Narrow Results

In this letter, by using the properties of the entropy function and the fundamental equation of thermodynamics, we discuss the reasons that there exist different proposals for relativistic temperature transformation. Further, we illustrate this point by studying a concrete thermodynamic system-blackbody radiation.

The problem of the Dirac particle submitted to a wave $(E,B)$ of a four-dimensional constant electromagnetic tensor is solved with the path integral approach via the use of Lorentz transformation and with an adequate choice for the velocity of the mobile referential.

We show that the supersymmetric action associated to the pair $(E,B)$ can be determined from that associated to the pair $(0,B^{\prime })$ and from that associated to the pair $(E^{\prime },0)$ following simple relations.

The wave functions and the energy spectrums are thus exactly determined and tested. Special cases are considered as well.

The theory of special relativity derives from the Lorentz transformation. The Lorentz transformation implies differential simultaneity and light speed isotropy. Experiments to probe differential simultaneity should be able to distinguish the Lorentz transformation from a kinematically-similar alternate transformation that predicts absolute simultaneity, the absolute Lorentz transformation. Here, we describe how published optical tests of light speed isotropy/anisotropy cannot distinguish between the two transformations. We show that the shared equations of the two transformations, from the perspective of the “stationary” observer, are sufficient to predict null results in optical resonator experiments and in tests of frequency changes in one-way light paths. In an influential 1910 exposition on differential simultaneity, Comstock described how a “stationary” observer would observe different clock readings for spatially-separated “moving” clocks. The difference in clock readings is an integral aspect of differential simultaneity. We derive the equation for the difference in clock readings and show that it is equivalent to the Sagnac correction that describes light speed anisotropies in satellite communications. We describe an experimental strategy that can measure the differences in spatially-separated clock times to allow a direct probe of the nature of simultaneity.

Rotational transformations describe relativistic effects in rotating frames. There are four major kinematic rotational transformations: the Langevin metric; Post transformation; Franklin transformation; and the rotational form of the absolute Lorentz transformation. The four transformations exhibit different combinations of relativistic effects and simultaneity frameworks, and generate different predictions for relativistic phenomena. Here, the predictions of the four rotational transformations are compared with recent optical data that has sufficient resolution to distinguish the transformations. We show that the rotational absolute Lorentz transformation matches diverse relativistic optical and non-optical rotational data. These include experimental observations of length contraction, directional time dilation, anisotropic one-way speed of light, isotropic two-way speed of light, and the conventional Sagnac effect. In contrast, the other three transformations do not match the full range of rotating-frame relativistic observations.

The simultaneity framework describes the relativistic interaction of time with space. The two major proposed simultaneity frameworks are differential simultaneity, in which time is offset with distance in “moving” or rotating frames for each “stationary” observer, and absolute simultaneity, in which time is not offset with distance. We use the Mansouri and Sexl test theory to analyze the simultaneity framework in rotating frames in the absence of spacetime curvature. The Mansouri and Sexl test theory has four parameters. Three parameters describe relativistic effects. The fourth parameter, $𝜖(v)$, was described as a convention on clock synchronization. We show that $𝜖(v)$ is not a convention, but is instead a descriptor of the simultaneity framework whose value can be determined from the extent of anisotropy in the unidirectional one-way speed of light. In rotating frames, one-way light speed anisotropy is described by the Sagnac effect equation. We show that four published Sagnac equations form a relativistic series based on relativistic kinematics and simultaneity framework. Only the conventional Sagnac effect equation, and its associated isotropic two-way speed of light, is found to match high-resolution optical data. Using the conventional Sagnac effect equation, we show that $𝜖(v)$ has a null value in rotating frames, which implies absolute simultaneity. Introducing the empirical Mansouri and Sexl parameter values into the test theory equations generates the rotational form of the absolute Lorentz transformation, implying that this transformation accurately describes rotational relativistic effects.

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.

It is generally assumed in the literature that a Lorentz transformation on a neutral current loop results in a moving current loop with a nonvanishing charge distribution and an electric dipole moment. We show in this paper that this is not, in fact, correct. The derivation that leads to the charge distribution was based on an incomplete Lorentz transformation, which transforms the charge-current four-vector $j^{\mu }=[\rho (r,t),j(r,t)]$, but not the space–time four-vector $x^{\mu }=(t,r)$. We show that completing the Lorentz transformation by using the variable $t^{\prime }$ in the moving frame, rather than keeping the rest frame time variable $t$, results in there being no induced charge density and no resulting electric dipole moment.

