Lorentz Transformations Research Articles

A Transformation Factor for Superluminal Motion That Preserves Symmetrically the Spacetime Intervals

While superluminal phenomena are not empirically substantiated, they present an intriguing hypothetical case. For this speculative framework, the Lorentz transformations would necessitate a revision: instead of the standard γ(x−vt), the absolute value of x′ ought to be expressed as γ(vt−x), because if v were to exceed c, then the interval vt traversed by the superluminal frame S′ would surpass the distance covered by light. Under the postulates of relativity, the subluminal scenario leads to the conventional Lorentz factor. Meanwhile, the superluminal scenario introduces an alternative transformation factor that accounts for the presence of the speed of light (c) barrier. This factor is also invariant within Minkowski spacetime, meaning it symmetrically preserves spacetime intervals. The details of this derivation become more evident when using a reverse coordinate system. This result is not, per se, evidence for the existence of superluminal phenomena, but it does allow us to speculate with a new argument about the possibility of their existence.

Gauged double field theory, current algebras and heterotic sigma models

We study the O(D, D + n) generalized metric and the gauge symmetries in the gauged double field theory (DFT) in view of current algebras and sigma models. We show that the O(D, D + n) generalized metric in the gauged DFT is consistent with the heterotic sigma models at the leading order in the α′-corrections. We then study the non-Abelian gauge symmetries and current algebras of heterotic string theories. We show that the algebras exhibit the correct diffeomorphism, the B-field gauge transformations of the background fields together with the non-Abelian gauge transformations possibly with the appropriate local Lorentz transformations.

Calculating the gravitational waves emitted from high-speed sources

The possibility of forming gravitational-wave sources with high center-of-mass (c.m.) velocities in the vicinity of supermassive black holes requires us to develop a method of deriving the waveform in the observer's frame. Here we show that in the limit where the c.m. velocity is high but the relative velocities of the components of the source are small, we can solve the problem by directly integrating the relaxed Einstein field equation. In particular, we expand the result into multipole components which can be conveniently calculated given the orbit of the source in the observer's frame. Our numerical calculations using arbitrary c.m. velocities show that the result is consistent with the Lorentz transformation of gravitational waves (GWs) to the leading order of the radiation field. Moreover, we show an example of using this method to calculate the waveform of a scattering event between the high-speed ($\ensuremath{\sim}0.1c$) stellar objects embedded in the accretion disk of an active galactic nucleus. Our multipole-expansion method not only has advantages in analyzing the results from stellar-dynamical models but also provides new insight into the multipole properties of the GWs emitted from a high-speed source.

Replicating physical motion with Minkowskian isorefractive spacetime crystals

Abstract Here, we show that isorefractive spacetime crystals with a travelling-wave modulation may mimic rigorously the response of moving material systems. Unlike generic spacetime crystals, which are characterized by a bi-anisotropic coupling in the co-moving frame, isorefractive crystals exhibit an observer-independent response, resulting in isotropic constitutive relations devoid of any bianisotropy. We show how to take advantage of this property in the calculation of the band diagrams of isorefractive spacetime crystals in the laboratory frame and in the study of the synthetic Fresnel drag. Furthermore, we discuss the impact of considering either a Galilean or a Lorentz transformation in the homogenization of spacetime crystals, showing that the effective response is independent of the considered transformation.

The Lorentz Transformation in a Fishbowl: A Comment on Cheng and Read’s “Why Not a Sound Postulate?”

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.

The Direct Cylindrical Boris Algorithm

A modification of Boris Algorithm in cylindrical coordinate used to solve Lorentz equation for axisymmetrical plasma simulation is proposed. The velocity updates are calculated directly using matrix operation. The inertial forces are evaluated at n-0.5 time steps. The algorithm is tested for several scenarios: electric field only, electric field dominated, |E| = |B|, ExB drift, gyration test, and a test devised by Delzanno. The result is compared to the standard Boris solver in cylindrical coordinate. The results show that even though generally the solver is not that accurate compared to the standard Boris solver, especially for a larger time step width, it is comparatively faster. Thus, the solver might be useful for plasma simulations that do not require detailed trajectory for each simulated particle.

Some Problems Found in the Proof of Lorentz Transformation

Some Problems Found in the Proof of Lorentz Transformation

Simulating noisy quantum channels via quantum state preparation algorithms

In Xin et al (2017 Phys. Rev. A 96 062303) and Wei et al (2018 Sci. China Phys. Mech. Astron. 61 70311), the authors reported an algorithm to simulate, in a circuit-based quantum computer, a general quantum channel (QC). However, the application of their algorithm is limited because it entails the solution of intricate non-linear systems of equations in order to obtain the quantum circuit to be implemented for the simulation. Motivated by this issue, in this article we identify and discuss a simple way to implement the simulation of QCs on any d-level quantum system through quantum state preparation algorithms, that have received much attention in the quantum information science literature lately. We exemplify the versatility of our protocol applying it to most well known qubit QCs, to some qudit QCs, and to simulate the effect of Lorentz transformations on spin states. We also regard the application of our protocol for initial mixed states. Most of the given application examples are demonstrated using IBM’s quantum computers.

