On Local and Global Measurements of the Speed of Light on Rotating Platforms

The paper shows that, conceptually and operationally, the speed of light measured locally in the inertial comoving frame of a point on the rim of a rotating disk is different from the one measured globally for a round trip along the rim, obtained dividing the length of the rim (as measured in the relative space of the disk) by the time of flight of the light beam (as measured by a clock at rest on the disk). As a consequence, contrary to some recent claims, the anisotropy found in the global value, obtained by the above procedure, in no way conflicts with the local isotropy, and the internal consistency of the special relativity theory remains unchallenged.     

On the Conventionality of Simultaneity

Starting from the experimental fact that light propagates over a closed path at speed c (L/c law), we show to what extent the isotropy of the speed of light can be considered a matter of convention. We prove the consistence of anisotropic and inhomogeneous conventions, limiting the allowed possibilities. All conventions lead to the same physical theory even if its formulation can change in form. The mathematics involved is that of gauge theories and the choice of a simultaneity convention is interpreted as a choice of the gauge. Moreover, we prove that a Euclidean space where the L/c law holds, gives rise to a spacetime with Minkowskian causal structure, and we exploit the consequences for the causal approach to the conventionality of simultaneity.     

Universal One-Way Light Speed from a Universal Light Speed Over Closed Paths

This paper gives two complete and elementary proofs that if the speed of light over closed paths has a universal value c, then it is possible to synchronize clocks in such a way that the one-way speed of light is c. The first proof is an elementary version of a recent proof. The second provides high precision experimental evidence that it is possible to synchronize clocks in such a way that the one-way speed of light has a universal value. We also discuss an old incomplete proof by Weyl which is important from an historical perspective.     

Relativistic Sagnac Effect and Ehrenfest Paradox

There seems to exist a dilemma in the literature as to the correct relativistic formula for the Sagnac phase-shift. The paper addresses this issue in the light of a novel, kinematically equivalent linear Sagnac-type thought experiment, which provides a vantage point from which the effect of rotation in the usual Sagnac effect can be analyzed. The question is shown to be related to the so-called rotating disc problem known as the Ehrenfest paradox. The relativistic formula for the Sagnac phase-shift seems to depend on the way the paradox is resolved. Kinematic resolution of the Ehrenfest paradox proposed by some authors predicts the usually quoted formula for the Sagnac delay but the resolution itself is shown to be based upon some implicit assumptions regarding the behaviour of solid bodies under acceleration. In order to have a greater insight into the problem, a second version of the thought experiment involving linear motion of a special type of a non-rigid frame of reference is discussed. It is shown by analogy that the usually quoted special relativistic formula for the Sagnac delay follows, provided the material of the disc matches the special type.     

Locality Hypothesis and the Speed of Light

The locality hypothesis is generally considered necessary for the study of the kinematics of non-inertial systems in special relativity. In this paper we discuss this hypothesis, showing the necessity of an improvement, in order to get a more clear understanding of the various concepts involved, like coordinate velocity and standard velocity of light. Concrete examples are shown, where these concepts are discussed.     

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.     

On attempts to rescue the conventionality thesis of distant simultaneity in str

Recently, some conventionalists have tried to rescue the conventionality of distant simultaneity by introducing a spatially dependent (x,y,z), where {1,2,3}. In this paper, we show that this attempt fails by providing a detailed analysis of the coordinate independent and non-conventional procedure for directly measuring the metricd _M ² on eventspace with respect to a physical radar coordinate system. The measuredd _M ² in turn provides the empirical basis for uniquely determining the hyperplanes of space for a given inertial observer in a way that makes absolutely no reference whatsoever to any kind of synchrony, whether spatially dependent or not except for the sole purpose of assigning physical coordinates to events.     

The Principle of Equivalence and the Twin Paradox

No Heading The canonical twin paradox is explained by making a correct use of the principle of equivalence. The role of the principle of equivalence is to provide a physical agent i.e gravity which can supply the required extra aging to the rocket-bound sibling during its acceleration phase through a gravitational time-offset effect. We follow an approach where a novel variation on the twin paradox is used to connect gravity with the desynchronization in the clocks of two spatially distant, identically accelerated observers. It is shown that this approach removes certain drawbacks of an earlier effort which claims to exploit the equivalence principle in explaining the differential aging in the paradox. * Author to whom all correspondences should be made.     

