Conformal proper times according to the Woodhouse causal axiomatics of relativistic spacetimes

TL;DR

This paper develops a conformal proper time framework based on Woodhouse causal axiomatics, introducing an extra variable and conformal structures to justify the chronometric hypothesis and address clock paradoxes in relativistic spacetimes.

Contribution

It introduces a novel conformal proper time concept derived from Woodhouse axioms, incorporating an extra variable and path-dependent scale factors to explain differential aging.

Findings

Proper times originate from conformal structures and projective structures assigned to particles.

Proper time parameterizations depend on physical process changes and conformal scale factors.

The approach extends beyond Weyl geometries, addressing clock effects more comprehensively.

Abstract

On the basis of the Woodhouse causal axiomatics, we show that conformal proper times and an extra variable in addition to those of space and time, precisely and physically identified from experimental examples, together give a physical justification for the `chronometric hypothesis' of general relativity. Indeed, we show that, with a lack of these latter two ingredients, no clock paradox solution exists in which the clock and message functions are solely at the origin of the asymmetry. These proper times originate from a given conformal structure of the spacetime when ascribing different compatible projective structures to each Woodhouse particle, and then, each defines a specific Weylian sheaf structure. In addition, the proper time parameterizations, as two point functions, cannot be defined irrespective of the processes in the relative changes of physical characteristics. These processes are included via path-dependent conformal scale factors, which act like sockets for any kind of physical interaction and also represent the values of the variable associated with the extra dimension. As such, the differential aging differs far beyond the first and second clock effects in Weyl geometries, with the latter finally appearing to not be suitable.