相对性原理对普遍定律和非普遍定律参考系变换性质的不同要求——关于协变性疑难的进一步讨论

提出普遍定律和非普遍定律以及“协变”与“可导出”的明确定义，证明狭义相对性原理（及其伽利略近似）要求在惯性系变换下，自然界普遍定律是协变的，非普遍定律不协变但是“可导出”的，一切定律都服从相对性原理，从而进一步解答了由爱因斯坦，朗道关于狭义相对性原理的一种错误表述所引起的“协变性疑难”，还将有关结论推广到广义相对性原理情况。     

Synchronization Gauges and the Principles of Special Relativity

The axiomatic bases of Special Relativity Theory (SRT) are thoroughly re-examined from an operational point of view, with particular emphasis on the status of Einstein synchronization in the light of the possibility of arbitrary synchronization procedures in inertial reference frames. Once correctly and explicitly phrased, the principles of SRT allow for a wide range of theories that differ from the standard SRT only for the difference in the chosen synchronization procedures, but are wholly equivalent to SRT in predicting empirical facts. This results in the introduction, in the full background of SRT, of a suitable synchronization gauge. A complete hierarchy of synchronization gauges is introduced and elucidated, ranging from the useful Selleri synchronization gauge (which should lead, according to Selleri, to a multiplicity of theories alternative to SRT) to the more general Mansouri–Sexl synchronization gauge and, finally, to the even more general Anderson–Vetharaniam–Stedmans synchronization gauge. It is showed that all these gauges do not challenge the SRT, as claimed by Selleri, but simply lead to a number of formalisms which leave the geometrical structure of Minkowski spacetime unchanged. Several aspects of fundamental and applied interest related to the conventional aspect of the synchronization choice are discussed, encompassing the issue of the one-way velocity of light in inertial and rotating reference frames, the global positioning system (GPS)s working, and the recasting of Maxwell equations in generic synchronizations. Finally, it is showed how the gauge freedom introduced in SRT can be exploited in order to give a clear explanation of the Sagnac effect for counter-propagating matter beams.     

On the Consistency between the Assumption of a Special System of Reference and Special Relativity

In a previous work, we have shown that the null result of the Michelson–Morley experiment in vacuum is deeply connected with the notion of time. The same is true for the postulate of constancy of the two-way speed of light in vacuum in all frames independently of the state of motion of the emitting body. The argumentation formerly given is very general and has to be true not only within Special Relativity and its “equivalence” of all inertial frames, but as well as in Lorentz-Poincaré scenario of a preferred reference frame. This paper is the second of a trilogy intending to revisit the foundations of Special Relativity, and addresses the question of the constancy of the one-way speed of light and of the differences and similarities between both scenarios. Although they manifestly differ in philosophy, it is debated why and how the assumption of a “special system of reference experimentally inaccessible” is indeed compatible with Einstein’s Special Relativity, as beautifully outlined and discussed by Bell [Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1988)]. This rather trivial statement is still astonishing nowadays to a big majority of scientists. The purpose of this work is to bring such assertion into perspective, widening the somewhat narrow view of Special Relativity often presented in textbooks and scientific papers.     

Axiomatization of Special Relativity in First Order Logic

The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecRel for special relativity proposed recently by Andréka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional space-time perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecRel⁺. Then we introduce an axiom of mass (AxMass) and take four-momentum conservation as an axiom (AxCFM) in SpecRel⁺. It turns out that the twin paradox and energy-mass relation can be derived from SpecRel⁺ logically. Hence, as an extension of SpecRel, SpecRel⁺ is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.     

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。     

Geometric Simultaneity and the Continuity of Special Relativity

In this note I briefly discuss some aspects of relative geometric simultaneity in special relativity. After saying a few words about the status and nature of Minkowski spacetime in special relativity, I recall a uniqueness result due to David Malament concerning simultaneity relative to an inertial worldline and an extension of it due to Mark Hogarth and I prove an extension of it for simultaneity relative to an inertial frame in time-oriented spacetimes. Then I point out that the uniqueness results do not generalise to definitions of simultaneity relative to the rotating disk. Finally, I evaluate some recent claims of Selleri in the light of the results. Whilst some of his claims are supported by the approach taken here, the conclusion he draws from these claims, that special relativity harbours a discontinuity and so stands in need of replacement, does not follow and is rejected.     

Modal Interpretations and Relativity

A proof is given, at a greater level of generality than previous no-go theorems, of the impossibility of formulating a modal interpretation that exhibits serious Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.     

Hamiltonian Formalism of de-Sitter Invariant Special Relativity

The Lagrangian of Einstein's special relativity with universal parameter c (SRc) is invariant under Poincaré transformation, which preserves Lorentz metric ημν. The SRc has been extended to be one which is invariant under de Sitter transformation that preserves so-called Beltrami metric Bμν. There are two universal parameters, c and R, in this Special Relativity (denoted as SRcR). The Lagrangian-Hamiltonian formulism of SRcR is formulated in this paper.The canonic energy, canonic momenta, and 10 Noether charges corresponding to the space-time's de Sitter symmetry are derived. The canonical quantization of the mechanics for SRcR-free particle is performed. The physics related to it is discussed.     

Hamiltonian Formalism of de-Sitter Invariant Special Relativity

The Lagrangian of Einstein's special relativity with universal parameter c (SR_c) is invariant under Poincaré transformation, which preserves Lorentz metric η_μν. The SR_c has been extended to be one which is invariant under de Sitter transformation that preserves so-called Beltrami metric B_μν. There are two universal parameters, c and R, in this Special Relativity (denoted as SR_cR). The Lagrangian-Hamiltonian formulism of SR_cR is formulated in this paper. The canonic energy, canonic momenta, and 10 Noether charges corresponding to the space-time's de Sitter symmetry are derived. The canonical quantization of the mechanics for SR_cR-free particle is performed. The physics related to it is discussed.     