Relativistic transformations of quasi-monochromatic paraxial optical beams

A monochromatic plane wave recorded by an observer moving with respect to the source undergoes a Doppler shift and spatial aberration. We investigate here the transformation undergone by a generic, paraxial, spectrally coherent quasimonochromatic optical beam (of finite transverse width) when recorded by a moving detector. Because of the space-time coupling intrinsic to the Lorentz transformation, the monochromatic beam is converted into a propagation-invariant pulsed beam traveling at a group velocity equal to that of the relative motion and which belongs to the recently studied class of ``space-time wave packets.'' We show that the predicted transformation from a quasimonochromatic beam to a pulsed wave packet can be observed even at terrestrial speeds.

Relativistic Bistatic Scattering of a High-Speed Moving Plasma Coated Object

Accurate modeling of relativistic electromagnetic scattering characteristics from high-speed motion of plasma coated objects is crucial for the development of hypersonic aircraft and their applications in the identification and surveillance of moving stealth targets. Nevertheless, a solution for bistatic polarized radar cross sections (RCSs) from a 3-D object with plasma coated layer in motion has yet to be obtained. This manuscript proposes a solution to this problem by employing a combination of the auxiliary differential equation (ADE) method with Lorentz finite-difference time-domain (FDTD) method. Utilizing the Lorentz transformation, this paper presents the transformation of parameters of the incident plane wave and dimensions of the object between the laboratory system that remains static and the rest system that remains stationary relative to the object in high-speed motion. The near-zone electromagnetic fields near the object are computed using the ADE method in the rest system, after which the near-field to far-field (NF-FF) transformation is employed to obtain the far-zone polarized scattered field. By applying Lorentz transformation to the coordinates, this paper presents a solution for the polarized scattering from moving plasma coated objects. Especially, radial components of the polarized scatterings are analyzed. The proposed method is validated through several numerical experiments, demonstrating its efficiency and accuracy.

Studies on the Optical Dispersion Parameters and Electronic Polarizability of Cadmium Sulphide Thin Film

Thin film of Cadmium Sulphide (CdS) was deposited onto a precleaned transparent glass substrate by chemical bath deposition technique from a bath containing Cadmium acetate, ammonium acetate, thiourea and ammonium hydroxide. The deposition time was varied from 10 minutes to 50 minutes at an interval of 20 minutes keeping the bath at a constant temperature of using 78HW-1 constant magnetic stirrer. CdS thin film was characterized by UV-Visible spectrophotometer within the wavelength range of 280 nm – 920 nm using Single – Beam Helios Omega UV – VIS spectrophotometer. The optical parameters; extinction coefficient, refractive index and dielectric constant of CdS thin film were analyzed from the absorption spectra and were found to be affected by the deposition time. The optical band gap energy was obtained by Tauc’s equation and were found to decrease from 3.78 eV – 3.70 eV as the deposition time increases. The dispersion parameters (dispersion energy , oscillation energy , moment of optical dispersion spectra and , static dielectric constant and static refractive index ) were calculated using theoretical Wemple-DiDomenico model. The result show that only and behaved differently but other parameters increase as the deposition time increases. The oscillator strength , oscillator wavelength , high frequency dielectric constant and high frequency refractive index were calculated using single Sellmeier oscillator model. While behaved differently other parameters increase as the deposition time increased. Also, Lattice dielectric constant , N/m* and plasma resonance frequency were equally obtained. While decrease with increase in deposition time, N/m* increase with deposition time. The electronic polarizability of CdS thin film was estimated by Lorenz - Lorentz equation and Clausius Mossotti local field polarizability model. The value is an indication that the films showed good response on the application of photon energy. However, its response reduces as the deposition time increases.

Simulation of XRD data by modified Arrhenius and Lorentz equations for ferroelectric ceramics having cubic, rhombohedral and tetragonal crystal structure

In the present, paper the simulation of XRD data by modified Arrhenius and Lorentz equations has been proposed for the first time which is new. The trial of simulations have been performed on ferroelectric ceramics [Ba(Nd0.1Ti0.8Nb0.1)TiO3]1-x[Na0.5Bi0.5TiO3]x (x = 0.25), Na(0.5-x)KxBi(0.5-x)DyxTiO3 (x = 0.0125) and (Ba0.997Nd0.003TiO3)+5% SiO2. The simulations performed on the above ceramics are in good agreement with the experimental data. Using the modified Arrhenius and Lorentz equations, we obtained the lattice parameters for the ceramic samples having cubic, rhombohedral and tetragonal symmetry. In addition to the lattice parameters, the activation energy for diffraction has also been evaluated. The simulations of XRD data using Arrhenius and Lorentz equations can also be extended to other compounds with different crystal symmetry.

