Hm, I’m talking about time reversible physical laws, not necessarily time symmetric physical laws, so my question is do you always get time-symmetric physical laws that are symmetric for any T, out of time-reversible physical laws?
See also this question in another comment:
For the physics case, I’m asking essentially whether there can be a physical rule (at least in a hypothetical universe different than our real one) that is time-reversible, but not having time shift symmetry, and thus not implying conservation of energy, or if time-reversible physical rules always imply time shift symmetry/time symmetry.
Another way to say it is I’m asking if there are hypothetical time-reversible rules that don’t have the first law of conservation of energy due to not implying time symmetry for any T.
I have edited the question to clarify what exactly I was asking.
Hm, I’m talking about time reversible physical laws, not necessarily time symmetric physical laws, so my question is do you always get time-symmetric physical laws that are symmetric for any T, out of time-reversible physical laws?
See also this question in another comment:
I have edited the question to clarify what exactly I was asking.