The Lorentz-Dirac equation in complex space-time

A hypothetical equation of motion is proposed for Kerr–Newman particles. It’s obtained by analytic continuation of the Lorentz-Dirac equation into complex space-time. A new class of “runaway” solutions are found which are similar to zitterbewegung. Electromagnetic fields generated by these motions are studied, and it’s found that the retarded (and advanced) times are multi-sheeted functions of the field points. This leads to non-uniqueness for the fields. With fixed weighting factors for these multiple roots, the solutions radiate. However, position dependent weighting factors can suppress radiation and allow non-radiating solutions. Motion with external forces are also considered, and radiation suppression is possible there too. These results are relevant for the idea that Kerr–Newman solutions provide insight into elementary particles and into emergent quantum mechanics. They illustrate a type of nascent wave-particle duality and complementarity in a purely classical field theory. Metric curvature due to gravitation is ignored.     

The fields of uniformly accelerated charges in de Sitter spacetime

The scalar and electromagnetic fields of charges uniformly accelerated in de Sitter spacetime are constructed. They represent the generalization of the Born solutions describing fields of two particles with hyperbolic motion in flat spacetime. In the limit Lambda-->0, the Born solutions are retrieved. Since in the de Sitter universe the infinities I+/- are spacelike, the radiative properties of the fields depend on the way in which a given point of I+/- is approached. The fields must involve both retarded and advanced effects: Purely retarded fields do not satisfy the constraints at the past infinity I-.     

A nonmetric lorentz-covariant theory of gravitation with spatial anisotropy

Gravitational field equations and an equation of motion for particles are constructed in a space with the Minkowski metric tensor on the basis of the most general Lagrangian for a spin-2 gravitational field which leads to a linear field equation. The retarded and advanced potentials are determined for an arbitrarily moving particle. Calculations are made of the motion of the perihelion of planets, the deflection of light rays in the field of the sun, the retardation of radar signals reflected from planetary surfaces, and the red shift in the levels of the hydrogen atom. An equation of motion is constructed for a particle in an external gravitational field with allowance for radiation reaction. The magnitude of the radiation reaction is determined by means of the retarded and advanced solutions using the methods of electrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 101–105. July, 1976.The author is grateful to the participants of a seminar conducted by Prof. D. D. Ivanenko for a useful discussion of the results of this paper, and to Prof. D. D. Ivanenko and Prof. V. I. Rodichev for their interest in this work and for helpful remarks.     

On the instantaneous form of the two-body equations of motion in fokker-wheeler-feynman electrodynamics

The motion of particles in the above theory is governed by functional differential equations containing both retarded and advanced times. We prove that at least in the special case of the two-body problem there exists an equivalent newtonian (i.e. single-time) equation of motion.     

The arrow of electromagnetic time and the generalized absorber theory

The problem of the direction of electromagnetic time, i.e., the complete dominance of retarded electromagnetic radiation over advanced radiation in the universe, is considered in the context of a generalized form of the Wheeler-Feynman absorber theory in an open expanding universe with a singularity atT=0. It is shown that the application of a four-vector reflection boundary condition at the singularity leads to the observed dominance of retarded radiation; it also clarifies the role of advanced and retarded waves in the emission of very weakly absorbed radiation such as neutrinos.     

On the non-uniform motion of dislocations: the retarded elastic fields,the retarded dislocation tensor potentials and the Liénard–Wiechert tensor potentials

The topic of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving dislocations. The retarded elastic fields produced by a distribution of dislocations and the retarded dislocation tensor potentials are determined. New fundamental key formulae for the dynamics of dislocations are derived (Jefimenko type and Heaviside–Feynman type equations of dislocations). In addition, exact closed-form solutions of the elastic fields produced by a dislocation loop are calculated as retarded line integral expressions for subsonic motion. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocation loop are given explicitly in terms of the so-called three-dimensional elastodynamic Liénard–Wiechert tensor potentials. The two-dimensional elastodynamic Liénard–Wiechert tensor potentials and the near-field approximation of the elastic fields for straight dislocations are calculated. The singularities of the near-fields of accelerating screw and edge dislocations are determined.     

Classical radiation reaction off-shell corrections to the covariant Lorentz force

We show that the problem of radiation reaction may be formulated in a space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode fields of the 0,1,2,3 components correspond to the Maxwell fields). The particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five-dimensional field equations provides the classical Abraham–Lorentz–Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution as well as an autonomous nonlinear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that the mass-shell deviation is bounded when the external field is removed.     

