Time of Philosophers, Time of Physicists, Time of Mathematicians

Abstract
Is presentism or possibilism compatible with Relativity ? This question has been much debated since the argument first proposed by Rietdijk and Putnam. The goal of this text is to study the implications of both special and general relativity, and quantum mechanics, on presentism, possibilism, and eternalism. We put the emphasis on the implicit metaphysical preconceptions underlying each of these different approaches to the question of time. We show that there exists a unique version of presentism which is both non trivial, in the sense that it does not reduce the present to a 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 the past light cone of that point. However, this compatibility is achieved at the cost of a renouncement to the notion of an objective, observer-independent reality. We also argue that no non-trivial version of presentism survives in general relativity, although, if some mechanism forbids the existence of closed timelike curves, then precisely one version of possibilism does survive. We remark that the quoted physical theories force the presentist/possibilist's view of reality to shrink and break up, whereas the eternalist, on the contrary, is forced to grant the status of reality to more and 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 propose him a "idealist deal": to accept a mathematical ontology in exchange for the assurance of surviving any physical theory.
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