Experimental and Real Coordinates in Space-Time Transformations

The experimental (apparent) space-time transformations connect coordinates altered by length contraction and clock retardation. When clocks are synchronized by means of light signals (Einstein–Poincaré procedure) or by slow clock transport, the experimental space-time. transformations assume the mathematical form of the Extended space-time transformations.⁽⁴⁾ These reduce to the Lorentz–Poincaré transformations when one of the frames they connect is the fundamental inertial frame. If the synchronization procedure were perfect, the experimental space-time transformations would assume the form of Selleris inertial transformations.⁽⁵⁾ The real space-time transformations are those which are disclosed when the systematic measurement distortions are corrected.     

Complex symmetries of electrodynamics

We prove that a set of nonsingular free solutions of Maxwell's equations forms a representation of the group obtained by analytic continuation of the Poincaré group to complex values of the group parameters, and that a set of singular solutions forms a representation of the group obtained by analytic continuation of the conformal group to complex values of the group parameters. These results are obtained by constructing a theory governing 2 × 2 complex matrix fields defined for complex values of position and time; the equations of this theory are invarient with respect to complex Poincaré transformations and complex conformal transformations, but the set of nonsingular solutions is in one-to-one correspondence with a set of nonsingular solutions of Maxwell's equations, and a similar correspondence exists for the singular solutions. Certain collections of solutions of Maxwell's equations for the field of a current form representations of these complex groups if both magnetic and electric currents are permitted, in which case complex transformations provide a natural connection between electric and magnetic charge. A class of complex transformations also yield natural relations between sources moving slower than light and sources moving faster than light.     

Statistical study of the radiation losses due to surface roughness for a dilectric slab deposited on a metal substrate

This paper presents an original method of analyzing radiation loss from dielectric slab with random wall imperfections. The method is based on Maxwell’s equations under their covariant form written in a non-orthogonal coordinate system. The solution is found by using a perturbation method applied to the smooth surface problem. The statistical characteristics of the radiation intensity, the average value and the probability density function, are analytically determined.     

Gravitational redshift of gravitational clocks

The gravitational redshift of gravitational clocks in a given weak gravitational field, within general relativity, is considered. Because the clocks in question have structure and dynamics determined by gravitational interactions, the full machinery of Einstein's equations must be used. Three specific examples are treated: (i) the redshift of the angular frequency of a rotating relativistic star in the gravitational field of a distant body; (ii) the redshift of the angular velocity of a slowly rotating black hole surrounded by an axisymmetric ring of matter; and (iii) the redshift of the observed orbital period of a nearly circular, post-Newtonian binary system in the field of a distant, third body. In all three cases the redshift is the same as if the clocks were non-gravitational, thereby governed by the Einstein equivalence principle. For an observer at infinity, the redshift $\text{Z ≡}\text{Δv}\text{v}$ is given by $\text{Z =}\text{?Gm}\text{Rc}{}^2$, where m is the mass of the distant object and R its distance from the clock in question. The result is independent of how relativistic the clock may be. The significance of this conclusion for the binary pulsar PSR 1913 + 16, where the gravitational redshift of the pulsar's frequency caused by the gravitational field of its companion is an observable effect, is discussed. The extent to which this result is a manifestation of the strong equivalence principle, satisfied, as far is known, only by general relativity, is also noted.     

On Transverse Electric (TE) wave propagation in a warm moving magnetoplasma with sinusoidal electron-density distribution

It has been shown, using the first three moment equations in conjunction with Maxwell's equations, that the wave equation for the TE mode in a warm moving stratified magnetoplasma transforms, for an assumed sinusoidal distribution of the electron density, to the standard form of the Hill's differential equation.     

Possible Minkowskian language in two-level systems

One hundred years ago, in 1908, Hermann Minkowski completed his proof that Maxwell’s equations are covariant under Lorentz transformations. During this process, he introduced a four-dimensional space called the Minkowskian space. In 1949, P.A.M. Dirac showed the Minkowskian space can be handled with the light-cone coordinate system with squeeze transformations. While the squeeze is one of the fundamental mathematical operations in optical sciences, it could serve useful purposes in two-level systems. Some possibilities are considered in this report. It is shown possible to cross the light-cone boundary in optical and two-level systems while it is not possible in Einstein’s theory of relativity.     

Propagation of Einstein's equations with quasi-maxwellian equations of gravity

We give the extra condition necessary to propagate Einstein's equations from a space-like hypersurface into space-time with quasi-maxwellian equations.     

