In the Born rule’s model of the universe, the future is non-deterministic.
That’s more like the Born-rule-as-interpreted-by-the-Copenhagen-interpretation.
If you apply time-reversal symmetry to the Born rule then the past becomes non-deterministic.
More accurately, the past always was non-deterministic.
What do you mean by “non-determinstic” ? The standard (single universe indeterministic) view is that past events occurred with a probability less than 1, ie they did not occur inevitably or necessarily. That is coupled with the idea that there is only one past state, and its can be assigned a probability of 1
for the purpose of calculating the probability of subsequent events .
But your past light cone is defined only in probabilities.
Huh? Whatever information you had about the past is observations, not uncollapsed wave functions.
You seem to be simultaneously appealing to time symmetry, and to Copenhagen (events occur probablistically as the result of WF collapse) whilst not noticing that the collapse postulate is not time-symmetrical.
That’s more like the Born-rule-as-interpreted-by-the-Copenhagen-interpretation.
Yes.
What do you mean by “non-determinstic” ? The standard (single universe indeterministic) view is that past events occurred with a probability less than 1, ie they did not occur inevitably or necessarily. That is coupled with the idea that there is only one past state, and its can be assigned a probability of 1 for the purpose of calculating the probability of subsequent events .
Yes. This is what I mean by “non-deterministic”.
...the collapse postulate is not time-symmetrical.
I think the time-symmetry of the collapse postulate is the crux of our disagreement. In Chapter 4 of Principles of Quantum Mechanics, Second Edition by R. Shankar, the collapse postulate is stated as follows.
III. 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.
According to in Chapter 11.5 Time Reversal Symmetry, time-reversal is performed by ψ→ψ∗. What happens if we plug this into postulate III?
|⟨ω|ψ⟩|2→|⟨ω|ψ∗⟩|2
If we can show that |⟨ω|ψ⟩|2=|⟨ω|ψ∗⟩|2 then the Born rule is time-symmetric.
What do you mean by “non-determinstic” ? The standard (single universe indeterministic) view is that past events occurred with a probability less than 1, ie they did not occur inevitably or necessarily. That is coupled with the idea that there is only one past state, and its can be assigned a probability of 1 for the purpose of calculating the probability of subsequent events .
Yes. This is what I mean by “non-deterministic”.
The standard view of non-determinism is supported by the standard take on Copenhagen, which includes the time-irreversability of collapse. Yet you are arguing for the time-reversibility of collapse. Why would you want to put forward a novel premise, if you are not drawing a novel conclusion?
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.
That’s more like the Born-rule-as-interpreted-by-the-Copenhagen-interpretation.
What do you mean by “non-determinstic” ? The standard (single universe indeterministic) view is that past events occurred with a probability less than 1, ie they did not occur inevitably or necessarily. That is coupled with the idea that there is only one past state, and its can be assigned a probability of 1 for the purpose of calculating the probability of subsequent events .
Huh? Whatever information you had about the past is observations, not uncollapsed wave functions.
You seem to be simultaneously appealing to time symmetry, and to Copenhagen (events occur probablistically as the result of WF collapse) whilst not noticing that the collapse postulate is not time-symmetrical.
Yes.
Yes. This is what I mean by “non-deterministic”.
I think the time-symmetry of the collapse postulate is the crux of our disagreement. In Chapter 4 of Principles of Quantum Mechanics, Second Edition by R. Shankar, the collapse postulate is stated as follows.
According to in Chapter 11.5 Time Reversal Symmetry, time-reversal is performed by ψ→ψ∗. What happens if we plug this into postulate III?
|⟨ω|ψ⟩|2→|⟨ω|ψ∗⟩|2
If we can show that |⟨ω|ψ⟩|2=|⟨ω|ψ∗⟩|2 then the Born rule is time-symmetric.
⟨V|V⟩=∑i|vi|2=∑i|v∗i|2=⟨V∗|V∗⟩⟨ψ|ψ⟩=⟨ψ∗|ψ∗⟩(⟨ψ|ψ⟩)∗=(⟨ψ∗|ψ∗⟩)∗|ψ∗⟩⟨ψ∗|=|ψ⟩⟨ψ|⟨ω|ψ∗⟩⟨ψ∗|ω⟩=⟨ω|ψ⟩⟨ψ|ω⟩|⟨ω|ψ∗⟩|2=|⟨ω|ψ⟩|2|⟨ω|ψ⟩|2=|⟨ω|ψ∗⟩|2
The standard view of non-determinism is supported by the standard take on Copenhagen, which includes the time-irreversability of collapse. Yet you are arguing for the time-reversibility of collapse. Why would you want to put forward a novel premise, if you are not drawing a novel conclusion?
This post about the time-reversibility of collapse sets the groundwork for a novel conclusion.
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.