We show that the claim by Franklin (Int. J. Mod. Phys. A35, 2050061 (2020)) with respect to the vanishing charge distribution over the perimeter of an electrically neutral moving current loop is erroneous and is based on a misinterpretation of physical meaning of Lorentz transformations. Moreover, we show that the development of nonvanishing electric dipole moment by a moving current loop (which we named as “relativistic polarization”) represents a direct implication of covariant formulation of classical electrodynamics of material media. In this respect, we analyze some subtle effects related to the motion of magnetic dipoles in an electromagnetic field and disclose their physical meaning.

We show that the attack on my paper, “Complete Lorentz transformation of a charge-current density,” by Kholmetskii, Missevitch, and Yarman in their paper, “Lorentz transformation of a charge-current density and ‘relativistic polarization’ of a moving current loop” is based on completely erroneous assumptions and equations.

We show that the comment by Franklin (Int. J. Mod. Phys. A 36, 2175001 (2021)) on our paper “Lorentz transformation of a charge-current density and “relativistic polarization” of a moving current loop” (Int. J. Mod. Phys. A 36, 2175001 (2021)), like the previous publication of this author entitled “Complete Lorentz transformation of a charge-current density” (Int. J. Mod. Phys. A 35, 2050061 (2020)), contains fundamental errors in the physical interpretation of Lorentz transformations, which are once again disclosed with some particular examples.

The Lorentz transformation describes differential simultaneity, which reflects the offsetting of time with distance between reference frames. Differential simultaneity is essential for Lorentz invariance. Here, the current experimental support for differential simultaneity is assessed. Differential simultaneity can be mathematically removed from the Lorentz transformation to produce an alternate transformation that describes relativistic effects in the absence of differential simultaneity. Differential simultaneity is shown to be required for Lorentz symmetry. The alternate transformation is used as a contrast for the Lorentz transformation to assess whether relativistic experiments provide definitive evidence for differential simultaneity. If the alternate transformation is compatible with an experiment, then the experiment does not provide definitive evidence for differential simultaneity because it can be explained in the absence of differential simultaneity. Here, the alternate transformation is shown to be compatible with the broad array of current relativistic experiments. This implies that current experiments do not provide definitive evidence for differential simultaneity. Thus, an essential aspect of Lorentz symmetry currently lacks definitive experimental support.

A v_J/c correction to the Shapiro time delay seems verified by a 2002 Jovian observation by VLBI. In this Essay, this correction is interpreted as an effect of the aberration of light in an optically refractive medium which supplies an analog of Jupiter's gravity field rather than as a measurement of the speed of gravity, as it was first proposed by other authors. The variation of the index of refraction is induced by the Lorentz invariance of the weak gravitational field equations for Jupiter in a uniform translational slow motion with velocity v_J=13.5 km/s. The correction on time delay and deflection is due not to the Kerr (or Lense-Thirring) stationary gravitomagnetic field of Jupiter, but to its Schwarzschild gravitostatic field when measured from the barycenter of the solar system.

By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.

We revise the Dirac equation for a free particle and investigate Lorentz transformations on spinors. We study how the spin quantization axis changes under Lorentz transformations, and evince the interplay between spin and momentum in this context.

Bell-like inequalities have been used in order to distinguish non-local quantum pure states by various authors. The behavior of such inequalities under Lorentz transformation (LT) has been a source of debate and controversies in the past. In this paper, we consider the two most commonly studied three-particle pure states, that of W and Greenberger–Horne–Zeilinger (GHZ) states which exhibit distinctly different types of entanglement. We discuss the various types of three-particle inequalities used in previous studies and point to their corresponding shortcomings and strengths. Our main result is that if one uses Czachor’s relativistic spin operator and Svetlichny’s inequality as the main measure of non-locality and uses the same angles in the rest frame (S) as well as the moving frame ($S^{\prime }$), then maximally violated inequality in S will decrease in the moving frame, and will eventually lead to lack of non-locality (i.e. satisfaction of inequality) in the $v\to c$ limit. This is shown for both the GHZ and W states and in two different configurations which are commonly studied (Cases 1 and 2). Our results are in line with a more familiar case of two particle case. We also show that the satisfaction of Svetlichny’s inequality in the $v\to c$ limit is independent of initial particles’ velocity. Our study shows that whenever we use Czachor’s relativistic spin operator, results draws a clear picture of three-particle non-locality making its general properties consistent with previous studies on two-particle systems regardless of the W state or the GHZ state is involved. Throughout the paper, we also address the results of using Pauli’s operator in investigating the behavior of $|S_v|$ under LT for both of the GHZ and W states and two cases (Cases 1 and 2). Our investigation shows that the violation of $|S_v|$ in moving frame depends on the particle’s energy in the lab frame, which is in agreement with some previous works on two and three-particle systems. Our work may also help us to classify the results of using Czachor’s and Pauli’s operators to describe the spin entanglement and thus the system spin in relativistic information theory.

