Poincaré’s Relativistic Physics: Its Origins and Nature

Henri Poincaré (1854–1912) developed a relativistic physics by elevating the empirical inability to detect absolute motion, or motion relative to the ether, to the principle of relativity, and its mathematics ensured that it would be compatible with that principle. Although Poincaré’s aim and theory were similar to those of Albert Einstein (1879–1955) in creating his special theory of relativity, Poincaré’s relativistic physics should not be seen as an attempt to achieve Einstein’s theory but as an independent endeavor. Poincaré was led to advance the principle of relativity as a consequence of his reflections on late nineteenth-century electrodynamics; of his conviction that physics should be formulated as a physics of principles; of his conventionalistic arguments on the nature of time and its measurement; and of his knowledge of the experimental failure to detect absolute motion. The nonrelativistic theory of electrodynamics of Hendrik A.Lorentz (1853–1928) of 1904 provided the means for Poincaré to elaborate a relativistic physics that embraced all known physical forces, including that of gravitation. Poincaré did not assume any dynamical explanation of the Lorentz transformation, which followed from the principle of relativity, and he did not seek to dismiss classical concepts, such as that of the ether, in his new relativistic physics. Shaul Katzir teaches in the Graduate Program in History and Philosophy of Science, Bar Ilan University.     

大尺度有效引力的E(2)规范理论模型

微波背景辐射的低l极矩的各向异性可能不能用微波背景辐射静止系boost到本动参考系来解释,我们推断boost对称性在宇宙学尺度上缺失,又由于单纯结合广义相对论和物质结构的标准模型不能解释星系以上尺度的引力现象,需要引入暗物质和暗能量.而迄今为止所有寻找暗物质粒子的实验给出的都是否定结果,暗能量的本质更是一个谜.因此,我们假设洛伦兹对称性是从星系以上尺度开始部分破缺,以非常狭义相对论对称群E(2)为例,用E(2)规范理论来构造大尺度有效引力理论,并分析了此规范理论的自洽性.从这些讨论中发现,当物质源即使为普通标量物质时,contortion也一般非零,非零contortion的存在会贡献一个等效能量动量张量的分布,它可能对暗物质效应给出至少部分的贡献.我们从对称性出发修改引力,有别于其他的修改引力理论.     

在工科物理中如何讲相对论动力学

讲相对论时学生已具有伽里略变换协变性和线性代数的知识,因此在工科物理中由洛伦兹变换协变性出发讲相对论动力学是可行的。教学的重点和难点在于如何让学生相信,相对论粒子的动量必须用四维动量来表达。     

The reconciliation of physics with cosmology

Astronomical observations of redshifts and the cosmic background radiation show that there is a local frame of reference relative to which the solar system has a well-defined velocity. Also, in cosmology the cosmological principle implies the existence of cosmic time and unique local reference frames at all spacetime points. On the other hand, in a fundamental postulate, the theory of special relativity excludes the possibility of the velocity of the Earth from entering into theories of local physics.The theory put forward in this paper resolves this conflict between local physics and cosmology. The theory retains the essential ingredient of the mathematical structure of special relativity, namely covariance under the Lorentz symmetry group, but changes radically the interpretation of the physical significance of the Lorentz transformation. The theory is based on the postulate that in free space the fundamental interactions in physics are propagated with constant velocity with respect to the local rest frame. In Minkowski spacetime the local rest frame of reference defines a unique time axis and consequently a unique three-dimensional spatial hyperplane. One particularly important result of this is that the theory includes the classical notion of simultaneity. From the fundamental postulate it follows that the equations of local physics, when expressed in terms of the rest frame coordinate system, must be covariant under the Lorentz symmetry group. By the identification of the local rest frame with the (unique) cosmological local reference frame the two theories become mutually consistent.The effects of the motion of the Earth on laboratory experiments are discussed. It is pointed out that existing experimental data do not discriminate between the present theory and that of special relativity: a proposal for an experimental test is made.Address for the academic year 1990–1991: 415 Graduate Studies Research Center, University of Georgia, Athens, Georgia 30602.     

