  Is presentism 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 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
backward 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, except if some mechanism forbids the existence of closed
timelike curves, in which case precisely one version of possibilism does
survive. We remark that the above 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 offer to him an "idealist deal": to accept a mathematical ontology in
exchange for the assurance of surviving any physical theory.
