Do metric standards contract?

We address the question: By what class of force-application programs must a meter stick initially at rest in an inertial frame be moved in order to transfer it to a relatively moving inertial frame without altering the internal energy state of the structure in the process? Such stress-free transfer of a metric standard is essential for moving-axis calibration (a neglected art in established relativity theory). In order to deduce the answer by reasonings appropriate to kinematics, it proves necessary to make an extension of the relativity principle to rectilinear (irrotational) accelerated motions, and to enhance the kinematic motion group accordingly. Since the physical motion groups differ, the answers we obtain to this and to the title question differ from those of special relativity. Our alternative kinematics thus leads to discrepancies that should be measurable atO(v ²/c ²).     

Is quantum theory compatible with special relativity?

How a proposed quantum nonlocal phenomenon could be incompatible with the requirements of special relativity is studied. To show this, the least set of assumptions about the formalism and the interpretation of non-relativistic quantum theory is considered. Then, without any reference to the collapse assumption or any other stochastic processes, an experiment is proposed, involving two quantum systems, that interacted at an arbitrary time, with results which seem to be in conflict with requirements of special relativity.     

New level of relativity

In their origins Einstein’s studies of relativity principles called into question the validity of important assumptions that had previously been made in formulating physical theories, assumptions made without investigation into alternatives. Examples of this include notions of absolute time and space, flat Euclidean geometry, and trivial topology. In this paper, we review an intermediate niche, differentiable (smooth) structure, which must be defined between topology and geometry. We now know that this choice need not be trivial. Just as it seemed for centuries to be obvious that space should be flat, so it would seem until recently that standard, trivial, smoothness for spacetime is the only choice. We now know that this is not true. In this paper we review these topics in the light of very surprising and often counter-intuitive mathematical discoveries of the last 20 years or so. Since our regions of observability are necessarily constrained we do not have any a priori justification for extending standard smoothness globally. This opens up the possibility of non-standard extension of solutions to field equations to exotically smooth regions, leading to examples such as exotic black holes and exotic cosmological models.     

Neutrino superluminality without Cherenkov-like processes in Finslerian special relativity

Recently, Cohen and Glashow [A.G. Cohen, S.L. Glashow, Phys. Rev. Lett. 107 (2011) 181803] pointed out that the superluminal neutrinos reported by the OPERA would lose their energy rapidly via the Cherenkov-like process. The Cherenkov-like process for the superluminal particles would be forbidden if the principle of special relativity holds in any frame instead violated with a preferred frame. We have proposed that the Finslerian special relativity could account for the data of the neutrino superluminality (arXiv:1110.6673 [hep-ph]). The Finslerian special relativity preserves the principle of special relativity and involves a preferred direction while consists with the causality. In this Letter, we prove that the energy–momentum conservation is preserved and the energy–momentum is well defined in Finslerian special relativity. The Cherenkov-like process is forbidden in the Finslerian special relativity. Thus, the superluminal neutrinos would not lose energy in their distant propagation.     

Conventionality of Simultaneity and the Tippe Top Paradox in Relativity

In this paper we critically examine a recently posed paradox (tippe top paradox in relativity) and its suggested resolution. A tippe top when spun on a table, tips over after a few rotations and eventually stands spinning on its stem. The ability of the top to demonstrate this charming feat depends on its geometry (all tops are not tippe tops). To a rocket-bound observer the top geometry should change because of the Lorentz contraction. This gives rise to the possibility that for a sufficiently fast observer the geometry of the top may get altered to such an extent that the top may not tip over! This is certainly paradoxical since a mere change of the observer cannot alter the fact that the top tips over on the table. In an effort to resolve the issue the authors of the paradox compare the equations of motion of the particles of the top from the perspective of the inertial frames of the rocket and the table and observe among other things that (1) the relativity of simultaneity plays an essential role in resolving the paradox and (2) the puzzle in some way is connected with one of the corrolaries of special relativity that the notion of rigidity is inconsistent with the theory. We show here that the question of the incompatibility of the notion of rigidity with special relativity has nothing to do with the current paradox and the role of the lack of synchronization of clocks in the context of the paradox is grossly over-emphasized. The conventionality of simultaneity of special relativity and the notion of the standard (Einstein) synchrony in the Galilean world have been used to throw light on some subtle issues concerning the paradox.     

P. A. M. Dirac und die Begründung der relativistischen Quantentheorie

P. A. M. Dirac and the Foundation of Relativistic Quantum Theory The unification of special relativity and quantum mechanics led to a new understanding of vacuum, declared the spin. A thorough analysis between both fundamental theories, however, shows inconsistencies too, unsolvable in the framework of quantum theory and theory of relativity. The are connected with the question: “Why is cosmos so big and are atoms so small?”.     

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.     

What if there are superluminal signals?

Recent experiments with microwaves indicate the existence of signals travelling faster than the vacuum velocity of light. At first glance these signals lead to paradoxical situations which seem to be in conflict with special relativity. We show that the arguments which lead to this contradiction presuppose that superluminal signals are not generally available and that the space-time geometry must be established by means of light rays. Hence we argue that superluminal signals will not necessarily invalidate special relativity. Received 1 July 1999     

“Almost” general relativity

We exhibit theories of gravitation leading to the same set of solutions with algebraically special Ricci tensor as Einstein's equations. Their sets of solutions with algebraically general Ricci tensor differ from general relativity. It will be difficult to empirically distinguish these theories from general relativity.     