From De Sitter Special Relativity and Snyder's Model to Complete Yang Model

The de Sitter special relativity on the Beltrami-de Sitter-spacetime and Snyder's model in the momentum space can be combined together with an IR-UV duality to get the complete Yang model at both classical and quantum levels, which are related by the proposed Killing quantization. It is actually a special relativity based on the principle of relativity of three universal constants (c,l_P,R).     

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.     

Noninertial Observers in Special Relativity and Clock Synchronization Debates

Selleri's arguments that a consideration of noninertial reference frames in the framework of special relativity identify “absolute simultaneity” as being “Nature's choice of synchronization” are considered. In the case of rectilinearly accelerating rockets, it is argued by considering two rockets which maintain a fixed proper separation rather than a fixed separation relative to the inertial frame in which they start from rest, that what seems the most “natural” choice for a simultaneity convention is problem-dependent and that Einstein's definition is the most “natural” (though still conventional) choice in this case. In addition, the supposed problems special relativity has with treating a rotating disk, namely how a pulse of light traveling around the circumference of the disk can have a local speed of light equal to c everywhere but a global speed not equal to c, and how coordinate transformations to the disk can give the Lorentz transformations in the limit of large disk radius but small angular velocity, are addressed. It is shown that the theory of Fermi frames solves both of these problems. It is also argued that the question of defining simultaneity relative to a uniformly rotating disk does not need to be resolved in order to resolve Ehrenfest's paradox.     

相对论中的若干“勾股定理”

本文总结了作者讲授电动力学与狭义相对论的若干心得与体会;运用四维闵可夫斯基空间张量的性质及其缩并运算法则,介绍了用各阶四维张量构造相对论不变量即四维标量的方法,进而在所得四维标量为负定的类时标量时,推导出若干典型的勾股关系,并应用或验证于若干简单情形.     

Relativity Groups for Spacetimes with Invariant Velocities

New relativity groups for spacetime admitting invariant velocities are considered. It is shown that most of them restrict the maximal allowed velocities of reference frames.     

Dirac Oscillator Under the New Generalized Uncertainty Principle From the Concept Doubly Special Relativity

We discuss one-dimensional Dirac oscillator, by using the concept doubly special relativity. We calculate the energy spectrum by using the concept doubly special relativity. Then, we derive another representation that the coordinate operator remains unchanged at the high energy while the momentum operator is deformed at the high energy so that it may be bounded from the above. Actually, we study the Dirac oscillator by using of the generalized uncertainty principle version and the concept doubly special relativity.     

The Limits of Special Relativity

The Special Theory of Relativity and the Theory of the Electron have had an interesting history together. Originally the electron was studied in a non-relativistic context and this opened up the interesting possibility that lead to the conclusion that the mass of the electron could be thought of entirely in electromagnetic terms without introducing inertial considerations. However the application of Special Relativity lead to several problems, both for an extended electron and the point electron. These inconsistencies have, contrary to popular belief not been resolved satisfactorily to date, even within the context of Quantum Theory. Thus they are not merely of historical interest. Nevertheless these and subsequent studies bring out the interesting result that Special Relativity (and the theory of the electron) breaks down within the Compton scale or when the Compton scale is not neglected. This again runs contrary to an uncritical notion that Special Relativity is valid for point particles. Furthermore, it is pointed out that experiments have been recently suggested to test these ideas. These considerations lead to a characterization of the Planck constant in classical terms.     

An Analytical Treatment of the Clock Paradox in the Framework of the Special and General Theories of Relativity

No Heading In this paper we treat the so called clock paradox in an analytical way by assuming that a constant and uniform force F of finite magnitude acts continuously on the moving clock along the direction of its motion assumed to be rectilinear (in space). No inertial motion steps are considered. The rest clock is denoted as (1), the to and fro moving clock is (2), the inertial frame in which (1) is at rest in its origin and (2) is seen moving is I and, finally, the accelerated frame in which (2) is at rest in its origin and (1) moves forward and backward is A. We deal with the following questions: (1) What is the effect of the finite force acting on (2) on the proper time interval ⁽²⁾ measured by the two clocks when they reunite? Does a differential aging between the two clocks occur, as it happens when inertial motion and infinite values of the accelerating force is considered? The special theory of relativity is used in order to describe the hyperbolic (in spacetime) motion of (2) in the frame I. (II) Is this effect an absolute one, i.e., does the accelerated observer A comoving with (2) obtain the same results as that obtained by the observer in I, both qualitatively and quantitatively, as it is expected? We use the general theory of relativity in order to answer this question. It turns out that _I = _A for both the clocks, ⁽²⁾ does depend on g = F/m, and = ⁽²⁾/⁽¹⁾ = (1 – ²atanhj)/ < 1. In it ; = V/c and V is the velocity acquired by (2) when the force is inverted.     

The Relativity of Indeterminacy

A long-standing tradition, largely present in both the physical and the philosophical literature, regards the advent of (special) relativity—with its block-universe picture—as the failure of any indeterministic program in physics. On the contrary, in this paper, we note that upholding reasonable principles of finiteness of information hints at a picture of the physical world that should be both relativistic and indeterministic. We thus rebut the block-universe picture by assuming that fundamental indeterminacy itself should also be regarded as a relative property when considered in a relativistic scenario. We discuss the consequence that this view may have when correlated randomness is introduced, both in the classical case and in the quantum one.     

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.     

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.