For the benefit of others reading this, in Shankar’s book referenced below, this is said to not be a full symmetry i.e. not always valid.
There is no reason to think that the evolution of the conjugate function will be the same as the evolution of the original function.
Also there is no time-reversed Copenhagen measurement process in the theory which he implicitly requires.
Think about a massive object like a planet moving from L to R. It is massive so quantum effects can be ignored. It is clearly not true that the planet would be measured as being in the same place 10 minutes ago and 10 minutes hence. So the statement “All possible futures are also possible pasts” is wrong.
Note, though, that time reversal is still an anti-unitary operator in quantum mechanics in spite of the hand-waving argument failing when time reversal isn’t a good symmetry. Even when time reversal symmetry fails, though, there’s still CPT symmetry (and CPT is also anti-unitary).
For the benefit of others reading this, in Shankar’s book referenced below, this is said to not be a full symmetry i.e. not always valid.
There is no reason to think that the evolution of the conjugate function will be the same as the evolution of the original function.
Also there is no time-reversed Copenhagen measurement process in the theory which he implicitly requires.
Think about a massive object like a planet moving from L to R. It is massive so quantum effects can be ignored. It is clearly not true that the planet would be measured as being in the same place 10 minutes ago and 10 minutes hence. So the statement “All possible futures are also possible pasts” is wrong.
Note, though, that time reversal is still an anti-unitary operator in quantum mechanics in spite of the hand-waving argument failing when time reversal isn’t a good symmetry. Even when time reversal symmetry fails, though, there’s still CPT symmetry (and CPT is also anti-unitary).