since then M.W. Evans has elevated this O(3) symmetry to the status of a new law of electromagnetics. As a law of physics must be invariant under admissible coordinate transforms, namely Lorentz transforms, in 2000 he published (...) a proof of the Lorentz invariance of O(3) symmetry of electromagnetic fields. As will be shown below this proof is incorrect; more, after simple correction it will turn out here that the O(3) symmetry cannot be Lorentz invariant. (shrink)

In the course of his work on optics and electrodynamics in systems moving through the ether, the 19th-century medium for light waves and electric and magnetic fields, Lorentz discovered and exploited the invariance of the free-field Maxwell equations under what Poincaré later proposed to call Lorentz transformations. To account for the negative results of optical experiments aimed at detecting the earth’s motion through the ether, Lorentz, in effect, assumed that the laws governing matter interacting with light (...) waves are Lorentz invariant as well. Like Lorentz, Einstein first encountered the Lorentz transformations in electrodynamics. Unlike Lorentz, for whom the transformation merely provided convenient mathematical substitutions, but like Poincaré, Einstein recognized that the Lorentz-transformed quantities are the measured quantities for the moving observer. More importantly, Einstein recognized that the Lorentz invariance of all physical laws had nothing to do with electrodynamics per se, but reflected the kinematics in a new relativistic space-time, to be named after Minkowski who worked out its geometry a few years later. (shrink)