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.     

基于相对性原理的多普勒效应公式推导

“大学物理”旨在向学生传递“联系”与“统一”的思想,但众多的教材在推导多普勒效应公式时却没有深入探寻“相对运动”与“频率变化”之间的联系和统一.作者从波长的定义着手,基于相对性原理,应用伽利略变换式对机械波的多普勒效应公式进行推导和应用验证;采用洛伦兹变化式对电磁波的多普勒效应公式进行推导.通过推导机械波和电磁波的多普勒效应公式,揭示了多普勒效应的频率变化实际是在不同惯性系中的测量结果.     

浅析洛伦兹变换的性质

本文从数学和物理学的角度分析、讨论了洛伦兹变换的两个重要性质,即“时空对称性”和“时空相对性”。最后又由时空对称平面图推导出了洛伦兹变换。     

On the Foundation of the Principle of Relativity

The relation of the special and the general principle of relativity to the principle of covariance, the principle of equivalence and Mach's principle, is discussed. In particular, the connection between Lorentz covariance and the special principle of relativity is illustrated by giving Lorentz covariant formulations of laws that violate the special principle of relativity: Ohm's law and what we call Aristotle's first and second laws. An Aristotelian universe in which all motion is relative to absolute space is considered. The first law: a free particle is at rest. The second law: force is proportional to velocity. Ohm's law: the current density is proportional to the electrical field strength. Neither of these laws fulfills the principle of relativity. The examples illustrate, in the context of Lorentz covariance and special relativity, Kretschmann's critique of founding Einstein's general principle of relativity on the principle of general covariance. A modification of the principle of covariance is suggested, which may serve as a restricted criterium for a physical law to satisfy Einstein's general principle of relativity. Other objections that have been raised to the validity of Einstein's general principle of relativity are based upon the preferred state of inertial frames in the general, as well as in the special theory, the existence of tidal effects in true gravitational fields, doubts as to the validity of Mach's principle, whether electromagnetic phenomena obey the principle, and, finally, the anisotropy of the cosmic background radiation. These objections are reviewed and discussed.     

谈狭义相对论时空理论教学——大学物理课程讲授狭义相对论之我见

依据狭义相对论基本原理和物理事例,导出钟慢、尺缩效应和同时相对性,再以此为据导出洛伦兹变换.     

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.     

Demonstrating additional law of relativistic velocities based on squeezed light

The special relativity is the foundation for many branches of modern physics, of which the theoretical results are far beyond our daily experience and hard to realized in kinematic experiments. However, its outcomes could be demonstrated by making use of the convenient substitute, i.e., the squeezed light in the present paper. The squeezed light is very important in the field of quantum optics, and the corresponding transformation can be regarded as the coherent state of SU(1,1). In this paper, the connection between the squeezed operator and the Lorentz boost is built under certain conditions. Furthermore, the additional law of relativistic velocities and the angle of the Wigner rotation are deduced as well.     

A canonical dynamics view of the Newtonian limit of general relativity

The Newtonian limit of general relativity was Jürgen Ehlers favourite model for limit relations between theories of physics. In this contribution, for the case of isolated systems, the Newtonian limit of general relativity will be illuminated from a canonical dynamics point of view. The canonical dynamics approach naturally supplies a post-Newtonian expansion of general relativity.     

Demonstrating an additional law of relativistic velocities based on squeezed light

The special relativity is the foundation for many branches of modern physics, of which the theoretical results are far beyond our daily experience and hard to realized in kinematic experiments. However, its outcomes could be demonstrated by making use of the convenient substitute, i.e., the squeezed light in the present paper. The squeezed light is very important in the field of quantum optics, and the corresponding transformation can be regarded as the coherent state of SU(1,1). In this paper, the connection between the squeezed operator and the Lorentz boost is built under certain conditions. Furthermore, the additional law of relativistic velocities and the angle of the Wigner rotation are deduced as well.     