Lorentz transformation of three dimensional gravitational wave tensor

Recently there has been more and more interest in the gravitational wave (GW) of moving sources. This paper introduces a Lorentz transformation problem of GWs. Although the Bondi-Metzner-Sachs (BMS) theory has in principle already included the Lorentz transformation of GWs, the transformation of the three-dimensional GW tensor has not been explicitly calculated before. Within four-dimensional spacetime, GWs have the properties of ‘boost weight zero’ and ‘spin weight 2’. This fact makes the Lorentz transformation of GWs difficult to understand. In the current paper, we adopt the traditional three-dimensional tensor description of a GW. Such a transverse-traceless tensor describes the GW freedom directly. We derive the explicit Lorentz transformation of the GW tensor. The transformation is similar to the Lorentz transformation for an electric field vector and a magnetic field vector which are three-dimensional vectors. Based on the deduced Lorentz transformation of the GW three-dimensional tensor, we can construct the gravitational waveform of a moving source with high speed if only the waveform of the corresponding rest waveform is given.

Nonparaxial Tilted Waveobjects

Simple closed-form analytical expressions for tilted astigmatic wave beams and wavepackets that are exact solutions of the wave equation are constructed. They are obtained through two different but equivalent derivations, one is based on a complex shift in the Bateman-type solutions, the other employs their Lorentz transformation. Analytic expressions for the propagation invariants: energy, momentum and orbital angular momentum of tilted waveobjects with general astigmatism are presented.

Magnetic Perturbations in Electron Phase‐Space Holes: Contribution of Electron Polarization Drift

AbstractElectron phase‐space holes, sometimes referred to as electron holes, are Debye‐scale plasma structures commonly observed in space plasmas. Although they are usually thought of as electrostatic structures, recent observations have shown that these structures are often accompanied by magnetic field perturbations. Such magnetic perturbations may originate from Lorentz transformation of the electric field, although it has been also suggested that localized currents caused by the electron E × B motion may also play a role. In this paper, we consider the contribution of electron polarization drift to the current and therefore the magnetic field perturbations, which is validated by comparison to Magnetospheric MultiScale observations of 69 electron holes based on a superposed epoch technique. Our results show that the magnetic perturbations caused by the electron polarization drift can be significant compared to Lorentz transformation effect, especially in regions with low magnetic strength and large electron density.

A Re-understanding of the Zero Result of the Michelson-Morley Experiment

As well-known that in order to explain the zero result of the Michelson-Morley experiments (M-M experiments), Lorentz proposed the Lorentz formula of coordinate transformation and led to the birth of Einstein's special relativity. The authors carefully re-examine the M-M experiment and find a serious problem. The premise of the M-M experimental calculations was that the light source was fixed on the absolutely stationary reference frame of the universe (or the ether stationary reference frame). However, in the actual experiments, the light source was fixed on the earth motion reference frame, moving and rotating with the interferometers, which lead to the invalid calculation result of the M-M experiment. In this paper, the correct calculation method is used to prove that the zero result of the M-M experiment can be well explained by using the Galilean relativity principle and the Galilean velocity addition rule. Therefore, the most important experimental foundation of special relativity does not exist. The Lorentz coordinate transformation formulas become unnecessary, and the principles of special relativity and the invariant speed of light are unnecessary too. The experimental tests of special relativity are also discussed briefly. It points out that these experiments are either wrong or have other explanations, and the explanations of special relativity are not unique ones. Physics should give up the Lorentz transformation formula and the Einstein's special relativity completely, introduce the cosmic absolute stationary reference frame, and establish the kinetic theory based on the mass-velocity formula which should be considered as an empirical formula, to solve the fundamental problems in astrophysics and cosmology thoroughly.

