No, it’s basically performed by t → -t. Because what you are reversing is a dynamic process.
Complex conjugation is a bookkeeping thing you need to do in quantum mechanics alone. In classical physics, t → -t is all you need to do.
then the Born rule is time-symmetric.
The Born rule shows how to get classical probabilities out of quantum amplitudes. It is not a dynamical process. Collapse is a process. The Born rule is not collapse (again), although both are involved in measurement.
It makes no sense to talk of reversing the Born rule, because its just a calculation. Collapse is a dynamical process, so it makes sense to talk of reversing collapse. But collapse cannot be reversed because it loses information. (There’s a reason why collapse is also known as reduction!)
The collapse postulate (not the Born rule) says:
If the particle is in a state |ψ⟩, measurement of the variable (corresponding to)
Ω will yield one of the eigenvalues ω with the probability P(ω)∝|⟨ω|ψ⟩|2. The state of the system will change from |ψ⟩ to |ω⟩ as a result of the measurement.
The state changes to one of the original eigenstates, and you cannot work back from that to get the original set of eigenstates and eigenvalues. In concrete terms, if a photon lands somewhere on a detector, you can’t use that information to infer back to its probabilities of landing elsewhere.
No, it’s basically performed by t → -t. Because what you are reversing is a dynamic process.
Complex conjugation is a bookkeeping thing you need to do in quantum mechanics alone. In classical physics, t → -t is all you need to do.
The Born rule shows how to get classical probabilities out of quantum amplitudes. It is not a dynamical process. Collapse is a process. The Born rule is not collapse (again), although both are involved in measurement.
It makes no sense to talk of reversing the Born rule, because its just a calculation. Collapse is a dynamical process, so it makes sense to talk of reversing collapse. But collapse cannot be reversed because it loses information. (There’s a reason why collapse is also known as reduction!)
The collapse postulate (not the Born rule) says:
The state changes to one of the original eigenstates, and you cannot work back from that to get the original set of eigenstates and eigenvalues. In concrete terms, if a photon lands somewhere on a detector, you can’t use that information to infer back to its probabilities of landing elsewhere.