Lorentz Transformations Research Articles

Effect of the Quadric Shear Zonal Flows and Beta on the Downstream Development of Certain Unstable Baroclinic Waves

Many factors are affecting the downstream development of baroclinic waves, among which zonal shear flow is one of the factors that need to be considered. In this paper, the influence of zonal shear flow and <em>β</em> on the downstream development of unstable chaotic baroclinic waves is studied from the two-layer model in a wide channel controlled by quasi-geostrophic potential vorticity equation. Through the obtained Lorentz equation, We concentrated on the influence of zonal shear flow (the second derivative of baseline zonal flow is not zero) on the downstream development of baroclinic waves. In the absence of zonal shear flow, chaotic behavior along feature points would occur, and the amplitude would change rapidly from one feature to another, that is, it would change very quickly in space. When zonal shear flow is introduced, the influence of zonal shear flow on the downstream development of unstable baroclinic waves is examined categorically. And from Lorentz’s final equation, we’re investigating a change in his solution. It is found that the zonal shear flow smoothes the solution of the equation and reduces the instability, and with the increase of zonal shear flow, the stability in space will increase gradually. The second derivative of the zonal shear flow (the quadrical shear flow) therefore has a major influence on the stability of space.

Relativistic thermodynamics on conveyor belt

Two thermodynamic processes are analysed by using a relativistic four-vector fundamental equation formalism: the launching of a projectile by forces produced by chemical reactions inside a cannon (equivalent to a person launching a ball) placed on a moving platform, a mechanical energy production process, and the Joule-Kelvin process implemented on a conveyor belt. Each process is first studied in frame S, in which the device—the cannon or the porous plug –, is at rest, obtaining its four-vector fundamental equation dE μ = δ W μ + δ Q μ . Using the Lorentz transformation, the corresponding four-vector equation in frame —in which the processes are carried out on a moving platform or a conveyor belt—, is obtained, obeying Einstein’s principle of relativity. For the relativistic description to be coherent, one has to assign linear momentum to the non-mechanical energies and consider their variations in the corresponding Newton’s second law equation and the relativistic non-simultaneity and conveyor belt effects. In relativistic thermodynamics, Newton’s second law and the first law of thermodynamics are not independent equations. It is shown that entropy variations and fuel consumption are frame independent magnitudes.

On the Hamilton–Poisson structure and solitons for the Maxwell–Lorentz equations with spinning particle

We construct the Hamilton–Poisson structure for the Maxwell–Lorentz equations with spinning extended charged particle. We calculate the integral kernel of the corresponding Poisson bracket. The calculation relies on the Hamilton least action principle which is proved using the Lie–Poincaré calculus. The Hamilton–Poisson structure turns out to be degenerate and admits a functional family of Casimir invariants. The structure is applied to the calculation of the solitons corresponding to the uniform motion and rotation of the particle. We calculate effective masses and momenta of inertia of the soltions.As an example, the Poisson structure is applied to the construction of the momentum map corresponding to the symmetry group of translations. All calculations are rigorously justified by the proof of the well-posedness and smooth approximations of solutions. The investigation is inspired by the problems of stability of solitons.

FDTD Analysis of Relativistic Bistatic Polarized Scattering From a High-Speed Moving Dielectric Coated Target

Development of hypersonic aircraft demands relativistic electromagnetic scattering modeling of a high-speed moving dielectric coated object, which is applied to the recognition and tracking of moving stealth object. However, far-zone polarized scatterings from a moving 3D dielectric coated object have not been investigated so far. This paper addresses this problem by combining the finite-difference time-domain method with Lorentz transformation (Lorentz-FDTD). Through Lorentz transformation and the principle of phase invariance, the frequency, propagation direction, magnitude of the incident plane wave and the size of the moving object in the laboratory frame, which is stationary with respect to the free space, are transformed to those in the rest frame that moves with the moving object. The scattered field near the object is solved by the FDTD method with full permittivity and conductivity tensors in the rest frame, then far-zone polarized scattered field is obtained by the implementation of near-to-far field transformation. Through Lorentz transformation for coordinates, the polarized Radar Cross Sections (RCSs) of moving plasma coated objects are solved. Especially, the scattering characteristics of radial radar cross sections of moving objects are discussed. Several numerical experiments are carried out, the efficiency and the accuracy of the proposed method are validated.

