CPT Violation and Energy Conservation: Explained!

[Silviu]

Hello! I read that natural processes are invariant under CPT (based on some theorem) and that CP violation was observed experimentally. So this would mean that there are processes that are violated under time reversal. However, based on Noether theorem, this would mean that the energy is not conserved in these kind of processes, but I read many times that it has been no process in which the conservation of energy to be violated. Can someone explain this to me and tell me where is the flaw in my logic? Thank you!

 

[haushofer]

Time reversal is a discrete transformation while noether' s theorem is about continuous transformations. How would you derive the breakdown of energy conservation from T-variance?

 

[no-ir]

See: https://www.physicsforums.com/threads/noether-theorem-cp-violation-energy-is-not-conserved.303056/. Basically, T is the discrete time-inversion symmetry $t \rightarrow -t$, whereas Noether's theorem applies only to continuous symmetries, like the time-translation symmetry $t \rightarrow t + \epsilon$ that gives energy conservation. Breaking T (i.e. breaking the isotropy of time) does imply breaking time-translation (i.e. the homogeneity of time), and it is the latter that gives energy conservation, not the former.

Of course, in general relativity energy conservation is more complicated and not necessarily well-defined, and in cosmological scenarios with the expansion of the universe time-translational symmetry, and thus energy conservation, are also violated. See:
https://physics.stackexchange.com/questions/74266/conservation-of-energy-and-cp-violation,
https://en.wikipedia.org/wiki/Conservation_of_energy#Relativity, and
https://en.wikipedia.org/wiki/ADM_formalism#ADM_energy_and_mass.