Clocks' synchronization without round-trip conditions

TL;DR

This paper introduces an improved clock synchronization method that removes the need for round-trip conditions, applicable to rotating frames and potentially impactful in physics, computer science, and communication theory.

Contribution

It presents a novel synchronization approach that overcomes the limitations of Poincaré-Einstein's method by averaging Sagnac holonomy, applicable to any measure on space.

Findings

The new method works in rotating frames.

It generalizes synchronization beyond irrotational frames.

It uses Alexander cohomology theory concepts.

Abstract

Poincar\'e-Einstein's synchronization convention is transitive, and thus leads to a consistent synchronization, only if some form of round-trip property is satisfied. An improved version is given here which does not suffer from this limitation and which therefore may find application in physics, computer science and communication theory. As for the application to physics, the round-trip condition required by the Poincar\'e-Einstein's synchronization convention corresponds to a vanishing Sagnac effect and thus to the selection of an irrotational frame. The corrected method applies also to rotating frames and shows that there is a consistent synchronization for every given measure on space. The correction to Poincar\'e-Einstein's amounts to an average of the Sagnac holonomy over all the possible triangular paths. The mathematics used is reminiscent of Alexander cohomology theory.