On the relativistic velocity composition paradox and the Thomas rotation

The non-commutativity and the non-associativity of the composition law of the non-colinear velocities lead to an apparent paradox, which in turn is solved by the Thomas rotation. A 3×3 parametric, unimodular and orthogonal matrix elaborated by Ungar is able to determine the Thomas rotation. However, the algebra involved in the derivation of the Thomas rotation matrix is overwhelming. The aim of this paper is to present a direct derivation of the Thomas angle as the angle between the composite vectors of the non-colinear velocities, thus obtaining a simplicity with which the rotation can be expressed. This allows the formulation of an alternative to the statement related to the necessity of the Thomas rotation of the Cartesian axes by the statement implying the necessity of the rotation of the direct (inverse) relativistic composite velocity to coincide with the inverse (direct) relativistic composite velocity.     

洛伦兹变换的一种新推导

对于洛伦兹变换中两个惯性系S和S′系的约定提出了新思路,使x轴与x′轴反向,从而使S和S′系完全对称,简化了推导过程;并根据约定,从狭义相对论的两条基本假设出发,严格地推导出了洛伦兹变换式.     

再谈洛伦兹变换的推导

评论了仅仅依据光速不变假设和相对性原理推导洛伦兹变换公式的方法.     

Axiomatic approach to the nonassociative group of relativistic velocities

The bizarre and counterintuitive noncommutativity and nonassociativity of the relativistic composition of noncollinear velocities is attributed to the presence of the Thomas rotation. The Thomas rotation, in turn, gives rise to anonassociative group structure for the set of relativistically admissible velocities. This nonstandard group structure has been observed in other contexts and, hence, merits axiomatization.     

On the relation of Thomas rotation and angular velocity of reference frames

In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing concepts, introduced in Rindler and Perlick (Gen Rel Grav 22:1067, 1990), is to consider a rotating reference frame co-moving with the gyroscope, and relate the precession of the gyroscope to the angular velocity of the reference frame. A recent paper (Herrera and di Prisco in Found Phys Lett 15:373, 2002), however, applies this principle to three different co-moving rotating reference frames and arrives at three different Thomas rotation angles. The reason for this apparent paradox is that the principle of Rindler and Perlick (Gen Rel Grav 22:1067, 1990) is used for a situation to which it does not apply. In this paper we rigorously examine the theoretical background and limitations of applicability of the principle of Rindler and Perlick (Gen Rel Grav 22:1067, 1990). Along the way we also establish some general properties of rotating reference frames, which may be of independent interest.     

关于高速运动物体视觉形象的讨论

讨论了高速运动物体上面元的朝向与可见性的关系．用狭义相对论进行了简单的理论计算,结果表明高速运动物体的可见部分正是经“Terrell转动”后“朝向”观察者的部分,该结论体现了狭义相对论的完美和对称．     

A modified Lorentz theory as a test theory of special relativity

A modified Lorentz theory (MLT) based on the generalized Galilean transformation has recently received attention. In the framework of MLT, some explicit formulas dealing with the one-way velocity of light, slow-clock transport and the Doppler effect are derived in this paper. Several typical experiments are analyzed on this basis. The results show that the empirical equivalence between MLT and special relativity is still maintained to second order terms. We confirm recent findings of other works that predict the MLT might be distinguished from special relativity at the third order by Doppler centrifuge experiments capable of a fractional frequency detection threshold of 10^–15.     

Thomas Rotation and Thomas Precession

Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. A straightforward derivation of the Fermi–Walker equation is also given. Besides the simplicity of calculations the absolute treatment of spacetime allows us to make a clear conceptual distinction between the phenomena of Thomas rotation and Thomas precession.Supported by Hungarian research fund OTKA-T048489.Supported by Hungarian research funds OTKA-T047276, F049457, T049301.     