Simulation of XRD data by modified Arrhenius and Lorentz equations for (Na0.5Bi0.5)0.94Ba0.06(Ti1-2xZrxCex)O3 ferroelectric ceramics having rhombohedral crystal structure

In the present paper ferroelectric ceramics with chemical formula (Na0.5Bi0.5)0.94Ba0.06(Ti1-2xZrxCex)O3 (x = 0.01, 0.02, 0.03 & 0.04) were prepared by calcinations at 900 °C for 2 h. X-ray diffraction (XRD) patterns were obtained on these ceramic samples. For the first time we have shown a procedure to obtain Lattice parameters (a, αo) and activation energy by simulation of XRD data with modified Arrhenius and Lorentz equations. The modified Arrhenius and Lorentz equation is found to best fit to the experimental XRD data. From this simulation studies we have obtained lattice parameters and activation energy for various range of two theta values. The average values of lattice parameters are 6.0933 Ao, 6.1050 Ao, 6.2372 Ao, & 6.3154 Ao for x = 0.01, 0.02, 0.03 & 0.04 respectively. The average values of angle in degrees are 89.20, 87.67, 89.99 & 89.27 for x = 0.01, 0.02, 0.03 & 0.04 respectively. The average values of activation energy are 345 meV, 483 meV, 557 meV & 709 meV for x = 0.01, 0.02, 0.03 & 0.04 respectively. The simulation of XRD data shown in this paper can also be extended to other compounds to obtain the lattice parameters and activation energy.

On the essence of time and Lorentz transformations

The reasons for the emergence and essence of the concept of time are discussed. It is argued that the concept of time in humans arose as a result of observing the movement of material objects and the course of various processes. The repeatability and periodicity of natural processes became the basis for the introduction of a quantitative measure of the duration of any movements and processes. The introduction of a quantitative measure made it possible to measure the duration of any movements and processes in comparison with the duration of stationary periodic processes chosen as units of measurement. The very same measure of the duration of any movement began to be called time. It is argued that the connection of the course of time with the stationary periodic motion of natural objects indicates the invariance of its course with respect to moving frames of reference. It is shown that time dilation and reduction in the size of spatial objects are the result of an incorrect interpretation of the results of Lorentz transformations.

Playing with two rays of light

The special theory of relativity is currently included in the curricula of high school in many countries. For this reason, we often organize in-depth lessons on this topic and, in this paper, we summarize a lecture that we have given in some extra activities addressed to last year high school students stimulating pupils “to play” with Lorentz transformations. We found a simple relation that allows us to deduce the rest length of a relativistic train without knowing the relative velocity and without using the lorentz factor and spacetime distortions.

An study on The Lorentz transformations and the nature of time

An study on The Lorentz transformations and the nature of time

Generalized Quantum Lagrangian

The paper concerns the formulation of a Lagrangian function compliant with classical, quantum and relativistic outcomes. The literature Lagrangians are reported with modified local Lorentz transformations, or with potentials inferred directly from the relativistic metric or with geometrical meaning. In this paper the Lagrangian is formulated via the concept of quantum uncertainty only, which allows a non-deterministic approach. This theoretical frame is proven useful to merge without additional hypotheses quantum and relativistic outcomes in a straightforward way.

An Algebraic Methodology for Generalizing the Lorentz Transformation Through Quartic Equation Solutions and f(z) gravitational theory

An Algebraic Methodology for Generalizing the Lorentz Transformation Through Quartic Equation Solutions and f(z) gravitational theory

The Interplay of Gravity and Lorentz Transformation Collaborating with ChatGPT

The Interplay of Gravity and Lorentz Transformation Collaborating with ChatGPT

Invariance of Maxwell’s equations to Lorentz transformations: conceptual bridges through derivation as an alternative to tensorial calculus