A relativistic analogue of the Kepler problem

The Poincaré invariant system of two point particles with an instantaneous interaction-at-a-distance originally proposed by Fokker is studied in the Hamiltonian formalism. The interaction, which agrees to first order in the coupling constant with the electromagnetic one obtained from the Liénard-Wiechert fields, is described in an advanced-retarded state space. The first particle moves in the advanced field of the second which in turn is subject to the retarded field of the first. The acceleration terms in the Liénard-Wiechert fields are neglected. In this theory the state space of the system is a twelve-dimensional manifold Σ and the motions are described as integral curves of a vector field that is obtained as the projection of the generator of time translations in space-time. The Poincaré group acts on this manifold Σ in a well-defined way and leaves a symplectic form ω invariant. Thus the set of all possible motions of this system can be studied by the methods of modern symplectic mechanics. In this paper the general method is explained and the set of all bounded motions for two equal rest masses and an attractive force is studied qualitatively and numerically. In the limit (binding energy)/(sum of rest masses) · (speed of light)² → 0 all the features of the classical Kepler motion are obtained.     

Bohmian Trajectories for Kerr–Newman Particles in Complex Space-Time

Complexified Liénard–Wiechert potentials simplify the mathematics of Kerr–Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known. A covariant theory due to Stueckelberg is used. This paper deviates from the traditional Bohmian interpretation of quantum mechanics since the electromagnetic interactions of Kerr–Newman particles are dictated by general relativity. A Gaussian wave function is used to produce the Bohmian trajectories, which are found to be multi-valued. A generalized analytic continuation is introduced which leads to an infinite number of trajectories. These include the entire set of Bohmian trajectories. This leads to multiple retarded times which come into play in complex space-time. If one weights these trajectories by their natural Bohmian weighting factors, then it is found that the particles do not radiate, that they are extended, and that they can have a finite electrostatic self energy, thus avoiding the usual divergence of the charged point particle. This effort does not in any way criticize or downplay the traditional Bohmian interpretation which does not assume the standard electromagnetic coupling to charged particles, but it suggests that a hybridization of Kerr–Newman particle theory with Bohmian mechanics might lead to interesting new physics, and maybe even the possibility of emergent quantum mechanics.     

Radiation Reaction of the Classical Off-Shell Relativistic Charged Particle

It has been shown by Gupta and Padmanabhan that the radiation reaction force of the Abraham–Lorentz–Dirac equation can be obtained by a coordinate transformation from the inertial frame of an accelerating charged particle to that of the laboratory. We show that the problem may be formulated in a flat space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode fields of the 0, 1, 2, 3 components correspond to the Maxwell fields). Without additional constraints, the particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five dimensional field equations provides the classical Abraham–Lorentz–Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution as well as an autonomous non-linear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that mass-shell deviation is bounded when the external field is removed.     

An advanced time approach for acoustic analogy predictions

This paper deals with a new interpretation of the retarded time approach that is widely used in the prediction of acoustic fields from moving sources.A hierarchical inversion between the emission time and the reception time leads to advanced time approach. This consists in projecting the current status of a source in the observer time domain where the received signal is progressively built.The practical relevance of this methodology lies on two statements: no retarded time equations must be solved; an aerodynamic noise prediction can be processed parallelly to the aerodynamic computation.Theoretically, the advanced time approach differs from the retarded time approach only in one aspect. A signal emitted at a given instant by a point source, moving at subsonic as well as supersonic velocity, is received only one time by an observer moving at subsonic velocity. Consequently, only one value of the advanced time corresponds to a value of the emission time. The advanced time approach is herein applied to a retarded time solution of the Ffowcs Williams and Hawkings equation proposed by Farassat. The noise radiated by elementary acoustic sources in complex motion is then computed and checked against analytical solutions.     

Dynamic chaos phenomenon and coherent radiation accompanying high energy particle motion through crystals

Abstract

A crystal has a regular structure, therefore every motion in such a structure seems to be regular. However, it is not actually so and even in perfect crystals the particle motion may be either regular or chaotic. Everything depends on the number of integrals of motion determining a particle trajectory.

The character of particle motion in a crystal, i.e. its regularity or chaoticity, affects many physical processes accompanying the particle motion through a crystal. In this paper we shall consider the effect of dynamic chaos on the coherent radiation of fast particles in a crystal.

We also consider the validity conditions of coherent radiation theory results, the role of the second and higher Born approximations in the radiation theory of fast particles in crystals, the continuous string approximation in this theory, the coherent radiation in the model of random strings, and the multiple scattering effect on the coherent radiation.     

