Particle Production in 5-Dimensional Cosmological Relativity

The 5-dimensional extension of cosmological special and general relativity is considered. In this framework it is possible to define a 5-dimensional perfect fluid stress-energy tensor and to unify the equations of perfect hydrodynamics in a single 5-dimensional tensor conservation law. This picture in principle permits to interpret particle production phenomena as cosmological effects, in the spirit of open system cosmology.     

Beltrami-de Sitter时空和de Sitter不变的狭义相对论

分析了在相对论体系中狭义相对性原理和宇宙学原理之间的关系以及Beltrami-de Sitter -陆启铿疑难.指出可以把狭义相对性原理推广到非零常曲率时空，在具有Beltrami度规 的de Sitter/反de Sitter时空中建立狭义相对论的运动学和粒子动力学. 在这类狭义相对 论中,相对于Beltrami坐标同时性，Beltrami坐标系就是惯性坐标系，相应的观测者为惯 性观测者; 对于自由粒子和光讯号, 惯性定律成立;可以定义可观测量,它们不但守恒而且还 满足推广的爱因斯坦关系.除了Beltrami坐标时同时性之外，对于共动观测, 还可以取固 有时同时性;此时，Beltrami度规成为Robertson-Walker型的度规，其3维空间是闭的,对 于平坦的偏离为宇宙学常数的量级.这表明,在这类狭义相对论中,相对性原理与“完美”宇 宙学原理之间存在内在联系,并不存在那些问题.进而,基于最新观测事实，重述了Mach原 理；指出对于Beltrami-de Sitter/反de Sitter时空，宇宙学常数恰恰给出惯性运动的起 源. 关键词： 狭义相对性原理 宇宙学原理 de Sitter不变的狭义相对论 Beltrami-de Sitter时空 同时性 Mach原理     

The arithmetic basis of special relativity

Under relatively general particle and rocket frame motions, it is shown that, for special relativity, the basic concepts can be formulated and the basic properties deduced using only arithmetic. Particular attention is directed toward velocity, acceleration, proper time, momentum, energy, and 4-vectors in both space-time and Minkowski space, and to relativistic generalizations of Newton's second law. The resulting mathematical simplification is not only completely compatible with modern computer technology, but it yields dynamical equations that can be solved directly by such computers. Particular applications of the numerical equations, which are either Lorentz invariant or are directly related to Lorentz-invariant formulas, are made to the study of a relativistic harmonic oscillator and to the motion of an electric particle in a magnetic field.     

Paths of spinning particles in general relativity as geodesics of an Einstein connection

This paper deals with the Papapetrou-Pirani equations of motion for a spinning test particle in general relativity. The motion of the center of mass can be represented by the geodesic equation of an affine connection that is the sum of the Christoffel connection and a tensor that depends on the Riemann-Christoffel curvature tensor, the mass of the particle, its 4-velocity, and its spin tensor. The connection is not unique, and here it is chosen to satisfy one of the basic geometrical principles of Einstein's unified field theory: The symmetric part of the fundamental tensor of the geometry is specified to be the metric tensor of general relativity. The special case of conformally flat space-times is discussed.     

The Bargmann-Wigner method in Galilean relativity

The equations of motion of a spin one particle as derived from Levy-Leblond's Galilean formulation of the Bargmann-Wigner equations are examined. Although such an approach is possible for the case of free particles, inconsistencies which closely parallel those encountered in the Bargmann-Wigner equations of special relaticity are shown to occur upon the introduction of minimal electromagnetic coupling. If, however, one considers the vector meson within the Lagrangian formalism of totally symmetric multispinors, it is found that the ten components which describe the vector meson in Minkowski space reduce to seven for the Galilean group and that in this formulation no difficulty occurs for minimal electromagnetic coupling.More generally it is demonstrated that one can replace Levy-Leblond's version of the Bargmann-Wigner equations by an alternative set which leads to the correct number of variables for the vector meson. A final extension consists in the proof that for all values of the spin the (Lagrangian) multispinor formalism implies the Bargmann-Wigner equations. Thus the problem of special relativity of seeking a Lagrangian formulation of the Bargmann-Wigner set is found to have only a somewhat trivial counterpart in the Galilean case.Research supported in part by the U.S. Atomic Energy Commission.     

