arXiv subjects
Publications and source records attributed to G. A. Kotel'nikov.
An experiment aimed at testing special relativity via a comparison of the velocity of a non matter particle (annihilation photon) with the velocity of the matter particle (Compton electron) produced by the second annihilation photon from the decay Na-22(beta^+)Ne-22 is proposed.
The kinematics of Compton-effect with violated invariance of the velocity of light has been considered. It has been shown that in this case faster-than-light motion of the Compton electron is possible. The motion (if it exists really) begins with the energy of the incident gamma-quantum above 360 keV.
The generalized definition of symmetry is formulated. Application of this definition for symmetric analysis of theoretical physics equations is considered. The version of electrodynamics is constructed permitting the faster-than-light motions of particles with real masses. Some elements of physical interpretation of the proposed theory are presented.
A variant of electrodynamics is constructed in which faster-than-light motions are possible.
By symmetry of the partial differential equation L'ϕ'(x')=0 with respect to the variables replacement x'=x'(x), ϕ'=ϕ'(Φϕ) it is advanced to understand the compatibility of engaging equations system Aϕ'(Φϕ)=0, Lϕ(x)=0, where Aϕ'(Φϕ)=0 is obtained from the initial equation by replacing the variables, L'=L, Φ(x) is some weight function. If the equation Aϕ'(Φϕ)=0 may be transformed to the form L(Ψϕ)=0, where Ψ(x) is the weight function, the symmetry will be named the standard Lie symmetry, otherwise the generalized symmetry. It is shown that with the given understanding of the symmetry, D'Alembert equation for one component field is invariant with respect to any arbitrary reversible coordinate transformations x'=x'(x). In particular, they contain the transformations of the conformal and Galilei groups realizing the type of standard and generalized symmetry for Φ(x)=ϕ'(x'\to x)/ϕ(x).
The violation of the invariance of the speed of light in Special Relativity has been made. The version of the theory (LSR) has been constructed in which the possibility of the superluminal motions are permitted. Some predictions of this theory are available for experimental check, for example, the measurements of aberration angles, the observation of distinctions between the redshifts in radio and optical ranges of a spectrum, the detection of superluminal objects in astrophysics and in time-flight experiments.
It is shown that the universal Newton time may be introduced in the classical electrodynamics. The statement results from an existence of the generalized symmetry of Maxwell equations with respect to Galilei transformations (physics/9701006). In the case of the extended Galilei transformations the postulate of invariance of the speed of light may be made compatible with the concept of the universal Newton time. Some physical consequences of the extended Galilei symmetry are considered.
It is shown that the transformations of the charge conjugation in classical electrodynamics and in quantum theory can be interpreted as the consequences of the symmetry of Maxwell and Dirac equations with respect to the inversion of the speed of light: c to -c; t to t; (x,y,z) to (x,y,z), where c is the speed of light; t is the time; x, y, z are the spatial variables. The elements of physical interpretation are given.
On the basis of the invariance of Dirac equation Lu(x,c)=0 with respect to the inversion of the speed of light Q:(x,c)=(x,-c), it is shown that the relationship [C,PTQ]u(x,c)=0 between the transformations of the charge conjugation C, the space inversion P, the time reversal T and the inversion of the speed of light Q is true. The charge conjugation in quantum theory may be interpreted as the consequence of the discrete symmetries reflecting the fundamental properties of space, time and speed of light.
An algorithm for studing the symmetrical properties of the partial differential equation of the type Lu=0 is proposed. By symmetry of this equation we mean the operators Q satisfying commutational relations of order p more than p=1 on the solutions u: [L...[L,Q]...]u=0. It is shown, that within the framework of the proposed method with p=2 the relativistic D'Alembert and Maxwell equations are the Galilei symmetrical ones. Analogously, with p=2 the Galilei symmetrical Schroedinger equation is the relativistic symmetrical one. In both cases the standard symmetries are realized with p=1.
An algorithm is proposed for research into the symmetrical properties of theoretical and mathematical physics equations. The application of this algorithm to the free Schrodinger equation permited us to establish that in addition to the known Galilei symmetry, the free Schrodinger equation possesses also the relativistic symmetry in some generalized sense. This property of the free Schrodinger equation permits the equation to be extended into the relativistic area of movements of a particle being studied.
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.