洛伦兹速度变换的一种直接推导方法

用光速不变原理直接导出洛伦兹速度变换式，并证明相对论性速度构成双曲几何的Beltrami-Klein模型。     

Lorentz变换和Maxwell方程的最简单形式

用Cifford代数来描述，Lorents变换和Maxwell方程组变得非常简单。例如，Maxwell方程成为□F=4πj/c，只一个方程就够了。     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

Thomas rotation and polarized light: A non-abelian geometric phase in optics

We describe anon-abelian Berry phase in polarization optics, suggested by an analogy due to Nityananda between boosts in special relativity and the effect of elliptic dichroism on polarized light. The analogy permits a simple optical realization of the non-abelian gauge field describing Thomas rotation. We also show how Thomas rotation can be understood geometrically on the Poincaré sphere in terms of the Pancharatnam phase.     

On the Meaning of Lorentz Covariance

In classical mechanics, Galilean covariance and the principle of relativity are completely equivalent and hold for all possible dynamical processes. In contrast, in relativistic physics the situation is much more complex. It will be shown that Lorentz covariance and the principle of relativity are not completely equivalent. The reason is that the principle of relativity actually only holds for the equilibrium quantities that characterize the equilibrium state of dissipative systems. In the light of this fact it will be argued that Lorentz covariance should not be regarded as a fundamental symmetry of the laws of physics.     

Dual properties of spacetime under an alternative Lorentz transformation

In flat spacetime, the fourth space coordinate in special relativity (SR) is equivalent to the coordinate time t_E. We will show, however, that this definition of physical time is not unique. Another natural choice of coordinate time, t_A, with absolute synchronization is allowed. Spacetime would exhibit dual properties, namely relativistic and absolute. In an arbitrary inertial frame, the relationship of the above two kinds of coordinate time corresponds to a resynchronization, and the Lorentz transformations can be written in an alternative form, which is called the generalized Galilean transformation (GGT). Although the absolute property is still hidden in nearly all types of experiments, the advantages of the above approach are as follows: (1) It will give us a deeper understanding of SR, including the basis of length contraction, time dilation and the interaction between moving objects and the physical vacuum. (2) It will provide a wider research domain than SR; for example, superluminal motion is predicted and has obtained growing experimental support.     

On the quantum Lorentz group

The quantum analog of Pauli matrices are introduced and investigated. From these matrices and an appropriate trace over spinorial indices we construct a quantum Minkowski metric. In this framework we show explicitly the correspondence between the SL(2,C) and Lorentz quantum groups. Five matrices of the quantum Lorentz group are constructed in terms of the R matrix of SL(2,C) group. These matrices satisfy Yang–Baxter equations and two of which have adequate properties tied to the quantum Minkowski space structure as the reality conditions of the coordinates and the symmetrization of the metric. It is also shown that the Minkowski metric leads to invariant and central lengths of four-vectors.     

Lorentz Transformation from Symmetry of Reference Principle

The Lorentz Transformation is traditionally derived requiring the Principle of Relativity and light-speed universality. While the latter can be relaxed, the Principle of Relativity is seen as core to the transformation. The present letter relaxes both statements to the weaker, Symmetry of Reference Principle. Thus the resulting Lorentz transformation and its consequences (time dilatation, length contraction) are, in turn, effects of how we manage space and time.     

关于狭义相对论中"洛仑兹变换导出"的讲法的沿革

洛仑兹变换是狭义相对论中的一个关键问题，本文旨在对各种讲法作比较，从而求得对此问题有较全面深入的认识。     

磁单极与磁洛伦兹力

概述了磁单极概念的历史发展,从洛伦兹变换出发,利用电磁场张量和四维力的协变性以及电荷相对论不变,直接证明了运动磁单极受磁洛伦兹力,建议了一个磁洛伦兹力的验证方案,并用磁洛伦兹力公式导出狄拉克电荷量子化条件．证明了磁洛伦兹力公式具有与库仑定律相同的精确度．     

大学物理教学中不应忽视电磁学与狭义相对论的内在联系

文章指出大学物理教学中关于电磁学和狭义相对论的缺憾,并提出了可行的教学方案.由此可以使学生深化对电磁场的认识,同时深刻理解狭义相对论时空观的内在意义.