Time of Philosophers, Time of Physicists, Time of Mathematicians

摘要

Is presentism compatible with relativity ? This question has been muchdebated since the argument first proposed by Rietdijk and Putnam. The goal ofthis text is to study the implications of relativity and quantum mechanics onpresentism, possibilism, and eternalism. We put the emphasis on the implicitmetaphysical preconceptions underlying each of these different approaches tothe question of time. We show that there exists a unique version of presentismwhich is both non-trivial, in the sense that it does not reduce the present toa unique event, and compatible with special relativity and quantum mechanics:the one in which the present of an observer at a point is identified with thebackward light cone of that point. However, this compatibility is achieved atthe cost of a renouncement to the notion of an objective, observer-independentreality. We also argue that no non-trivial version of presentism survives ingeneral relativity, except if some mechanism forbids the existence of closedtimelike curves, in which case precisely one version of possibilism doessurvive. We remark that the above physical theories force thepresentist/possibilist's view of reality to shrink and break up, whereas theeternalist, on the contrary, is forced to grant the status of reality to moreand more entities. Finally, we identify mathematics as the "deus ex machina"allowing the eternalist to unify his vision of reality into a coherent whole,and offer to him an "idealist deal": to accept a mathematical ontology inexchange for the assurance of surviving any physical theory.