Time/CPT symmetry is at heart of many models of physics, like unitary evolution in quantum mechanics, or Lagrangian formalism we use from classical mechanics, electromagnetism, up to general relativity and quantum field theories.
In theory we should be able to decompose any scenario (history of the Universe?) into ensemble of Feynman diagrams, apply CPT symmetry to all of them, getting CPT analogue of entire scenario (?)
There are many QM-based experiments which kind of use time symmetry (?), for example (slides with links):
Wheeler experiment, delayed choice quantum eraser (DCQE), “asking photons where they have been”, “photonic quantum routers”, Shor algorithm as more sophisticated DCQE.
However, this symmetry is quite nonintuitive, very difficult to really accept – mainly due to irreversibly, thermodynamical counterarguments (are there other reasons?)
Can e.g. this conflict with 2nd law of thermodynamics be resolved by just saying that symmetry of fundamental theories can be broken on the level of solution, like throwing a rock into symmetric lake surface?
Are all processes reversible? (e.g. wavefunction collapse, measurement)
So is our world time/CPT symmetric?
What does it mean?
Personally I interpret it that we live in 4D spacetime, (Einstein's) block universe/eternalism: only travel through some solution (history of the universe) already found in time/CPT symmetric way, like the least action principle or Feynman path/diagram ensemble - is it the proper way to understand this symmetry?
Are there other ways to interpret it?