This has been bugging me for a while, so I'm really hoping someone can give me a good answer. Please get as technical as necessary, I'm a 4th year HE physics grad student so I do know my stuff! Why is the time-reversal operator made anti-unitary in quantum mechanics? It is very straight forward to show that an object with positive rest mass, when viewed from a reference frame going the opposite direction through time (still time-like though), will have negative energy. Negative energy particles don't quite behave as you might naively expect though, and their interactions with positive energy particles are very foreign (two particles with opposite energy and opposite velocities will have a space-like 4-momentum). QFT is a relativistic theory, so I'm completely baffled why negative energy states have , almost artificially, been ruled out by making the time-reversal operator anti-unitary! I was taking a look at what the time-reversal operator does in certain situations, and the complex conjugation component really just seems to effectively reverse the sign of the rest mass. So basically the time-reversal of a state with positive rest mass and positive energy will have negative rest mass and positive energy. This all seems fine, except for the interpretation that antiparticles are equivalent to particles under time reversal, since the two particles would have opposite signed rest mass!