You are confusing separate operators and introducing your own notation, and it has led to comments six deep because you refuse to distinguish T from CPT symmetry. Moreover, it leads to you contradicting yourself: In one paragraph you agree that T is not separately a good symmetry, and then in the next you say that you “prefer to describe [physics] in terms of simple T symmetry”.
Paragraph 1 was me trying to “phrase this in language you are more likely to understand”
Paragraph 2 was me using the language I would normally use.
So: that was not a case of me “contradicting” myself at all.
If you simply reverse T, and the whole universe starts to run backwards, then it makes an awful lot of sense to call the universe “T symmetric”, IMHO, conventional terminology or no. Then it is time to start saying “T”—instead of “CPT”—since the old “T” has turned out to be not a fundamental or interesting concept.
Paragraph 1 was me trying to “phrase this in language you are more likely to understand”
Paragraph 2 was me using the language I would normally use.
So: that was not a case of me “contradicting” myself at all.
If you simply reverse T, and the whole universe starts to run backwards, then it makes an awful lot of sense to call the universe “T symmetric”, IMHO, conventional terminology or no. Then it is time to start saying “T”—instead of “CPT”—since the old “T” has turned out to be not a fundamental or interesting concept.
Anyway, I think a miscommunication.