I Does Time-Symmetry Imply Retrocausality? How does the Quantum World Say “Maybe”?

[DrChinese]

"For successive, non-destructive projective measurements with discrete results, each measurement with measuring value can be regarded as preparation of a new state whose state vector is the corresponding eigenvector , to be used for the calculation of subsequent time evolution and further measurements." -- A. Neumaier
https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/

Do you disagree with this rule?

There may be intermediate states, I don’t know what happens in between. They just cannot be the ones claimed. That is 100% classical logic, and fails.

 

[Sambuco]

I am. I don't think you're reading me.

Yes, I'm reading you. Thanks for your answer

No, it's not. See my response to @Morbert in post #99 just now. There's a reason why, in the PF Insights article referenced, the projection postulate is stated in the very limited way it's stated. Going beyond that very limited statement, and applying it the way you're applying it, is not the slam dunk you seem to think it is.

Now, I understand your objection much better. Let me address this with a simple example. A two-particle system is initially prepared in the state $\ket{\Psi_{12}(t_0)} = \frac{1}{\sqrt{2}} (\ket{\uparrow_{1z}} \otimes \ket{\uparrow_{2z}} + \ket{\downarrow_{1z}} \otimes \ket{\downarrow_{2z}})$. Then, at time $t_1$ Alice measures the spin of particle 1 along the $z$-axis and obtains spin-up, while later, at time $t_2$ Bob measures the spin of particle 2 along the $z$-axis. We want to know what the state of particle 2 is between Alice's and Bob's measurements, i.e., at any time $t$ $(t_1 < t < t_2)$. Since that Alice measured spin-up, we know from the initial state that Bob will certainly measure spin-up. Therefore, the quantum state of particle 2 before Bob's measurements should be $\ket{\psi_2(t_1<t<t_2)} = \ket{\uparrow_{2z}}$, since this is the only quantum state that assures us that Bob's measurement will give the result "spin-up" with a probability of 1. So, how we could obtain the quantum state of particle 2 after Alice's measurement, given the initial state and the result of Alice's measurement? Well, it's pretty obvious that the mathematical operation that makes particle 2 to end up in the state $\ket{\psi_2(t_1<t<t_2)} = \ket{\uparrow_{2z}}$ is the application of the projector $P_{\uparrow_{1z}} = \ket{\uparrow_{1z}}\bra{\uparrow_{1z}} \otimes I$ onto the initial state of the entire system. As is evident, the projector only acts on particle 1. This is the definition of the collapse postulate when applied to entangled states as found in standard QM textbook (e.g., Zweibach's).

So, we can begin to discuss whether this state of particle 2 after Alice's measurement is ontic or not, whether this "collapse" is a physical process or simply a mathematical step to predict the probabilities of future measurements, but that's a separate topic. We aren't there yet.

Do you have another way to apply the collapse postulate than the one I explain here?

As evidenced by the fact that, as I've already commented, we have had references given in this thread on both sides of the question.

What references? I don't see any that point to the way I apply the collapse postulate, as defined in the QM textbooks I mentioned, as being flawed.

To avoid confusion, I'm not saying this is the only way to analyze these kinds of experiments.
What I'm saying is that it's the way to analyze them if you use the Schrödinger equation in its usual form, that is, by allowing the quantum state to evolve forward-in-time.

Lucas.

 

[PeterDonis]

We want to know what the state of particle 2 is between Alice's and Bob's measurements

And as soon as you ask that question, you've adopted a particular interpretation--you've assumed that the question has a meaningful answer. There are QM interpretations in which it doesn't.

 

[PeterDonis]

Do you have another way to apply the collapse postulate than the one I explain here?

Yes: don't apply it at all, because applying it means assuming that the question you're using it to answer even has a meaningful answer in the first place.

 

[DrChinese]

Let me address this with a simple example. A two-particle system is initially prepared in the state |Ψ12(t0)⟩=12(|↑1z⟩⊗|↑2z⟩+|↓1z⟩⊗|↓2z⟩). Then, at time t1 Alice measures the spin of particle 1 along the z-axis and obtains spin-up, while later, at time t2 Bob measures the spin of particle 2 along the z-axis. We want to know what the state of particle 2 is between Alice's and Bob's measurements, i.e., at any time t (t1<t<t2). Since that Alice measured spin-up, we know from the initial state that Bob will certainly measure spin-up. Therefore, the quantum state of particle 2 before Bob's measurements should be |ψ2(t1<t<t2)⟩=|↑2z⟩, since this is the only quantum state that assures us that Bob's measurement will give the result "spin-up" with a probability of 1.

You can't speculate on what happens between (or outside of) measurements! How many times has this message been said about QM?

While it is true that Bob's outcome is certain (as you say), it is conditioned on Alice's choice. And it is equally true that Alice's outcome is conditioned (mathematically the same) on Bob's later choice. Neither of these statements is more true than the other. (See separate post for more on this.)

And I repeat what has yet to be refuted: Were Bob really in the state you claim, that photon could not be used for entanglement swapping. See my post #89.

 

[Morbert]

If you have two entangled particles, A and B, and you make a measurement on A, the projection postulate, as it's stated in the article, only allows you to apply it to A; it does not allow you to apply it to B, because you didn't measure B.

A and B are entangled, and hence in an inseperable state, so a projective measurement on A projects the entire system onto a new state as per rule 7. Indeed, this is how, in entanglement swapping, a BSM on particles 2&3 can project particles 1&4 onto a Bell state. I.e.
$$\frac{(\ket{\phi^+}\bra{\phi^+}_{23}\otimes I_{14})\ket{\Psi}}{\sqrt{\bra{\Psi}(\ket{\phi^+}\bra{\phi^+}_{23}\otimes I_{14})\ket{\Psi}_{}}} = \ket{\phi^+}_{23}\ket{\phi^+}_{14}$$

Yes: don't apply it at all, because applying it means assuming that the question you're using it to answer even has a meaningful answer in the first place.

