The Minkowski metric is time reversal symmetric. The bigger question in particle physics is "what are the symmetries of the action?"
It's not time reversal symmetric, but it's probably [CPT][1] (charge-parity-time reversal) symmetric.
If you forget about quantum field theory and consider classical physics in Minkowski space (or Cartesian space), then t -> -t indeed doesn't change the physical laws. You could tell the two apart, though, provided that the system is far from thermal equilibrium (e.g. "why is this egg uncracking spontaneously?").
It's not time reversal symmetric, but it's probably [CPT][1] (charge-parity-time reversal) symmetric.
If you forget about quantum field theory and consider classical physics in Minkowski space (or Cartesian space), then t -> -t indeed doesn't change the physical laws. You could tell the two apart, though, provided that the system is far from thermal equilibrium (e.g. "why is this egg uncracking spontaneously?").
[1]: https://en.wikipedia.org/wiki/CPT_symmetry