Proper-Time Relativistic Dynamics and the Fushchych-Shtelen Transformation

Abstract

We report on a new formulation of classical relativistic Hamiltonian mechanics which is based on a proper-time implementation of special relativity using a transformation from observer proper-time, which is not invariant, to system proper-time which is a canonical contact transformation on extended phase-space. This approach does not require the use of time as a fourth coordinate and so we prove that it satisfies the two postulates of special relativity. In the free particle case, our transformation theory generates a Poincaré group which fixes time (system proper-time). We prove that the Fushchych-Shtelen transformation is an element of our group, which fixes time for Maxwell’s equations. In the interaction case, our transformation theory allows us to avoid the no-interaction theorem. We show that the Santilli Isotopes appear naturally when interaction is turned on.     

Curved traversable wormholes in (3+1)-dimensional spacetime

We present the general method of constructing curved traversable wormholes in (3+1)-d spacetime and proceed to thoroughly discuss the physics of a zero tidal force metric without cross-terms. The (3+1)-d solution is compared with the recently studied lower-dimensional counterpart, where we identify that the much richer physics—involving pressures and shear forces of the mass-energy fluid supporting the former—is attributed to the mixing of all three spatial coordinates. Our (3+1)-d universe is the lowest dimension where such nontrivial terms appear. An explicit example, the static zero tidal force (3+1)-d catenary wormhole is analysed and we show the existence of a geodesic through it supported locally by non-exotic matter, similar to the (2+1)-d version. A key difference is that positive mass-energy is used to support the entire (3+1)-d catenary wormhole, though violation of the null energy condition in certain regions is inevitable. This general approach of first constructing the geometry of the spacetime and then using the field equations to determine the physics to support it has the potential to discover new solutions in general relativity or to generalise existing ones. For instance, the metric of a time-evolving inflationary wormhole with a conformal factor can actually be geometrically constructed using our method.     

THE PROBLEM OF MOTION IN THE KALUZA THEORY

It is shown that the equations of motion for a charged massive particle are consequences of the field equations in Kaluza unification theory of gravitation and electromagnetism, i.e., the equations of motion for the particle can be deduced from Kaluza field equations, just as that in Einstein's theory of motion of general relativity the equations of motion for a massive particle are consequences of the Einstein equations. Furthermore, the Lorentz equations for a particle maving in the Maxwell electromagnetic field on the Minkowskian space-time can also be obtained from the Maxwell equations by means of the Kaluze mechanism of the Maxwell theory.     

The principle of equivalence and theories of gravity

We construct classical theories of gravity on the basis of special relativity and the Einstein-Infeld accelerating-elevator thought experiment. The resulting theories share most of the main features of general relativity, namely the nonlinear character of the theory, the metrical significance of the gravitational potentials and the geodesic equation of particle motion. They differ from general relativity in at most nonlinear terms in the gravitational constant G in their equations of particle motion and field equations.     

牛顿力学中的惯性质量与狭义相对论中的惯性质量

分别详细说明了在牛顿力学中和在狭义相对论中,惯性和惯性质量的概念是如何引入的.明确地阐述了狭义相对论同牛顿力学相类似,物体(可视为质点或粒子)的固有质量(或静止质量)就是其惯性质量.通过分析,指出并强调了运动质量只是个规定,并非物体惯性的大小真的随运动发生了改变.最后还对静止质量为零、速度为光速的粒子只遵从狭义相对论而...     

Symmetry and invariance

The concept of invariance relates to both the intrinsic symmetries of physical systems and the symmetry of the set of equivalent reference frames used to observe them. Standard algebraic expressions for electrostatic potentials and crystal-field effective operators display both types of invariance. The concept of a reference frame is generalized to that of an ‘observing system’, which can, for example, be the basis states of a quantum system. This idea is related to Racah’s mathematical machinery for evaluating the matrix elements of many-electron 4f open-shell states in lanthanide ions. It is argued, on the basis of computational flexibility and ease of interpretation, that all equations that represent physical processes be expressible in terms of invariants of the set of observing systems. This ‘Principle of Invariance’ is then applied to special relativity, leading to a simple geometrical interpretation of Maxwell’s electromagnetic field equations. The close relationship between Dirac’s relativistic wave equation and Maxwell’s equations is then exposed. This leads to the concept of an inner structure of space-time and the reinterpretation of particle spin. Finally, it is shown that the use of invariants in relativity theory identifies a set of observing systems with a higher symmetry than that of Minkowski space-time.     

