# Clarification on CPT symmetry

CPT symmetry, as I understand it, holds that if all charge, parity, and time were reversed (a mirror-image antimatter time-reversed universe), that universe would behave identically to our current universe. Or the laws would still be valid, that is, the same laws that are accurate for describing and predicting our universe would be accurate for describing and predicting the CPT-reversed one.

Assuming that's correct (enough), my question is, does the above statement mean that our universe and a CPT-reversed one are identical? Or instead does it mean that the two simply behave and evolve according to the same laws? The sillier way of asking this is something like, if you could take an electron and CPT-reverse it in a lab, is it now identical to the original electron, at least in its behavior?

I'm not a physicist by training, so thanks in advance for any answers or clarifications!

When we talk about CPT symmetry we tend to mean that the Standard Model is CPT symmetric, though the theorem applies to any quantum field theory that is Lorentz invariant and local. Suppose we define an operator $\text{CPT}$ that carries out the CPT transformation then the states of our theory, i.e. the states of our quantum fields, are left invariant by the transformation:
$$\text{CPT}|\Psi\rangle = A|\Psi\rangle$$
where $A$ is just a constant. Or put another way, the states of our theory are eigenfunctions of the $\text{CPT}$ operator.
• And $A$ is state dependent, or is it global? I'm thinking parity, for instance $A=\mp 1$ for (pseudo)vectors--so it depends on the state, and as long as they don't mix (e.g. you beta decay momentum is aligned with your nuclear spin) you're parity invariant. – JEB Mar 6 '18 at 16:56