Time 'betwins'

TL;DR

This paper proposes a novel resolution to the Langevin Twins paradox using a new Punctual Equivalence Principle within scale gravity, linking time discrepancies to thermodynamic laws.

Contribution

It introduces the Punctual Equivalence Principle and applies scale gravity to resolve the Twins paradox, highlighting conformal geometry's role in proper time determinism.

Findings

Resolution of the Twins paradox without triangular spacetime diagrams

Identification of conditions for determinism and under-determinism of proper times

Potential connection between time discrepancies and thermodynamic laws

Abstract

Discussions on the Langevin Twins 'paradox' are most often based on a "triangular" diagram which outlines the twins spacetime travels. It won't be our way, avoiding what we think to be a problem at the basis of numerous controversies. Our approach relies on a fundamentally different Equivalence Principle, namely the so-called "Punctual Equivalence Principle", from which we think that a very conformal aspect proceeds. We present a resolution of this paradox in the framework of the so-called "scale gravity". This resolution hinges on a clear determinism of the Twins proper times, in some definite situations, and a fundamental under-determinism in some other particular ones, the physical discrimination of which being achieved out of a precise mathematical description of conformal geometry. Moreover, we find that the time discrepancy between the twins, could somehow be at the root expression of the second fundamental law of thermodynamics.