The attempt of this paper is to suggest a new theoretical medium to support the efforts of building particle models as mechanical field structures. The medium model is based on two simple fundamental assumptions. All the properties of the medium, as counterparts in this medium of the well-known physics laws, including energy and momentum conservations, Lorentz transformation and special relativity, electromagnetic interaction, etc., are derived from these two assumptions. The governing equations are established based on the derived properties. Some steady solutions as well as the feasibility of interpreting these solutions as particles are also briefly discussed.

Here, we present a new physical quantity with the aim of unifying the structure of physics. The basic assumption starts with a reduction of all the natural forces into a single force. As a first step, we combine Coulomb’s law and the law of gravity into a single law. Astonishingly, this new law introduces a force never before described, which takes the form of a mass–charge force. This new force may be responsible for holding together the atomic nucleus, counteracting the Coulomb repulsive force. As such, this nuclear force could also be integrated into the new force law. A reduction of the natural forces into a single force would also reduce the number of conservation laws. The discussion herein focuses only on whether gravitational and inertial masses are identical or have different properties: if velocity increases, inertial mass also increases, but gravitational mass appears to remain constant. Furthermore, this may make it possible to measure absolute $\gamma$ factors which are given by the quotient of the inertial and gravitational masses. If true, this would invalidate one of the postulates of the theory of special relativity, leaving the theory of relativity open to new interpretations. Introduction of the new quantity, the complex number consisting of charge and mass $(bq,m_0)$, would not, however, invalidate other well-known formulas of physics, for the following reasons: with respect to all equations relating to gravitational mass, the charges usually sum to zero, yielding $q=0$ and $(bq,m_0)\cong m$, leading to no inconsistencies; with respect to all equations relating to charge, the error would similarly be negligible, since charge changes through m only by adding the summand $m∕b$. Since the gravitational mass of an electron is very small, precise measurements are needed to verify this proposed complex relationship. The inertial mass would remain as has been established.

Classical mechanics, relativity, electrodynamics, and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the necessary number of postulates. We uncover an intrinsic connection of these areas of physics and describe them using a common symplectic Hamiltonian formalism. Our approach is based on a proper distinction between variables and constants, i.e. on a basic but rigorous ontology of time. We link these concepts with theobvious conditions for the possibility of measurements. The derived consequences put the measurement problem of quantum mechanics and the Copenhagen interpretation of the quantum mechanical wave function into perspective. According to our (onto-) logic, we find that spacetime cannot be fundamental. We argue that a geometric interpretation of symplectic dynamics emerges from the isomorphism between the corresponding Lie algebra and the representation of a Clifford algebra. Within this conceptional framework, we derive the dimensionality of spacetime, the form of Lorentz transformations and of the Lorentz force and fundamental laws of physics as the Planck–Einstein relation, the Maxwell equations, and finally the Dirac equation.

Special Relativity is absolutely basic for our understanding of physical phenomena. It has been invented to overcome the incompatibility of Newtonian mechanics and electrodynamics. The foundations as well as the predictions of Special Relativity have been tested in many respects and with very high accuracy. Here we shortly review the foundations of Special Relativity and report on various attempts to model theoretically violations of Special Relativity. We describe experiments testing the foundations and the predictions of Special Relativity and also discuss ongoing projects to improve the accuracy of these tests even more.

A macroscopic object equipped with synchronized clocks is examined. General physical relations are directly derived from Lorentz transformations for the case of one-dimensional motion (along the X axis) – the uncertainty relation of the object’s x coordinate and the projection of its impulse along the X axis, p_x, and the uncertainty relation of the object’s observation time, t, and its energy, E. The uncertainty relations take the form dp_xdx > H and dEdt > H. The H value in the relation has action dimensions and is dependent upon the precision of the rod’s clocks and its mass. It is shown that if the macroscopic object in and of itself performs the function of an ideal physical clock, the uncertainty relations derived in the limiting case then take the usual form of dp_xdx ≥ h and dEdt ≥ h, where h is the Planck constant.