New Perspectives on the Relativistically Rotating Disk and Non-Time-Orthogonal Reference Frames

The rotating disk problem is analyzed on the premise that proper interpretation of experimental evidence leads to the conclusion that the postulates upon which relativity theory is based, particularly the invariance of the speed of light, are not applicable to rotating frames. Different postulates based on the Sagnac experiment are proposed, and from these postulates a new relativistic theory of rotating frames is developed following steps similar to those initially followed by Einstein for rectilinear motion. The resulting theory agrees with all experiments, resolves problems with the traditional approach to the rotating disk, and exhibits both traditionally relativistic and non-relativistic characteristics. Of particular note, no Lorentz contraction exists on the rotating disk circumference, and the disk surface, contrary to the assertions of Einstein and others, is found to be Riemann flat. The variable speed of light found in the Sagnac experiment is then shown to be characteristic of non-time-orthogonal reference frames, of which the rotating frame is one. In addition, the widely accepted postulate for the equivalence of inertial and non-inertial standard rods with zero relative velocity, used liberally in prior rotating disk analyses, is shown to be invalid for such frames. Further, the new theory stands alone in correctly predicting what was heretofore considered a spurious non-null effect on the order of 10^–13 found by Brillet and Hall in the most accurate Michelson-Morley type test to date. The presentation is simple and pedagogic in order to make it accessible to the non-specialist.     

基于狭义相对论的同时性对长度收缩佯谬的认识

利用狭义相对论对同时性的理解,指出了关于一种长度收缩佯谬解释的不妥之处,并解释了改进后的关于长度收缩佯谬的提法,证明了在不同参照系上的观测者观测所得到的结论相同.     

Noninvariant one-way speed of light and locally equivalent reference frames

We consider an isotropical inertial reference frame (“stationary”) and in it a uniformly rotating circular platform of radiusR. The velocity of light relative to the rim of the platform is calculated and found to have values necessarily different fromc. This remains the same ifR is increased but the peripheral velocity is kept constant. Since by so doing any small piece of the circumference can be considered better and better at rest in a (“moving”) inertial system, the velocity of light relative to this system can be deduced. Noninvariant values are obtained and shown to coincide with the predictions of our recently published “inertial transformations”.     

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.     

Reference Frames and Rigid Motions in Relativity: Applications

The concept of rigid reference frame and of constricted spatial metric, given in the previous work [Class. Quantum Grav. 21, 3067 (2004)] are here applied to some specific space-times: in particular, the rigid rotating disc with constant angular velocity in Minkowski space-time is analyzed, a new approach to the Ehrenfest paradox is given as well as a new explanation of the Sagnac effect. Finally the anisotropy of the speed of light and its measurable consequences in a reference frame co-moving with the Earth are discussed.     

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.     

Derivation of the General Case Sagnac Result Using Non-Time-Orthogonal Analysis

The Sagnac time delay and fringe shift dependency on angular velocity and enclosed area are derived from the rotating reference frame using non-time-orthogonal (NTO) tensor analysis. NTO analysis differs from traditional approaches by postulating that the continuous and single valued nature of physical time constrains simultaneity in a rotating frame to be unique (and thus not a matter of convention.) This implies anisotropy in the physical, local speed of light and invalidity of the hypothesis of locality for NTO frames. The Sagnac relationship for the most general case, in which the area enclosed is not circular and does not have the axis of rotation passing through its center, is determined.     

基于同时的相对性对钟慢尺缩效应的再认识

同时的相对性、钟慢效应和尺缩效应是狭义相对论时空观的主要内容.鉴于同时性是时空测量的基础,本文从同时的相对性出发详述了对钟慢效应和尺缩效应的再认识:钟慢效应是运动时钟走时率变慢和校表问题的综合表现,其实质是同时的相对性在时间量度上的直接反映;尺缩效应的实质是同时的相对性在空间量度上的反映,也是不同观测者对同一客观事实的不同时空描述.     

Time on a rotating platform

Traditional clock synchronisation on a rotating platform is shown to be incompatible with the experimentally established transformation of time. The latter transformation leads directly to solve this problem through noninvariant one-way speed of light. The conventionality of some features of relativity theory allows full compatibility with existing experimental evidence.     

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.     

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.