NON-UNIQUE SIMULTANEITY ON ISOCHRONES OF THE ROTATING DISK: A TIMELOOP IN SPECIAL RELATIVITY?

摘要

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.