Comparing age and ageing of two twins (theory of relativity)
Résumé
More than one century after his statement by Langevin in 1911, the twins paradox continues to generate heated debate in the physics community. If it is so, this is not because not having discovered errors in calculation or reasoning made by some rather than by others; nor because not having found discriminant experiments for assigning an age rather an other to such entity, different from its twin, as if this were to be imposed by reality. For us, this shows that the problem is still ill-posed. Certainly, with the theory of relativity, the idea of an absolute time which would be the same everywhere is abandoned; but, wanting to give it its own local value, wanting to attach it to any particle of matter, we continue to absolutise time. Time has no substantial value that would need nothing else to be defined. Its value is relational: time is set by an abstraction process, from the mutual relationships of objects to each others in space (otherwise why would it change with movement?). In this process, arbitrary conventions (left to free will) are still needed, and open to a plurality of interpretations. We focus on the conceptual level, and do not discuss in detail the equations provided by physicists. On simple examples, we illustrate the variety of differences in age (in one direction or the other, or the lack of difference, meeting with the different viewpoints encountered) that can be attributed to twins, depending on the agreements made to measure time, and on the physical model chosen. We show how equations of relativity at large are present in these situations. The equations cannot be used without an interpretation, that of the choice made for assessing time. This did not arise when time was defined by itself, without the need to choose (to show) a movement. One should distinguish between age (in relation to a simple reckoning) and aging (in relation to phenomena that must be discussed in each case).