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.     

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.     

Euclidean Special Relativity

New four coordinates are introduced which are related to the usual space-time coordinates. For these coordinates, the Euclidean four-dimensional length squared is equal to the interval squared of the Minkowski space. The Lorentz transformation, for the new coordinates, becomes an SO(4) rotation. New scalars (invariants) are derived. A second approach to the Lorentz transformation is presented. A mixed space is generated by interchanging the notion of time and proper time in inertial frames. Within this approach the Lorentz transformation is a 4-dimensional rotation in an Euclidean space, leading to new possibilities and applications.     

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.     

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.     

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.     

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).     

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.     

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.     

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.     

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.     

On the Principle of Relativity

In a recent article [1] M.A. Oliver argues there is a conflict between Einstein's Special Theory of Relativity (STR) and Cosmology. In ascertaining this conflict (see below), Oliver finds allies in Bergmann [2] and Bondi [3]. To resolve this conflict, he proposes to restore the classical (mechanical) concepts of space and time [1, p.666] and an absolute rest-frame. I shall devote a few words (1) to the Principle of Relativity and (2) to the notion of cosmic time in cosmology; this enables me (3) to argue that the alleged conflict between STR and Cosmology is based on a misunderstanding of the Principle of Relativity. (4) Finally I take a critical look at Oliver's allies.     

The End Results of General Relativity Theory Via Just Energy Conservation and Quantum Mechanics

Herein we present a whole new approach that leads to the end results of the general theory of relativity via just the law of conservation of energy (broadened to embody the mass and energy equivalence of the special theory of relativity) and quantum mechanics. We start with the following postulate. Postulate: The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this, as much as its binding energy vis-á-vis the gravitational field of concern.     

A Possible Modification of Einstein's Theory of General Relativity

This article suggests a new metric theory of gravitation, in which metric field is determined not only by matter and nongravitational field but also by vector graviton field, and in principle there is no need to introduce the Einstein's tensor. In order to satisfy automatically the geodesic postulate, an additional coordinate condition is needed.For the spherically symmetric static field, it leads us to quite different conclusions from those of Einstein's general relativity in the interior region of the surface of infinite redshift. Accurate to the first order of GM/r, it obtains the same results about the four experimental tests of general relativity.     

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.     

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.     

Derivation of Dirac's Equation from the Evans Wave Equation

The Evans wave equation [1] of general relativity is expressed in spinor form, thus producing the Dirac equation in general relativity. The Dirac equation in special relativity is recovered in the limit of Euclidean or flat spacetime. By deriving the Dirac equation from the Evans equation it is demonstrated that the former originates in a novel metric compatibility condition, a geometrical constraint on the metric vector qused to define the Einstein metric tensor. Contrary to some claims by Ryder, it is shown that the Dirac equation cannot be deduced unequivocally from a Lorentz boost in special relativity. It is shown that the usually accepted method in Clifford algebra and special relativity of equating the outer product of two Pauli spinors to a three-vector in the Pauli basis leads to the paradoxical result X = Y = Z = 0. The method devised in this paper for deriving the Dirac equation from the Evans equation does not use this paradoxical result.