The multipole particle and the Papapetrou equation

The conclusion is made that the supplementary conditions of Pirani, Dixon, or others, which close the system of dipole equations of the general theory of relativity for a test particle and as a result make it possible to uniquely calculate the motion of such a particle, in essence determine the internal structure of the particle. The conclusion is made against the background of the solution of the problem of the multipole expansion of the tensor density along a line and a multipole formulation of the equations of motion of a body. It is shown that the Papapetrou equations can be employed to calculate the behavior of particles only if information contained in the dipole equations is used.S. Ordzhonokidze Aeronautical Institute, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 43–48, October, 1994.     

Conventionalism and general relativity

We argue that the geometry of spacetime is a convention that can be freely chosen by the scientist; no experiment can ever determine this geometry of spacetime, only the behavior of matter in space and time. General relativity is then rewritten in terms of an arbitrary conventional geometry of spacetime in which particle trajectories are determined by forces in that geometry, and the forces determined by fields produced by sources in that geometry. As an example, we consider radial trajectories in the field of a single particle expressed in the spacetime of special relativity.     

Classical spin theory

Tensor and vector equations of motion of a classical charged particle with spin have been derived within the framework of the special theory of relativity on the basis of Frenkel's tensor. The anomalous magnetic moment of the particle is considered in a natural manner in deriving the equations. The expression for the forces acting on the particle is constructed with consideration of the effect of spin on the motion trajectory. The spin equations proved to coincide with those obtained previously by Nyborg and Good. The properties of these equations have been studied, and it has been shown that the various equations are in fact variant forms of one and the same equation. In the absence of an anomalous magnetic moment the tensor equation coincides with Frenkel's spin equation, and in the same situation the vector equation transforms to the equation obtained by Tamm. In the special case of homogeneous fields the vector equation coincides with the well-known Bargmann-Michel-Telegdi equation. In conclusion we present spin motion equations for a particle with electric and magnetic charges.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 67–76, February, 1980.     

Cylindrically symmetric Brans–Dicke–Maxwell solutions

We investigate cylindrically symmetric vacuum solutions with both null and non-null electromagnetic fields in the framework of the Brans–Dicke theory and compare these solutions with some of the well-known solutions of general relativity for special values of the parameters of the resulting field functions. We see that, unlike general relativity where the gravitational force of an infinite and charged line mass acting on a test particle is always repulsive, it can be attractive or repulsive for Brans–Dicke theory depending on the values of the parameters as well as the radial distance from the symmetry axis.     

Kaluza理论的运动定律

本文指出,如同在广义相对论中粒子运动方程是场方程的推论一样,在引力场与电磁场的Kaluza统一理论中,粒子的运动方程也是场方程的一个推论,即带电粒子在引力场和电磁场中的运动方程可以从Kaluza统一理论中的场方程推导出来。本文进而在Minkowski时空的条件下,借助Maxwell理论的Kaluza形式,得到Maxwell方程也包含了带电粒子运动方程的结论。 关键词：     

A possible unification of Newton's and Coulomb's forces

We have considered electric charge as the fourth component of the particle momentum in five-dimensional space–time. The fifth dimension has been compactified on a circle with an extremely small radius determined from the fundamental physics constants. First, we have given equations in the framework of five-dimensional special relativity and determined the corresponding reduction to four-dimensional space–time. Then, in order to obtain an appropriate charge-to-mass ratio and to avoid the Fourier modes problem, we have considered the propagation of an off-mass shell particle in the five-dimensional space–time which can be interpreted as the motion of an on-mass shell particle in the four-dimensional world we experience. As an example, we have discussed the five-dimensional kinematic equations associated with the electron-positron annihilation process into two photons. Finally, the consequences on the gravitational interaction between two elementary charged particles has been studied. As a main result, we have obtained a unification of Newton's gravitational and Coulomb's electrostatic forces.