  From the Physics point of view, time is now best described through General
Relativity, as part of space-time which is a dynamical object encoding gravity.
Time possesses also some intrinsic irreversibility due to thermodynamics,
quantum mechanical effects... This irreversibility can look puzzling since
time-like loops (and hence time machines) can appear in General Relativity (for
example in the Goedel universe, a solution of Einstein's equations). We take
this apparent discrepancy as a warning bell pointing to us that time as we
understand it, might not be fundamental and that whatever theory, lying beyond
General Relativity, may not include time as we know it as a fundamental
structure. We propose therefore, following the philosophy of analog models of
gravity, that time and gravity might not be fundamental per se, but only
emergent features. We illustrate our proposal using a toy-model where we show
how the Lorentzian signature and Nordstroem gravity (a diffeomorphisms
invariant scalar gravity theory) can emerge from a timeless non-dynamical
space.
