The aim of this talk is to offer a critical overview of the current philosophical debate in the
philosophy of the future, stressing the close connections between physics and metaphysics. I will
discuss linear and branching-time models, underlining their relations with the debate on tense
realism, that is, the debate about whether the flow of time is a genuine feature of reality.
This talk is devoted to the main philosophical questions on time travel. It is usually held that the past
cannot the changed. But what about the future? I will argue that the answer crucially depends on
the hypothesis that reality contains a further temporal dimension, the so-called hypertime.
I survey briefly the main lessons about the nature of physical time from (special
and general) relativistic physics. They amount to a progressive dismissal of
commonsensical assumptions about time and a difficult learning process about what
are its real physical features. I then outline how the search for a quantum theory
of gravity and spacetime is challenging, even more, our understanding of...