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Non-unique simultaneity on isochrones of the rotating disk: A timeloop in special relativity?
Abstract
Can several simultaneities exist simultaneously, as Einstein proposed in 1905? The example of a circular return, introduced in the same paper, produces an "aging paradox." The latter is a special case to the more general "paradox of clock synchronization" on the rotating disk, as Pellegrini and Swift called it, or synonymously "synchronization gap, " Cohen's term. The underlying mathematical fact is a non-transitivity of simultaneity implicit in special relativity and, more specifically, flat Minkowski space. Two neighboring twin clocks on a circular train are linked by three simultaneities at a time, one direct, the other two via the full circle in the right or the left direction, respectively. This helicoidal multi-simultaneity should be reflected in temporal recurrences of a characteristic distribution ("chirps"). A confirmed chirp will be a manifest timeloop. However, this prediction, made by a flat stationary spacetime, is contradicted by both general relativity and common sense. Thus, a clash between special relativity and both general relativity and reality may have been accomplished.
... The question of simultaneity gave place to many debates, and poses various problems and paradoxes in the framework of the standard relativity. One thinks of the twin paradox, but also of the problems of seemingly « multi-simultaneity » for rotating discs [12], to say nothing of the simple relativity of simultaneity. To be brief, let us say that one can resolve these difficulties while considering simply that time corresponds to the position of a moving point to which various observers in relative movement attribute the same movement characteristics. ...
... This is the case for example on earth with the apparent movement of the sun, if it is considered as the sole means to measure time. While using these results on a disc (and with light movement), one retrieves the gaps described by Rössler et al. [12]. Simply, one interprets them while saying that, after a turn around the disk, the gap is normal and can be ignored, or treated as a mere convention. ...
When we discover the world, neither space nor time are shown to us and named as such, and we have neither rulers nor clocks independent from it. Practically, it is within the phenomena that we choose what allows us to think and to build space (material points declared to be bound together in an immobile way), and what allows us to think and to reckon time (one or several material points declared to be mobile with respect to the first ones). These two immobility and mobility decrees cannot be stated the one without the other, and contain an irreducible part of limitation and of arbitrary. They manifest the fundamental link between the concepts of space and time, disclosing the essential meaning of the theory of relativity, which is not structurally linked to the properties of light. This theory is discussed and it is proposed to modify it and to extend it, in order to give a better account of the inseparable duality of time and space. This point of view may help solve the numerous problems which have been seen in relativity theory by various researchers. (to appear, Galilean Electrodynamics, 2005)
... De même, s'il va plus vite que la course du soleil, il arrive avant d'être parti ! 12 Mais il n'y a rien de bizarre concrètement. Des questions analogues à celles développées ici se retrouvent dans la discussion de la synchronisation des horloges sur des disques (apparition de « multi-simultanéités », voir par exemple les travaux de Rössler et al., 2002, discutés dans Guy, 2004). ...
discussion of the twins paradox (theory of relativity) - discussion du paradoxe des jumeaux (théorie de la relativité)
of a paper in process of writing
Nous devons renoncer à l'idée d'un temps autonome et séparé du monde, et l'envisager comme une façon indissociable de penser l'espace, comme la relativité nous y invite. Pour désigner cette association primaire de l'espace et du temps que les sciences cognitives nous révèlent aussi, nous utiliserons le mot « mouvement ». Le mouvement engendre d'un coup l'espace et le temps comme deux faces inséparables de la même substance : l'espace comme point de vue global, simultané, cardinal, immobile, réversible, et le temps comme point de vue analytique, séquentiel, ordinal, mobile, irréversible. Ce point de vue permet de relire certains aspects du fonctionnement de la physique et de commencer à soulager certaines difficultés qui s'y présentent.
The method of synchronizing clocks in accelerating frames through the use of electromagnetic signals can be tested experimentally by considering clocks placed in a set of synchronous satellites about Earth's equator. In synchronizing the clocks in a circuit about the equator, a large measurable time difference (9 μsec) is obtained between the two clocks in the same satellite from which the synchronization process is started and completed. Similarly, Earth's rotation may cause discrepancies in terrestrial time keeping.
It is shown that it is possible by using the lack of synchronization of clocks by light signal synchronization in circular orbits to test for the dragging of inertial frames in Einsteins's theory of general relativity. Possible experiments are discussed.
In 1908 Einstein and Laub used special relativity to predict that a moving magnetic dipole develops an electric dipole moment. The classic 1913 experiment of Wilson and Wilson on a polarizable, permeable medium rotating in an external magnetic field has long been cited as verifying this prediction. We argue that since the experiment involved rotation rather than uniform translation, it did not test special relativity. The analysis should properly be done in a rotating coordinate system. The field equations for a rotating object are well known and the analysis is straightforward, but the result disagrees with the Wilson experiment. After carefully examining all steps in the derivation, we conclude that either the experiment is wrong or the theoretical analysis must be modified. One possible resolution of the conflict is the hypothesis that the dielectric constant ε and permeability mu are well defined only in a frame in which the medium is at rest and time and space are orthogonal coordinates.
A consistent relativistic kinematic description of a rotating disk is given. The disk is described from the point of view of an inertial observer momentarily at rest relative to a point on the periphery of the disk, and as observed in a coordinate system SS' rotating with the disk. The kinematic resolution of Ehrenfest's paradox is stated. Also the following elements of the description are analyzed: (a) the transformation of time from an inertial system, where the axis of the disk is at rest, to SS' (b) the spatial geometry in SS' and (c) the velocity of light in SS'. The procedure for synchronization of the coordinate clocks on the disk is stated explicitly.