LU(1)群的引力规范场球对称静态解

寻找引力规范理论场方程的严格解要比寻找Einstein场方程的严格解更为困难。但是,对某些物理问题来说,能够求得牛顿型近似解和后牛顿型的近似解就足够了。本文研究了一种Lorentz群和U(1)群为规范群的引力规范理论,求得了带电粒子的球对称静场的特殊有挠解,并求得了有挠的一阶近似解。     

L?(1)群的引力规范场球对称静态解

寻找引力规范理论场方程的严格解要比寻找Einstein场方程的严格解更为困难。但是,对某些物理问题来说,能够求得牛顿型近似解和后牛顿型的近似解就足够了。本文研究了一种Lorentz群和U(1)群为规范群的引力规范理论,求得了带电粒子的球对称静场的特殊有挠解,并求得了有挠的一阶近似解。 关键词：     

线性引力论的引力磁分量及其磁效应

根据广义相对论,弱场近似条件下引力场中不仅含有经典的牛顿引力场,还存在一种类比于磁场概念的引力"磁"场,引力磁场的命名借用了电动力学中磁场的概念.为了研究引力磁场的物理性质和它引发的一些关联效应,本文首先从线性爱因斯坦方程出发,利用相似变换的方法从方程的二级张量场中分解出了引力的"磁"分量并定义了引力磁场;在此基础上考虑了一种通有匀速流体的环状微管模型,通过电动力学的分析方法研究了远离微管区域的引力磁场分布特征,重点在计算过程中改进了以往对这类环状模型引力磁场的计算方法,表明了这类模型的引力磁场远场分布模式与磁偶极子磁场的远场分布类似;之后利用类磁场的性质研究了引力磁场的动力学特征,首次研究了测试粒子在线性时变引力磁场及余弦时变引力磁场中的运动规律,同时通过设计一种具有双层结构且通有加速流动流体的环状微管模型改进了前人对时变引力磁场中引力感应、惯性系拖曳现象的研究办法,从更清晰的角度用更简单的数学通过引力电磁理论研究和展示了引力感应现象和广义相对论中的惯性系拖曳现象.全文为引力磁场及其关联效应的研究提供了一些新的方法和思路.     

《从零学相对论》连载(22)

正8.5.3牛顿引力论对星光偏角的推导[选读]索尔德纳在1801年推导星光偏角公式时,光速的有限性已被证实.只要承认光的微粒说并默认光微粒(即现在的光子)在引力场中的表现与普通质点的唯一不同就是以光速运动,就不难用牛顿引力论推出偏角公式.此式的推导方法很多,现在介绍一种"借他山之石"的简便方法.首先考虑质量为m的普通质点在太阳附近飞过时因受太阳引力而出现的偏角.这种情况与卢瑟福1911年研究的α粒子散射类似,因此可以借用其     

引力的"磁性"是怎么回事

爱因斯坦广义相对论的重要结论之一是引力也应有“磁”分量，两个旋转物体之间会有引力“磁”矩的相互作用．而按牛顿引力论，两个物体的引力只决定于二者的质量，并不与二者旋转运动方向有关．因此，检验是否存在引力“磁”分量，乃成为区别牛顿引力论与广义相对论的关键之一．检验的方法是利用旋转物体，例如，在空间放置一个陀螺，按牛顿理论。     

Brans-Dicke引力理论的弱场近似

Brans-Dicke引力理论是重要的修正引力理论之一,其对于研究星体运动、宇宙演化以及解释宇宙现象等起着重要的作用.寻找Brans-Dicke引力理论场方程的解对于Brans-Dicke引力理论的研究和发展具有重要意义.但由于Brans-Dicke引力理论场方程本身的高度非线性性,使得一般情况下精确求解非常困难,特殊情况下也只能求得部分精确解.幸运的是大多数情况下引力场比较弱,且在低速的条件下求场方程的近似解相对容易.本文基于弱场低速条件,详细地求解了Brans-Dicke引力理论的弱场低速近似解.首先基于弱场条件,将标量场和度规写为一阶微扰展开的形式;然后将标量场和度规代入相应的场方程得到相应的线性场方程,通过选取特定的规范条件进一步简化线性场方程;最后求解出简化的线性场方程的低速近似解.本文的求解方法可以为Brans-Dicke引力理论的教学和研究提供有益的参考.     

荷电天体引力场中试验粒子进动的后牛顿解法

采用后牛顿近似方法分析讨论了荷电天体引力场(即Reissner-Nordstr(o)m度规场)中试验粒子的轨道进动情况,给出了荷电量Q对试验粒子轨道进动的影响.     

