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George J. Spix

Publications and source records attributed to George J. Spix.

14 recordsLinked to original sources
arXiv2008

Matrix-based approach to electrodynamics in media

The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation group SO(3.C) is demonstrated explicitly. In vacuum case, the matrix form includes four real $4 \times 4$ matrices $α^{b}$. In presence of media matrix form requires two sets of $4 \times 4$ matrices, $α^{b}$ and $β^{b}$ -- simple and symmetrical realization of which is given. Relation of $α^{b}$ and $β^{b}$ to the Dirac matrices in spinor basis is found. Minkowski constitutive relations in case of any linear media are given in a short algebraic form based on the use of complex 3-vector fields and complex orthogonal rotations from SO(3.C) group. The matrix complex formulation in the Esposito's form,based on the use of two electromagnetic 4-vectors, $e^α(x) = u_β F^{αβ}(x), b^α (x) = u_β \tilde{F}^{αβ}(x) $ is studied and discussed. It is argued that Esposito form is achieved trough the use of a trivial identity $I=U^{-1}(u)U(u)$ in the Maxwell equation.

math-ph↗
arXiv2007

Maxwell equations in Riemannian space-time, geometry effect on material equations in media

The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical structure of the curved model is studied. Metrical structure of the curved space-time generates effective constitutive equations for electromagnetic fields, the form of four corresponding symmetrical tensors is found explicitly for general case of an arbitrary Riemannian space - time. Four constitutive tensors are not independent and obey some additional constraints between them. Several simple examples are specified in detail:itis given geometrical modeling of the anisotropic media (magnetic crystals) and the geometrical modeling of a uniform media in moving reference frame in the Minkowsky electrodynamics -- the latter is realized trough the use of a non-diagonal metrical tensor determined by 4-vector velocity of the moving uniform media. Also the effective material equations generated by geometry of space of constant curvature (Lobachevsky and Riemann models) are determined.

physics.class-ph↗
arXiv2006

Relativistic aberration effect on the the light reflection law and the form of reflecting surface in a moving reference frame

The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays. The form of the reflection law in the moving reference frame is substantially modified and includes an additional parameter which is the velocity vector of the reference frame. It is shown that the reflected ray, as measured by a moving observer, would not in general be in the same plane as the incident and normal rays. A general method to transform the form of any rigid surface in 3-dimensional space with respect to the arbitrary directed relative motion of the reference frame is detailed. This method is based on the light signals processes and the invariance of the light velocity under Lorentz transformations. It is shown that a moving observer will measure a plane surface as a hyperboloid. That observer will also measure a spherical surface as an ellipsoid. A right line in the plane is seen by a moving observer as a hyperbola. The whole analysis is extended to the case of a uniform media.

physics.gen-ph↗
arXiv2006

On the different forms of the Maxwell's electromagnetic equations in a uniform media

Two known, alternative to each other, forms of the Maxwell's electromagnetic equations in a moving uniform media are investigated and discussed. Approach commonly used after Minkowski is based on the two tensors: H^{ab} = (D, H /c) and F^{ab} = (E, cB) which transform independently of each other at Lorentz transitions; relationships between fields change their form at Lorentz transformations and have the form of the Minkowski equations depending on the 4-velocity u^{a} of the moving media under an inertial reference frame. So, the electrodynamics by Minkowski implies the absolute nature of the mechanical motion. An alternative formalism (Rosen and others) may be developed in the new variables. This form of the the Maxwell's equations exhibits symmetry under modified Lorentz transformations in which everywhere instead of the vacuum speed of light c is used the speed of light in the media, kc . In virtue of this symmetry we might consider such a formulation of the Maxwell theory in the media as invariant under the mechanical motion of the reference frame.In connection with these two theoretical schemes, a point of principle must be stressed: it might seem well-taken the requirement to perform Poincare-Einstein clock synchronization in the uniform medias with the help of real light signals influenced by the media, which leads us to the modified Lorentz symmetry.

hep-th↗
arXiv2006

Is the assumption of a special system of reference consistent with Special Relativity? Definitely yes, special approaches show it!

We compare the results obtained by interpreting some fundamental relativistic experiments from the point of view of two alternative theories: Einstein's special relativity theory and the Lorentz-Poincare theory admitting the existence of a special reference frame relative to which we can measure absolute velocities. The experiments that we consider here are the time dilation, the radar echo, the Doppler Effect and the radar detection. The most important result is that both theories lead to the Lorentz-Einstein transformations for the space-time coordinates of the same event. This conclusion enables us to assert that the anisotropy in the light propagation fades away in the case of these particular experiments

physics.gen-ph↗
arXiv2006

Relativistic derivations of the electric and magnetic fields generated by an electric point charge moving with constant velocity

We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the fields are measured. The same equations were previously derived in a relatively complicated way2 based exclusively on general electromagnetic field equations and without making use of retarded potentials or relativistic equations

physics.gen-ph↗
arXiv2005

Special relativity without distant clock synchronization

Observers at rest in two inertial reference frames are located within the propagation space of the same electromagnetic wave. Raising receiving antennas in a suitable way, these observers use the electromagnetic oscillations in the wave as an electromagnetic clock. The invariance of the wave phase ensures that the observers of the two frames detect the same phase of the oscillation when they are located at the same point in space and consequently theirs synchronization proceeds automatically. Because the Doppler Effect is free of any clock synchronization, we use the formula that accounts for this effect for deriving the basic formulas of relativistic kinematics.

physics.gen-ph↗
arXiv2005

Illustrating the relativity of simultaneity

We present a relativistic space-time diagram that displays in true magnitudes the readings (daytimes) of two inertial reference frames clocks. One reference frame is the rest frame for one clock. This diagram shows that two events simultaneous in one reference frames are not compulsory simultaneous in the other frame. This approach has a bi-dimensional character.

physics.gen-ph↗
arXiv2005

Illustrating the Michelson-Morley experiment

Considering that the rays in the Michelson-Morley interferometer perform the radar detection of its mirrors, we use a relativistic diagram that displays, at a convenient scale, their location and the path of the rays. This approach convinces us that the rays that come from the two arms interfere with zero phase difference without using the usual ingredient, length contraction.

physics.gen-ph↗
arXiv2005

Illustrating Einstein's special relativity: A relativistic diagram that displays in true values the components of a four vector

After having shown that the corresponding components of a four vector transform via the same transformation factors as the space-time coordinates of the same event do, we design a relativistic diagram that displays in true values theirs components. One diagram works for events generated by tardyons whereas a second diagram works for events generated by light signals or photons. We consider both approaching and receding tardyons respectively photons in each case. We also show how the relativistic diagram for radar and photographic detections of moving profiles.

physics.gen-ph↗
arXiv2005

Illustrating the space-time coordinates of the events associated with the apparent and the actual position of a light source

We present a space-time diagram that displays in true values the space- time coordinates of events associated with the apparent and actual positions of a point like source moving with constant velocity. We use it in order to construct the actual shape of a moving luminous profile or to determine the relationship between apparent and actual distances. We show that the simple fact that light propagates at finite speed has important consequences like "length contraction" or "length dilation" the effects being sensitive against the "approaching" and the "receding" character of the source relative to an observer located at the origin of the inertial reference frame

physics.gen-ph↗