Synchronized clocks and time on a rotating disc

TL;DR

This paper investigates the synchronization of clocks on a rotating disc, demonstrating that rotating clocks have the same period as stationary ones and exploring implications for simultaneity, invariance, and interference without relying on relativity theory.

Contribution

It provides a detailed analysis of clock synchronization and time measurement on a rotating disc, challenging assumptions from relativity and introducing a generalized Fermat's principle.

Findings

Rotating clocks have the same period as stationary clocks when measured externally.

Absolute simultaneity and invariance of flight times are established on a rotating disc.

The analysis is independent of relativity, relying on dimensional and logical arguments.

Abstract

Basic for the definition of 'time' are clocks operating under stationary conditions. The periods of two clocks can be compared with each other via two return experiments. The central clock mediates between the rotating and the inertial frame. Dimensional arguments and a detailed deduction show that the period of a rotating clock, measured externally in the inertial system, is the same as the internally defined one. There is a common synchron-time, especially 'absolute' simultaneity and invariance of flight times hold. This allows a new discussion of the twin problem. The invariance of a rotating circle allows the transference of the inertial polar coordinates to the rotating plane. The flight time of a light pulse obeys a generalized Fermat's principle. If rays are well defined, this time of flight determines the phase shift of the wave and the result of interference experiments. All general considerations and proofs are independent of the relativity theory, especially of the concept of local inertial systems and differential-geometrical techniques.