相对论性粒子的拉格朗日方程的推导

一、引言 相对论性粒子的拉格朗日(Lagrange)方程通常是由哈密顿(Hamilton)原理推导出来的[1-3].在本文中,我们由牛顿第二定律出发,推导出拉格朗日方程与相应的相对论性粒子的拉格朗日方程.二、相对论性的拉格良日方程 相对论性粒子的运动方程是其中F是作用在粒子上的力. P=ma (2)这里F是粒子的动量,a是粒子的速度,并且粒子的相对论性的质量m为 　 我们假定,粒子不受约束.同时采用广义坐标q1,q2和q3来描述粒子的运动.在广义坐标中,粒子的位矢表示为 广义坐标中的速度矢量 用a与(1)式点乘,利用方程(5),得其中Qi是广义力.现在把方程(6)可写…     

牛顿万有引力定律的建立

万有引力定律的建立是牛顿“从运动现象研究自然力”的一个最辉煌的范例．本文将依据牛顿在各个时期写的手稿与论著，探讨牛顿论证的特色以及牛顿引力思想的发展过程．     

利用扭秤检验牛顿反平方定律在近距离范围的正确性

许多理论模型预言牛顿引力反平方定律在近距离下将发生偏离.本文简要介绍了牛顿反平方定律的实验检验现状,给出了利用精密扭秤技术检验近距离反平方定律的实验原理和实验结果,分析了扭秤实验的热噪声和灵敏度.     

Poincaré引力规范场和1/2自旋粒子的运动

木文以Poinaré群作为引力规范群,在有挠率和曲率的空间中,讨论了当引力拉氏量包含场强的线性项与二次项时体系的运动方程,指出球对称真空静引力场方程在“宏观”极限下可以得到Schwarzchild解,因此它与目前关于广义相对论的实验验证是一致的,但在“微观”极限下,方程预示着一种新的短程作用,讨论了自旋1/2的粒子作为检测粒子在这种球对称真空静场中的运动,指出运动方程只与仿射联络的黎曼部分有关,并和广义相对论的相应方程具有同样的形式。 关键词：     

A coupled theory of electromagnetism and gravitation

A coupling electromagnetism with a previously developed scalar theory of gravitation is presented. The principle features of this coupling are: (1) a slight alteration to the Maxwell equations, (2) the motion of a charged particle satisfies an equation with the Lorentz force-appearing on the right side in place of zero, and (3) the energy density of the electromagnetic field appears in the gravitational field equation in a manner similar to the mass term in the Klein-Gordonequation. The field of a static, spherically symmetric charged particle is computed. The electromagnetic field gives rise to l/r ² terms in the gravitational potential.     

On calculation of magnetic-type gravitation and experiments

The linearized Einstein equations are written in the same form as the Maxwell equation. In the case of a weak stationary field and low velocity, the geodesic equations are written in the form of the Lorentz equation of motion. We suggest that the existence of the magnetic-type gravitation predicted by GR is equivalent to the existence of the gravitational wave predicted by GR. The Schiff effect is explained as one of the magnetic-type gravitation and the new effect is given. The Hall-type gravitational experiment is studied.     

Nonlinear equations of the gravitational field in the special theory of relativity

It is proposed that the nonlinearity of the field be taken into account with the help of a method which essentially consists of the fact that the structure of the Lagrangian, expressed in terms of the potential of the field and its derivatives, is not known a priori, but is obtained from a solution of the self-action equation in phase space in which the Lagrangian is the unknown. This equation has a solution and the Lagrangian turns out to be a nonpolynomial function with respect to the field potential. The gravitational field equations following from the variational principle have a similar structure to the equations of general relativity and coincide with them in the linear approximation. The equations of other fields taking into account gravitation, as well as the equation of motion of a test particle in a gravitational field, are constructed.     

Embedding of Particle Waves in a Schwarzschild Metric Background

The special and general relativity theories are used to demonstrate that the velocity of an unradiative particle in a Schwarzschild metric background, and in an electrostatic field, is the group velocity of a wave that we call a particle wave, which is a monochromatic solution of a standard equation of wave motion and possesses the following properties. It generalizes the de Broglie wave. The rays of a particle wave are the possible particle trajectories, and the motion equation of a particle can be obtained from the ray equation. The standing particle wave equation generalizes the Schrödinger equation of wave amplitudes. The particle wave motion equation generalizes the Klein–Gordon equation; this result enables us to analyze the essence of the particle wave frequency. The equation of the eikonal of a particle wave generalizes the Hamilton–Jacobi equation; this result enables us to deduce the general expression for the linear momentum. The Heisenberg uncertainty relation expresses the diffraction of the particle wave, and the uncertainty relation connecting the particle instant of presence and energy results from the fact that the group velocity of the particle wave is the particle velocity. A single classical particle may be considered as constituted of geometrical particle wave; reciprocally, a geometrical particle wave may be considered as constituted of classical particles. The expression for a particle wave and the motion equation of the particle wave remain valid when the particle mass is zero. In that case, the particle is a photon, the particle wave is a component a classical electromagnetic wave that is embedded in a Schwarzschild metric background, and the motion equation of the wave particle is the motion equation of an electromagnetic wave in a Schwarzschild metric background. It follows that a particle wave possesses the same physical reality as a classical electromagnetic wave. This last result and the fact that the particle velocity is the group velocity of its wave are in accordance with the opinions of de Broglie and of Schrödinger. We extend these results to the particle subjected to any static field of forces in any gravitational metric background. Therefore we have achieved a synthesis of undulatory mechanics, classical electromagnetism, and gravitation for the case where the field of forces and the gravitational metric background are static, and this synthesis is based only on special and general relativity.     

