Why is it important that the combination of charge, parity & time reversal symmetry not violated?

Question

If looking for more particles or decays that violate CP symmetry can explain why there is so few antimatter in the known universe, I guess finding things that violate CPT symmetry might helps clear up some mystery about the universe. However all physics textbook insist that cpt symmetry must be conserved, why so?

Answer 1

I would advise you to read carefully this link. As a summary:

1) CPT invariance is an experimental observation, that means all data fitted by the standard model of particle physics have CPT invariance. Thus at the moment it is a law, i.e.axiomatic, as much as for classical gravitation Newtons law is observational and axiomatic.

2) It has been shown that if CPT is violated Lorenz invariance is violated, and there are no experimental observation supporting this, and innumerable measurements that validate Lorenz invariance.

Georg Ludens, Wolfgang Pauli and Julian Schwinger independently showed that invariance under Lorentz transformations implies CPT invariance.

Answer 2

All Lorentz invariant theories are CPT invariant. Hence if you violate CPT invariance, you violate Lorentz invariance, and that's a big no-no.