Na tradição do campo disciplinar da Física, e nos respectivos manuais didáticos, a invariância das equações de Maxwell por transformações de Lorentz é usualmente apresentada via cálculo tensorial, do que decorre que seu ensino seja postergado até que (supostamente) os estudantes-alvo dominem esse formalismo. Isso pode acarretar, em disputas curriculares as mais disformes, que muitos sequer tenham acesso instrucional a esse tópico, com relevantes implicações para o conhecimento avançado da Física Moderna e Contemporânea. Desse diagnóstico, desenvolvemos uma alternativa de se proceder àquela apresentação usando-se apenas operações básicas da derivação, como a regra da cadeia. Na direção dos processos de ensino e aprendizagem associáveis, sustentamo-nos no aporte teórico das pontes conceituais, por nós desenvolvido a partir da epistemologia cognitiva de objeto homólogo de Gérard Vergnaud. Esse artifício de congruência referencial buscou estabelecer a transitabilidade das maneiras, sem hierarquização, mas com evidente implicação de que a alternativa demonstrada poderia facilmente ser introduzida em disciplinas iniciais de Eletromagnetismo, tipicamente realizadas no primeiro ciclo dos cursos de Física e Engenharia, contribuindo para a retomada progressiva do assunto em módulos avançados.

Magnetic Frenet curves on para-Sasakian manifolds

The study of magnetic curves, seen as solutions of Lorentz equation, has been done mainly in 3-dimensional case, motivated by theoretical physics. Then it was extended in higher dimensions, as for instance in K?hlerian or Sasakian frame. This paper deals for the first time in literature with magnetic Frenet curves in higher dimensional paracontact context. Several classifications are provided here for different types of magnetic curves on para-Sasakian manifolds. Some relations between magnetic Frenet curves and Lorenz force are obtained on these spaces and examples of magnetic curves associated to paracontact magnetic fields are constructed. Some explicit equations of the paracontact magnetic curves on the classical para-Sasakian manifold (R2n+1, ?, ?, ?, 1) are given at the end.

The Existence of a Universal Frame of Reference, in Which it Propagates Light, is Still an Unresolved Problem of Physics

Abstract: This article shows that the existence of a universal frame of reference, in which light propagates, is still an unresolved problem of physics. The analyzed articles show that the rejection of the idea of ether due to Michelson-Morley’s and Kennedy-Thorndike’s experiments was too hasty. The zero results of these experiments can be explained by the theory with a universal frame of reference, in which light propagates. The fact that one-way speed of light has never been accurately measured and that there is a well-documented effect showing the anisotropy of space from the perspective of our frame of reference, which is the dipolar anisotropy of cosmic microwave background radiation, further substantiates theories with a universal frame of reference. The article shows that the null result of the Michelson-Morley and Kennedy-Thorndike experiments does not determine the Lorentz symmetry. Keywords: Lorentz transformation, Coordinate and time transformation, Universal frame of reference, Anisotropy of cosmic microwave background radiation, One-way speed of light.

On isospin and flavour of leptons and quarks

Isospin emerges naturally from the Lorentz transformation of spinors, if they are based on the vector representation of the Lorentz group. The resulting extended Dirac equation for a massive spin-one-half fermion has two new additional degrees of freedom associated with the up and down components of isospin. This doublet is interpreted as describing the electron and neutrino. It is adjoined with the SU(2) symmetry group. The extended Dirac equation appears in six versions which are connected by similarity transformations. It is argued that this trait may explain the occurrence of the three families of the leptons and suggested that flavour arises genuinely from the algebraic properties of the extended Dirac equation. Its solutions are discussed and the physical role of isospin is elucidated. Isospin symmetry can be gauged, which leads to a weak-interaction-type theory and is valid for finite initial mass. Breaking the isospin SU(2) symmetry yields the correct electric charges of the particles by means of the electroweak unification procedures of the standard model.

Lorentz Gauge and Coulomb Gauge for Tetrad Field of Gravity

In general relativity, an inertial frame can only be established in a small region of spacetime, and local inertial frames are mathematically represented by a tetrad field in gravity. The tetrad field is not unique due to the freedom to perform Lorentz transformations in local inertial frames, and there exists freedom to choose the local inertial frame at each spacetime point. The local Lorentz transformations are known as non-Abelian gauge transformations for the tetrad field, and to fix the gauge freedom corresponding to the Lorentz gauge ∂μAμ=0 and the Coulomb gauge ∂iAi=0 in electrodynamics, the Lorentz gauge and Coulomb gauge for tetrad fields are proposed in the present work. Moreover, properties of the Lorentz gauge and the Coulomb gauge for tetrad fields are discussed to show their similarities to those in electromagnetic fields.

