Time 'betwins'

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” (GB01), 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. Work presented at the “1rst International Conference on the Ontology of Spacetime”, 11–14 May 2004, University of Concordia, Montréal (QC), Canada. PREPRINT INLN #2004/11 PACS numbers: 01.70.+W Philosophy of science, 02.40.-k Geometry, differential geometry, and topology, 02.40.Hw Classical differential geometry, 03.30.+p Special relativity, 04.20.-q Classical general relativity, 04.20.Cv Fundamental problems and general formalism, 04.90.+e Other topics in general relativity and gravitation. I. TRIANGULAR DIAGRAMS Very often, discussions on the Langevin twins paradox are based on a “triangular” diagram, and we would like, first, just to recall a little problem of distance measurement, evaluation and/or conception in spacetime, which appeared in one of the lightest “triangle” approach given by H. Bondi (Bon57) and in fact historically due to Lord Halsbury (see H. Dingle’s work in (Cha93)) and involving three unaccelerated observers. Bondi considered diagrams (refered as the Fig. 2 and Fig. 3 in his 1957 paper) that can be assembled in a unique diagram as follows (Figure 1.) with the so-called apex at the crossing point Y: