Maybe because of my relative unfamiliarity I seemed surprising that complex conjuation is how you do time-reversal. Where one does pull that from? I do know that a lot of things are required to be hermitian which essentially means that the complex conjucate needs to be equal to the standard in magnitude.
Does me being classical mean that I am definetely in this state and not in any other state ie there is less different looking microstates. Wouldn’t that mean that it is a macrostat of exactly one micro state?
Reading up on entropy I was of the understanding that one can’t make arbitrary collections of microstates into macro sttes but they must be carved “right” in some sense. And that experts disagree what the requirements are.
If the present is a degenerate macrostate and the bidirectional graph is supposed to be about microstates there should be atleast two balloons included in the present.
Demanding that the time reversal operator leaves Q unchanged but reverses the sign of P (which is how time reversal in classical mechanics works) means that the time reversal operator has to be implemented by an anti-unitary operator. More hand-wavingly, since the Schrodinger equation gives e−iHt as the forward time evolution of a state ψ, e+iHt (flipping the sign of time) should give the backward time evolution. But that’s just the normal time evolution of ψ∗ as you can see if you just conjugate the Schrodinger equation.
See also this paper for more discussion on why the time reversal operator ought to behave in this way and on time reveral in general.
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).
Maybe because of my relative unfamiliarity I seemed surprising that complex conjuation is how you do time-reversal. Where one does pull that from? I do know that a lot of things are required to be hermitian which essentially means that the complex conjucate needs to be equal to the standard in magnitude.
Does me being classical mean that I am definetely in this state and not in any other state ie there is less different looking microstates. Wouldn’t that mean that it is a macrostat of exactly one micro state?
Reading up on entropy I was of the understanding that one can’t make arbitrary collections of microstates into macro sttes but they must be carved “right” in some sense. And that experts disagree what the requirements are.
If the present is a degenerate macrostate and the bidirectional graph is supposed to be about microstates there should be atleast two balloons included in the present.
I too would like to see a citation for this proposition
> In quantum mechanics, time-reversal is performed by complex conjugation ψ→ψ∗
I worked my way through the QM textbook and this does not compute AFAIK.
Demanding that the time reversal operator leaves Q unchanged but reverses the sign of P (which is how time reversal in classical mechanics works) means that the time reversal operator has to be implemented by an anti-unitary operator. More hand-wavingly, since the Schrodinger equation gives e−iHt as the forward time evolution of a state ψ, e+iHt (flipping the sign of time) should give the backward time evolution. But that’s just the normal time evolution of ψ∗ as you can see if you just conjugate the Schrodinger equation.
See also this paper for more discussion on why the time reversal operator ought to behave in this way and on time reveral in general.
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).
Chapter 11 Section 5 “Time Reversal Symmetry” of Principles of Quantum Mechanics, Second Edition by R. Shankar.
Whenever time appears in the wave equations it’s multiplied by i, so taking the complex conjugat is equivalent to replacing t with -t.
You’re not classical, you just decohere very quickly.
For the rest, I’d have to think about your question more before answering.