Quantized fields in interaction with external fields

We consider a massive, charged, scalar quantized field interacting with an external classical field. Guided by renormalized perturbation theory we show that whenever the integral equations defining the Feynman or retarded or advanced interaction kernel possess non perturbative solutions, there exists anS-operator which satisfies, up to a phase, the axioms of Bogoliubov, and is given for small external fields by a power series which converges on coherent states. Furthermore this construction is shown to be equivalent to the one based on the Yang-Källen-Feldman equation. This is a consequence of the relations between chronological and retarded Green's functions which are described in detail.     

An exact solution for uniformly accelerated particles in general relativity

We present an exact solution of the Einstein empty-space equations referring to four particles in relative motion. The particles move with different uniform accelerations relative to a co-ordinate system which is Minkowskian at infinity, except in certain directions. If positive and negative masses are allowed, the particles can move freely under their own gravitation; if all four masses are positive, stresses extending to infinity are needed to cause the motion, but two of the particles can move freely. There are three results of interest. First, the field can be described in terms of a classical potential which is the average of retarded and advanced potentials corresponding to the particles. Secondly, the field at spatial infinity is entirely different from that of a static mass, and theg _ik fall off like the inversesquare of the distance. Thirdly, the world-lines of free particles are geodesics of the space-time.     

The Wheeler-Feynman absorber theory: A reinterpretation?

The “reinterpretation” of the Wheeler-Feynman absorber theory of radiation, as presented by H. Price in Refs. 1 and 2, is shown not to be a reinterpretation of the mathematical framework of the theory, but an alteration of the theory, which renders it asymmetric. It is shown that Price is mistaken in accusing Wheeler and Feynman of presenting flawed arguments as to whether the advanced and retarded components are distinct; and about the reasons for excluding the time-reversed version of the absorber theory.     

Relativistic electron motion in FEL-like fields taking retarded interactions into account

Summary The interaction of two charged particles both with each other (via Lienard-Wiechert retarded potentials) and with the wiggler field of an FEL structure, along which they are launched, is computed by means of the numerical integration of the relativistic motion equations, taking also an incoming laser wave into account. The bunching effect characterizing the collective behaviour of an electron beam in FEL-like fields is simulated by assuming one of the particles to be a suitable macrocharge.     

Should advanced interaction be a priori ignorable?

We discuss a delicate status of advanced interaction in the formalism of the time symmetric AAD approach to simple dynamical problems (motion with the uniform acceleration and the circular-orbit motion). An exclusive (although often unrespected) feature of AAD theory is that no a priori elimination of advanced interaction is in itself admissible. We verify this property on a point-like particle, subjected separately both to the electro-dynamical and linear interactions. The trial proves that such a rigorous requirement of theory has a positive impact on the conservation of inertia principle confirming the fact that the problem of inertia is a physical attribute associated necessarily with the advanced interaction. It is also shown that in the case of weak linear interaction there is a possibility to construct the model of a particle, close to the Wigner free point-like particle, with the internal degrees of freedom that involve both the retarded and advanced components of linear AAD four-potential. In the canonical scenario of model, with constraints on the light cone and the advanced interaction present, there appears as a result of AAD formalism the free-point particle endowed with its trembling motion. Dedicated to the memory of Prof. Milan Petrás on the occasion of his unattained seventy fifth birthday.     

Characteristics of electrons moving in a magnetic field at low energy levels

The motion and radiation of electrons moving in a magnetic field at low energy levels are investigated using quantum theory. An important difference between the results obtained and the equations of classical theory is established. It is shown that the radiation essentially depends on the orientation of the particle spins. The existence of a metastable excited state of the electron is revealed. Radiation in super-high fields is demonstrated.     

电子在激光驻波场中运动产生的太赫兹及X射线辐射研究

采用单电子模型和经典辐射理论分别对低能和高能电子在线偏振激光驻波场中的运动和辐射过程进行了研究. 结果表明: 垂直于激光电场方向入射的低速电子在激光驻波场中随着光强的增大, 逐渐从一维近周期运动演变为二维折叠运动, 并产生强的微米量级波长的太赫兹辐射; 高能电子垂直或者平行于激光电场方向入射到激光驻波场中, 都会产生波长在几个纳米的高频辐射; 低能电子与激光驻波场作用中, 激光强度影响着电子的运动形式、辐射频率以及辐射强度; 高能电子入射时, 激光强度影响了电子高频辐射的强度, 电子初始能量影响着辐射的频率; 电子能量越高, 产生的辐射频率越大. 研究表明可以由激光加速电子的方式得到不同能量的电子束, 并利用电子束在激光驻波场的辐射使之成为太赫兹和X射线波段的小型辐射源. 研究结果可以为实验研究和利用激光驻波场中的电子辐射提供依据.