PT-Symmetry and the existence of a preferred reference frame

Question

(I am new to quantum field theory and I am still learning about symmetries and gauge theories, so please forgive this question if it is naïve, the formulation is not entirely rigorous in a mathematical sense.)

Relativity requires that there is no preferred reference frame of the universe, e.g. all inertial reference frames are equally valid. However, the universe is asymmetric under parity transformations, and seems to also be asymmetric under parity/time transformations, only under parity/time/charge transformations is the universe symmetric.

Does this imply that relativity's claim of the equality of reference frames is false? PT-asymmetry must be "with respect" to some absolute reference frame? Evidently, GR and QFT are not compatible at the moment, but does the standard model propose an absolute reference frame?

Answer 1

If P and T are good symmetries in any one specific reference frame then they are good symmetries in any frame in a Lorentz invariant theory.

Answer 2

Discrete symmetries such as parity are not discussed in special relativity. You are allowed to break the parity symmetry in special relativity (or any other discrete symmetry). Special relativity says that the laws of physics must be invariant under any continuous transformation of the coordinate systems. Parity and time reversal are not continuous.

That explains why in special (and even general) relativity we always study the transformation of this type.

$\frac{\partial x^\mu}{\partial x'^\nu}$

In another word, parity does not have a generator. Poincaré group are the symmetries of special relativity it includes 4 translations, 3 rotations and 3 boosts. as you can see parity and is not in the list.