The foundations of relativity

In a previous paper a stochastic foundation was proposed for microphysics: the nonrelativistic and relativistic domains were shown to be connected with two different approximations of diffusion theory; the relativistic features (Lorentz contraction for the coordinate standard deviation, covariant diffusion equation) were not derived from the relativistic formalism introduced at the start, but emerged from diffusion theory itself. In the present paper these results are given a new presentation, which aims at elucidating not the foundations of quantum mechanics, but those of relativity. This leads to a discussion of points still controversial in the interpretation of relativity. In particular two problems appear in a new light: the character of time and length alterations, and the privileged role of the velocityc. Besides, the question of a possible limitation of relativity (and more generally of the laws of mechanics) in the domain of particle substructure is raised and supported by exemples drawn from the hydrodynamical model of a spinned particle. Suggestions are presented for the possibility of a deeper conceptual unification of special and general relativity.     

相对性原理及其对自然界定律的协变性要求--机械能守恒定律协变性疑难的解答

阐明狭义相对性原理的准确含义,批出它并不要求自然界每条定律都单独协变,但要求每条定律至少属于一个协变集合,给出最小协变集的求法。表明机械能守恒定律满足狭义相对性原理及其对自然界定律的协变性要求,还指出一切社会科学定律也都满足狭义相对性原理。     

A Nontemporal Probabilistic Approach to Special and General Relativity

We introduce a discrete probabilistic model of motion in special and general relativity that is shown to be compatible with the standard model in the statistical limit.     

Cayley parametrization of semisimple lie groups and its application to physical laws in a (3+1)-dimensional cubic lattice

The assumption of a discrete space-time is expressed mathematically by restricting the space-time variables to the field of integer numbers, and by restricting to the field of rational numbers the functions describing the laws of motion. This rational character must be preserved under the transformations connecting different systems of reference. The Cayley parametrization of semisimple Lie groups, and in particular of the Lorentz group, satisfies this condition if we require these parameters to take only integer values. The rational points of the most frequently used transcendental functions are obtained with the help of the integer complex and hypercomplex numbers. Some applications are made concerning the laws of motion in special relativity defined over a (3+1)-dimensional cubic lattice.     

Spacetime Embedding Diagrams for Black Holes

We show that the 1 + 1 dimensional reduction(i.e., the radial plane) of the Kruskal black hole canbe embedded in 2 + 1 Minkowski spacetime and discuss howfeatures of this spacetime can be seen from theembedding diagram. The purpose of this work iseducational: The associated embedding diagrams may beuseful for explaining aspects of black holes to studentswho are familiar with special relativity, but notgeneral relativity.     

Notes on relativistic equations of spin motion

Grounds and applications of Bargmann-Michel-Telegdi equations for the precession of the polarization vector of relativistic particles are considered. A critical question in the discussion is the orientation of the rest frame reference vectors. Møller reference frames which keep constant the mutual orientation of the two infinitely close in time rest frames are shown to have a special role. The generally covariant form of the equations is discussed. The assertion that the principle of relativity is violated in the phenomenon of spin precession is proved to be untrue.     

Classification of Teleparallel Homothetic Vector Fields in Cylindrically Symmetric Static Space-Times in Teleparallel Theory ofGravitation

In this paper we classify cylindrically symmetric static space-timesaccording to their teleparallel homothetic vector fields using directintegration technique. It turns out that the dimensions of the teleparallelhomothetic vector fields are 4, 5, 7 or 11, which are the same in numbers asin general relativity. In case of 4, 5 or 7 proper teleparallel homotheticvector fields exist for the special choice to the space-times. In the caseof 11 teleparallel homothetic vector fields the space-time becomes Minkowskiwith all the zero torsion components. Teleparallel homothetic vector fieldsin this case are exactly the same as in general relativity. It is importantto note that this classification also covers the plane symmetric static space-times.     

Mathematical Structures of Space-Time

At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general relativity, and the conditions for their existence are discussed. The causality conditions are studied through an analysis of strong causality, stable causality and global hyperbolicity. In looking at the asymptotic structure of space-time, we focus on the asymptotic symmetry group of Bondi, Metzner and Sachs, and the b-boundary construction of Schmidt. The Hamiltonian structure of space-time is also analyzed, with emphasis on Ashtekar's spinorial variables. Finally, the question of a rigorous theory of singularities in space-times with torsion is addressed, describing in detail recent work by the author. We define geodesics as curves whose tangent vector moves by parallel transport. This is different from what other authors do, because their definition of geodesics only involves the Christofel symbols, though studying theories with torsion. We then prove how to extend Hawking's singularity theorem without causality assumptions to the space-time of the ECSK theory. This is achieved studying the generalized Raychauduri equation in the ECSK theory, the conditions for the existence of conjugate points and properties of maximal timelike geodesics. Our result can also be interpreted as a no-singularity theorem if the torsion tensor does not obey some additional conditions. Namely, it seems that the occurrence of singularities in closed cosmological models based on the ECSK theory is less generic than in general relativity. Our work is to be compared with important previous papers. There are some relevant differences, because we rely on a different definition of geodesics, we keep the field equations of the ECSK theory in their original form rather than casting them in a form similar to general relativity with a modified energy-momentum tensor, and we emphasize the role played by the full extrinsic curvature tensor and by the variation formulae.     

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).     

McGuire-Ruffini solution in new general relativity

We obtain a solution of new general relativity from a solution of Einstein's general relativity which includes many known solutions, such as Kerr-Newman-Kasuya, Kerr-Newman, Kerr, and NUT, as special cases.