Gravitational collapse and naked singularities

Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for research in this field. In the absence of a general proof for censorship, many examples have been proposed, in which naked singularity is the outcome of gravitational collapse. Recent developments have revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of ‘effective naked singularities’, which will be quite helpful because general relativity has limitation in its application at the high-energy end. The appearance of naked singularities is not detestable but can open a window for the new physics of strongly curved space-times.     

Gravitational and electroweak unification by replacing diffeomorphisms with larger group

The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers will agree whether any given quantity is conserved. Alternatively, and equivalently, it is defined by the assumption that all observers will agree that the general relativistic wave equation describes the propagation of light. Thus, the group replacement is analogous to the replacement of the Lorentz group by the diffeomorphisms that led Einstein from special relativity to general relativity, and is also consistent with the assumption of constant light velocity that led him to special relativity. The enlarged covariance group leads to a non-commutative geometry based not on a manifold, but on a nonlocal space in which paths, rather than points, are the most primitive invariant entities. This yields a theory which unifies the gravitational and electroweak interactions. The theory contains no adjustable parameters, such as those that are chosen arbitrarily in the standard model.     

Generalized Edwards Transformation and Principle of Permutation Invariance

The relativity of simultaneity is generalized by using the concept of synchronization gauge. The Lorentz transformation is derived without the postulate of the universal limiting speed, and a generalized Edwards transformation is obtained by using the principle of permutation invariance (covariance). It is shown that the existences of the one-way universal limiting speed (in the Lorentz transformation) and the constancy of the two-way average speed of light (in the Edwards transformation) are the necessary consequences of the principle of permutation invariance that is consistent with the postulate of relativity. The connection between the Edward transformation and the general coordinate transformation is discussed, and based on this, we find that the physical meaning of the Edwards parameter, which indicates anisotropy of the speed of light, is a gravitomagnetic potential of the spacetime.     

Geodesically equivalent metrics in general relativity

We discuss whether it is possible to reconstruct a metric from its nonparameterized geodesics, and how to do it effectively. We explain why this problem is interesting for general relativity. We show how to understand whether all curves from a sufficiently big family are nonparameterized geodesics of a certain affine connection, and how to reconstruct algorithmically a generic 4-dimensional metric from its nonparameterized geodesics. The algorithm works most effectively if the metric is Ricci-flat. We also prove that almost every metric does not allow nontrivial geodesic equivalence, and construct all pairs of 4-dimensional geodesically equivalent metrics of Lorentz signature.     

Are the invariance principles really truly Lorentz-covariant?

It is shown that some sections of the invariance (or symmetry) principles, such as the space reversal symmetry (or parityP) and time reversal symmetryT (of elementary particle and condensed matter physics, etc.), are not really truly Lorentz covariant and hence are dependent on the chosen inertial frame; while the world parity or the proper parityW (i.e., the spacetime reversal symmetryPT) is a truly Lorentz covariant concept, the same for all inertial observers. The basic reason for this is that in theMinkowskian space-time continuum frames of special relativity (in contrast to the space and time frames) one cannot change either space or time keeping the other one fixed and also maintain the causality requirements that all world space mappings should be timelike. Indeed, I find that the Dirac-Wigner and Lee-Yang, etc. sense of Lorentz invarianceis not in full compliance with the Einstein-Minkowskirequirements of the Lorentz covariance (in conjunction with the causality requirements) of all physical laws (i.e., the worldspaceMach principle).     

A Study of Gaugeon Formalism for QED in Lorentz Violating Background

At the energy regimes close to Planck scales, the usual structure of Lorentz symmetry fails to address certain fundamental issues and eventually breaks down, thus paving the way for an alternative road map. It is thus argued that some subgroup of proper Lorentz group could stand consistent and might possibly help us to circumvent this problem.It is this subgroup that goes by the name of Very Special Relativity(VSR). Apart from violating rotational symmetry,VSR is believed to preserve the very tenets of special relativity. The gaugeon formalism due to type-I Yokoyama and type-II Izawa are found to be invariant under BRST symmetry. In this paper, we analyze the scope of this invariance in the scheme of VSR. Furthermore, we will obtain VSR modified Lagrangian density using path integral derivation. We will explore the consistency of VSR with regard to these theories.