The cosmological term in the Einstein theory

It is proved that it is necessary to introduce in Einstein's equations a cosmological term proportional to the square of the λ-field strength which is related to the Lorentz group representation class ρμ = 0.     

Maxwell's equations in anisotropic space

In terms of the covariance of equations under a generalized galilean transformation, a general expression of Maxwell's equations in anistropic space is given here.     

Superposition de deux ondes d'indices d'heterogeneite differents

Heterogeneous plane and uniform electromagnetic waves are particular solutions of Maxwell's equations. The sum of two of these solutions of the same frequency is generally not a wave of the same kind. A new type of interference appears for two heterogeneous plane and uniform components of different heterogeneity. The experimental proof of this phenomenon would show the dependence of the phase velocity on the heterogeneity. In the general case, the equal-amplitude surfaces of the various fields components are different; the same holds for the equal-phase surfaces. It is not always possible to define an eikonal and a wave surface for such a solution of Maxwell's equations. These difficulties disappear for waves of equal or opposite heterogeneity index.     

Stationary electromagnetic fields around a rotating black hole

The general stationary solution of Maxwell's equations in the Kerr background geometry is given. Future applications are outlined.     

Black holes as solitons

We remark that exact classical Schwarzschild-like solutions to Einstein's (and possibly f gravity) equations provide examples of realistic solitons.     

A Possible Reinterpretation of Einstein’s Equations

In this paper, we first review Huei’s formulation in which it is shown that the linearized Einstein equations can be written in the same form as the Maxwell equations. We eliminate some imperfections like the scalar potential which is ill linked to the electric-type field, the Lorentz-type force which is obtained with a time independence restriction and the undesired factor 4 which appears in the magnetic-type part. Second, from these results and in the light of a recent work by C.C. Barros, we propose an extension of the equivalence principle and we suggest a new interpretation for Einstein’s equations by showing that the electromagnetic Maxwell equations can be derived from a new version of Einstein’s ones.     

Equivalence of the thin-grating decomposition and coupled-wave analysis of thick holographic gratings

The method of thin grating decomposition, which is derived entirely from thin-grating diffraction theory, is shown analytically to be equivalent to the coupled-wave solution of Maxwell's equations for a thick sinusoidal grating.     

Absorption of gravitational waves by an excited vacuum space-time

We discuss modifications of Einstein's equations generated by vacuum fluctuations of the gravitational field. A special case of excitation is shown to be responsible by absorption of gravitational waves.     

Minimal differential equations for the Kilmister-Yang model of gravity

We present simplified, minimal differential equations for static, isotropic spacetimes of the Kilmister-Yang model. The equations are of second order, but contain two arbitrary constants and, hence, unlike Einstein's model, possess a variety of solutions. Several examples are discussed.     

Radiating bodies and naked singularities

A previously published exact solution of Einstein's equations representing a contracting radiating star is discussed and shown to provide an example of a naked singularity produced from initially regular conditions.     

Affine Metrics: An Structure for Unification of?Gravitation and Electromagnetism

This paper is mainly intended to define a mathematical framework for unification of gravity and electromagnetism. The main idea is that affine concepts replace linear concepts in the context of general relativity. First, we introduce affine metrics on affine spaces,and then generalize semi-Riemannian manifolds to affine semi-Riemannian manifolds and investigate their associated connections and geodesics and curvatures. Then we apply these concepts to space-times in order to combine Maxwell’s and Einstein’s field equations into one equation.     

Exact bianchi type I solutions with a cosmological constant

We present exact solutions of Einstein's field equations with a cosmological constant. The space-time considered here is a Bianchi type I and includes an electromagnetic field.     

Multipartite Quantum Clock Synchronization under The Influence of Unruh Thermal Noise

A protocol for multipartite quantum clock synchronization is performed under the influence of Unruh thermal noise. The dynamics of multipartite quantum system consisting of Unruh–DeWitt detectors when one of the detectors is accelerated are obtained. To estimate the time difference between the clocks, the time probability is calculated and how the probability is influenced by the Unruh thermal noise and other factors is analyzed. It is shown that both relativistic motion and interaction between the atom and the external scalar field affect the choice of optimal number of excited atoms in the initial state, which leads to a higher clock adjustment accuracy. Time probabilities for different types of initial states approach the same value in the limit of infinite acceleration, while tend to different minimums with increasing number of atoms. In addition, the accuracy of clock synchronization using a pair of entangled clocks in two‐party system is always higher than in a multipartite system, while the optimal Z‐type multipartite initial state always performs better than the W‐type state.