Mass-velocity Formula and Mass-energy Relation Cannot Be Derived Based on Lorentz Velocity Transformation

The most important achievement of the Einstein's special relativity was to derive the mass-velocity formula and the famous mass-energy relation from the Lorentz velocity transformation formula. Based on the mass-velocity formula, the dynamics of special relativity was established. In this paper, six derivation methods of the mass-velocity formula in special relativity are re-analyzed, including the elastic collision and the inelastic collision of two particles, the particle splitting processes, and the force moment balance methods based on the Lorentz velocity transformation formula, as well as the method to consider the symmetry principle without using the Lorentz transformation formula. It is pointed out that all of them have serious problems so that they cannot hold actually. Besides, it is pointed out that the method of Hamiltonian action to derive the mass-velocity has nothing to do with the Lorentz velocity transformation and does not belong to the category of special relativity. Therefore, the conclusion of this paper is that it is impossible to derive the mass-velocity formula and the mass-energy relation based on the Lorentz velocity transformation formula. The mass-velocity formula can only be considered as an empirical formula which cannot be derived in theory and have nothing to do with special relativity. If the mass-velocity formula and the mass-energy relationship are correct, it just means that Einstein's special relativity is not true.

The Failure of Both Einstein’s Space-time Theory and His Equivalence Principle and Their Resolution by the Uniform Scaling Method

The Lorentz transformation (LT) makes three predictions which are not consistent with one another: Lorentz-FitzGerald length contraction (FLC), time dilation (TD) and light-speed equality for observers in relative motion to one another. The LT also stands in violation of the Law of Causality because it fails to recognize that inertial clocks can never change their rate spontaneously. Einstein’s light-speed postulate (LSP) is shown to be unviable by considering a case in which a light source passes by a stationary observer at the same time that it emits a light pulse in the same direction. It is found that, in contradiction to the LSP, that the classical velocity (Galilean) transformation (GVT) is applicable when two observers in relative motion deduce the speed of a light wave. The Newton-Voigt transformation (NVT) is consistent with the Law of Causality because it assumes space and time do not mix. The NVT is nonetheless consistent with the relativistic velocity transformation (RVT) and also with Einstein’s mass-energy equivalence relation E=mc2. The ratio Q of clock rates for two inertial rest frames S and S’ is required input for the NVT. Experimental data obey the Universal Time-dilation Law (UTDL) which states that the measured time Δt obtained by a inertial clock for a given event is inversely proportional to γ(v)= (1-v2c-2)-0.5v, where v is the speed of the clock relative to a specific rest frame referred to as the objective rest frame ORS. The value of Q when the clock of the observer in at rest in S while that of another observer is at rest in the object’s rest frame S’ is obtained from the UTDL as the ratio γ(v’)/γ(v). The Uniform Scaling method considers Q to be a conversion factor between the units of time in the two rest frames. It is found that the conversion factors for all other physical properties are integral multiples of Q. Kinetic scaling of the properties insures that the laws of physics are the same in each inertial frame, as required .........

Time is suspect!

‘That it is possible to find the form of the Lorentz transformations without requiring the speed of light to be the same in every inertial system is rediscovered about every thirty years and, rightly, forgotten.’ This proposition alongside the doctoral dissertation of Hendrik Smid in 1986 provides food for thought: Is the light postulate of special relativity, which gives the speed of light in vacuum its status of maximum and unchanging speed, indeed not necessary? What kind of physical world are you then left with? What could be the value of discussing this in class? In this paper we show how the Lorentz transformation, which describes the relationship between two coordinate systems moving relative to each other at a constant speed, can indeed be derived by replacing the light postulate by another assumption, namely the requirement of closure under composition of transformations that relate inertial frames of reference (i.e. two successive coordinate transformations of certain type can be written as one transformation of the same type). Although well known in specialised literature of physics research, the remarkable insight that is somehow buried in nature is hardly mentioned in pre-university and bachelor’s physics courses and textbooks. Yet, the presented comprehensible approach may support the understanding and plausibility of the abstract subject of special relativity. Mathematics may go too far for an average pre-university student, but this subject would certainly not be out of place in an undergraduate physics course or a physics teacher course. Although many teachers do not know that the light postulate of special relativity can be replaced by another assumption or may not appreciate such replacement as part of their teaching of the topic, it offers in our opinion an opportunity to inform students that a critical look at postulates and an investigation of alternatives is an essential part of the nature of science.

On the Stability of Solitons for the Maxwell-Lorentz Equations with Rotating Particle

We prove the stability of solitons of the Maxwell–Lorentz equations with extended charged rotating particle. The solitons are solutions which correspond to the uniform rotation of the particle. To prove the stability, we construct the Hamilton–Poisson representation of the Maxwell–Lorentz system. The construction relies on the Hamilton least action principle. The constructed structure is degenerate and admits a functional family of the Casimir invariants. This structure allows us to construct the Lyapunov function corresponding to a soliton. The function is a combination of the Hamiltonian with a suitable Casimir invariant. The function is conserved, and the soliton is its critical point. The key point of the proof is a lower bound for the Lyapunov function. This bound implies that the soliton is a strict local minimizer of the function. The bound holds if the effective moment of inertia of the particle in the Maxwell field is sufficiently large with respect to the “bar moment of inertia".