This question came across my mind when I read section 2.6, but it does not have close relation to the content of the book. If we apply a time reversal to 4-momentum, the 0-component(i.e. the energy) will become negative, and this is why time-reversal operator on quantum states must be antilinear according to Weinberg. I wonder how we interpret the negative energy if there were no quantum mechanics, i.e. if we only have classical description, it seems energy will inevitably become negative after time reversal, how do we resolve this?