Extension of Galilean invariance to uniform motions for a relativistic equation of fluid flows

Galilean invariance and the Lorentz transformation are the two pillars of mechanics that an equation of motion must respect. The objective is to extend the Galilean invariance to uniform rotational motion and to expansion motion of which motion at constant translational velocity is only a special case. The second goal is to show that the discrete equation of motion is naturally relativistic without using the Lorentz transformation. The realization of these two aims leads to different concepts of special relativity: (i) space is homogeneous and isotropic and (ii) time, which flows regularly, is invariant by translation. These invariances, symmetric for translation and rotation, observed by the discrete equation of motion give it fundamental conservation properties to extend the scope of the equations of fluid mechanics to other fields of physics.

Lorentz-covariant kinetic theory for massive spin- 1/2 particles

We construct a matrix-valued spin-dependent distribution function (MVSD) for massive spin-$1/2$ fermions and study its properties under Lorentz transformations. Such transformations result in a Wigner rotation in spin space and in a nontrivial matrix-valued shift in space-time, which corresponds to the side jump in the massless case. We express the vector and axial-vector components of the Wigner function in terms of the MVSD and show that they transform in a Lorentz-covariant manner. We then construct a manifestly Lorentz-covariant Boltzmann equation which contains a nonlocal collision term encoding spin-orbit coupling. Finally, we obtain the spin-dependent distribution function in local equilibrium by demanding detailed balance.

Basic postulates of some coordinate transformations within material media

This paper aims to explore the physical quantities of several invariants, including the basic postulates of some types of crucial coordinate transformations, conservation laws, and continuity equations, in the electromagnetic and gravitational fields. Maxwell first utilized quaternions to describe the electromagnetic theory. Subsequent scholars make use of octonions to study the physical properties of electromagnetic and gravitational fields simultaneously, including the octonion field strength, field source, angular momentum, torque, and force. When an octonion coordinate system transforms rotationally, the scalar part of one octonion will remain unchanged, although the vector part of the octonion may alter. In the octonion space O, some invariants can be derived from this octonion property. A part of these invariants can be selected as the basic postulates of Galilean transformation or Lorentz transformation. Similarly, several invariants can be derived from the octonion property in the transformed octonion space Ou, and the invariants can be chosen as the basic postulates of a few new types of coordinate transformations. Furthermore, the combination of invariants in the octonion spaces can be applied as the basic postulates of some new coordinate transformations, relevant to the norm of physical quantities. Through the analysis, it is easy to find that each conserved quantity has its preconditions from the perspective of octonion spaces. This is helpful to deepen the further understanding of the physical properties of conservation laws and other invariants.

Entanglement-enhanced test proposal for local Lorentz-symmetry violation via spinor atoms

Invariance under Lorentz transformations is fundamental to both the standard model and general relativity. Testing Lorentz-symmetry violation (LSV) via atomic systems attracts extensive interests in both theory and experiment. In several test proposals, the LSV violation effects are described as a local interaction and the corresponding test precision can asymptotically reach the Heisenberg limit via increasing quantum Fisher information (QFI), but the limited resolution of collective observables prevents the detection of large QFI. Here, we propose a multimode many-body quantum interferometry for testing the LSV parameter &amp;#x03BA; via an ensemble of spinor atoms. By employing an N-atom multimode GHZ state, the test precision can attain the Heisenberg limit &amp;#x0394;&amp;#x03BA;&amp;#x221D;1/(F2N) with the spin length F and the atom number N. We find a realistic observable (i.e. practical measurement process) to achieve the ultimate precision and analyze the LSV test via an experimentally accessible three-mode interferometry with Bose condensed spin-1 atoms for example. By selecting suitable input states and unitary recombination operation, the LSV parameter &amp;#x03BA; can be extracted via realizable population measurement. Especially, the measurement precision of the LSV parameter &amp;#x03BA; can beat the standard quantum limit and even approach the Heisenberg limit via spin mixing dynamics or driving through quantum phase transitions. Moreover, the scheme is robust against nonadiabatic effect and detection noise. Our test scheme may open up a feasible way for a drastic improvement of the LSV tests with atomic systems and provide an alternative application of multi-particle entangled states.