Equation of Motion of a Spinning Test Particle in Gravitational Field

Based on the coupfing between the spin of a particle and gravitoelectromagnetic field, the equation of motion of a spinning test particle in gravitational field is deduced. From this equation of motion, it is found that the motion of a spinning particle deviates from the geodesic trajectory, and this deviation originates from the coupling between the spin of the particle and gravitoelectromagnetic field, which is also the origin of Lense-Thirring effects. In post-Newtonian approximations, this equation gives the same results as those of Mathisson-Papapetrou equation. Effect of the deviation of geodesic trajectory is detectable.     

Kosmologische Lösungen der lorentzinvarianten Gravitationstheorie

In the framework of the Lorentz invariant theory of gravitation a cosmology in the flat space-time is investigated. As in the Newtonian cosmology we start from an infinitely extended system of incoherent matter under the influence of its own gravitational field. The field equations, the equations of motion and the world postulate of homogenity and isotropy for geodetic observes lead then to the Friedman equation. In order to handle the coupled system of equations for the gravitational field and the matter a conveniant approximation method is developed. The calculations are carried out in the second order of this method. The Einstein theory, which is in some respect equivalent to the Lorentz invariant theory of gravitation, serves as a guiding principle for our formal developements. On the other hand the flat space-time cosmology presented here, gives rise to a new interpretation of the Einstein Cosmology.     

A Generally Covariant Wave Equation for Grand Unified Field Theory

A generally covariant wave equation is derived geometrically for grand unified field theory. The equation states most generally that the covariant d'Alembertian acting on the vielbein vanishes for the four fields which are thought to exist in nature: gravitation, electromagnetism, weak field and strong field. The various known field equations are derived from the wave equation when the vielbein is the eigenfunction. When the wave equation is applied to gravitation the wave equation is the eigenequation of wave mechanics corresponding to Einstein's field equation in classical mechanics, the vielbein eigenfunction playing the role of the quantized gravitational field. The three Newton laws, Newton's law of universal gravitation, and the Poisson equation are recovered in the classical and nonrelativistic, weak-field limits of the quantized gravitational field. The single particle wave-equation and Klein-Gordon equations are recovered in the relativistic, weak-field limit of the wave equation when scalar components are considered of the vielbein eigenfunction of the quantized gravitational field. The Schrödinger equation is recovered in the non-relativistec, weak-field limit of the Klein-Gordon equation). The Dirac equation is recovered in this weak-field limit of the quantized gravitational field (the nonrelativistic limit of the relativistic, quantezed gravitational field when the vielbein plays the role of the spinor. The wave and field equations of O(3) electrodynamics are recovered when the vielbein becomes the relativistic dreibein (triad) eigenfunction whose three orthonormal space indices become identified with the three complex circular indices (1), (2), (3), and whose four spacetime indices are the indices of non-Euclidean spacetime (the base manifold). This dreibein is the potential dreibein of the O(3) electromagnetic field (an electromagnetic potential four-vector for each index (1), (2), (3)). The wave equation of the parity violating weak field is recovered when the orthonormal space indices of the relativistic dreibein eigenfunction are identified with the indices of the three massive weak field bosons. The wave equation of the strong field is recovered when the orthonormal space indices of the relativistic vielbein eigenfunction become the eight indices defined by the group generators of the SU (3) group.     

Motion of a particle in the field of a rotating body in the post-Newtonian approximation. Alternative solutions

The components of the gravitational field are compared in the post-Newtonian approximation in the geometric (Einstein tensor) and field (Maxwellian vector form) theories of gravitation. The fundamental difference of these fields in the motion of a test particle is shown. The feasibility of qualitative detection of the vortex component of the gravitational field is found experimentally. The scheme for an alternate experiment is given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 15–18, May, 1990.The author thanks A. S. Lantsev for the experimental part of the article presented here.