This is an issue of formalism. A forward-in-time analysis of entanglement swapping experiments with the basic rules of quantum mechanics reproduces all correlations in entanglement swapping experiments. That is an interpretation-independent statement.

 

[PeterDonis]

A and B are entangled, and hence in an inseperable state, so a projective measurement on A projects the entire system onto a new state as per rule 7.

No, that's not what rule 7 says. That's why I quoted from further on in the article, to make it clear how limited the statement of rule 7 in the article actually is.

 

[PeterDonis]

This is an issue of formalismi

Formalism and interpretation. You are adopting an interpretation in which a "forward in time analysis", applying the projection postulate as you do, makes sense. But there are interpretations for which it does not make sense.

A forward-in-time analysis of entanglement swapping experiments with the basic rules of quantum mechanics reproduces all correlations in entanglement swapping experiments. That is an interpretation-independent statement.

You're quibbling. Basically you're saying that what a particular interpretation says is interpretation independent. I suppose there is a way of reading those words so that statement is true, but it's irrelevant to what we're discussing here. The analysis you're doing only makes sense on certain interpretations. That's also an interpretation independent statement, if you insist on looking at it that way. And it leaves us right back at the same impasse--which, as I've already pointed out several times now, is not resolvable here.

 

[DrChinese]

Here is an interesting experiment* from over 20 years ago, and it highlights the difficulty of making statements about particles when they are not observed.

Take a single photon and send it to a beam splitter which then routes it either to Alice or Bob. If Bob detects it, then with certainty of 1 Alice did not. Seems simple enough, right? Alice's measurement choices are irrelevant (since the photon did not go to her), and her final state can be absolutely described as "nothing".

Not so fast, my friends! Alice's actions DO steer Bob's results! This is the analog to what I have been saying about trying to make a hard statement about what happens to photon 2 when entangled photon 1 is measured. There is interplay between photons 1 and 2 that is invariant as to time order of measurement. Their joint state is relevant until both as measured. Check this baby out:

Experimental Proof of Nonlocal Wavefunction Collapse for a Single Particle Using Homodyne Measurement

"Despite Bob’s lack of trust in Alice, she can convince him that her choice of measurement setting, θ, steers his quantum state proving that his system has no local quantum description."

You can see from Fig. 2 how Bob's detection results change conditioned on Alice's measurement setting, even though she detects nothing. Although this experiment is on single photons (a novel approach), their result applies to our 2 photon description equally.

In other words: there is no local unmeasured quantum state of photon 2 independent of photon 1, as a naive picture might suggest. The reality of photon's 1 outcome is affected by the choice of measurement on photon 2, and vice versa, independent of time ordering. Obviously no local forward-in-time-only description can reproduce the results of the cited experiment. The effect can even be considered a form of Delayed Choice experiment, if Bob measures before Alice.

I almost expect some denials here, since some people don't accept the conclusions of top experimentalists such as Ma, Zeilinger, etc. This particular paper has 60+ citations. Ma has 234+, Megidish 106+. Just saying: these are uncontroversial conclusions within the scientific community.


* Co-authored by Howard Wiseman, who has participated on PF in the past.

 

[Morbert]

No, that's not what rule 7 says. That's why I quoted from further on in the article, to make it clear how limited the statement of rule 7 in the article actually is.

The von Neumann projection postulate does not carve out exceptions for entangled systems. So long as the measurements are projective, an application of rule 7 will reliably reproduce the statistics of successive measurements. There's no contradiction with this and what you quoted.

You are adopting an interpretation in which a "forward in time analysis", applying the projection postulate as you do, makes sense. But there are interpretations for which it does not make sense.

You're quibbling. Basically you're saying that what a particular interpretation says is interpretation independent. I suppose there is a way of reading those words so that statement is true, but it's irrelevant to what we're discussing here. The analysis you're doing only makes sense on certain interpretations. That's also an interpretation independent statement, if you insist on looking at it that way. And it leaves us right back at the same impasse--which, as I've already pointed out several times now, is not resolvable here.

@DrChinese 's position is not "A forward-in-time analysis reproduces the statistics of entanglement swapping experiments, but I do not adopt any interpretations which ascribes ontic significance to this analysis." His position is "A forward-in-time analysis fails to reproduce the statistics of entanglement swapping experiments."

This "quibble" is what is stifling any sort of progress in the discussion. But I will happily move on if I am wrong: @DrChinese , do you in fact accept that a forward-in-time analysis, as an operational "shut up and calculate" application of rules, reproduces the statistics of entanglement-swapping experiments even if you have some objection to interpretations which ascribe ontic significance to this analysis?

 

[Morbert]

I almost expect some denials here, since some people don't accept the conclusions of top experimentalists such as Ma, Zeilinger, etc.

Have Ma or Zeilinger ever commented on the different interpretations of their experiments? This is not a rhetorical question. I am actually curious.

 

[PeterDonis]

The von Neumann projection postulate does not carve out exceptions for entangled systems.

The projection postulate doesn't have to carve out any such exception. It says, in the form in the article you referenced, that you only project the things that get measured. Whether those things are entangled with other things has nothing to do with it.

Applying the postulate so that it also projects things you didn't measure, if they're entangled with things you did measure, is interpretation dependent. That's why the article doesn't state the postulate that way --because the article has to state it in a way that applies regardless of what QM interpretation you adopt.

 

[PeterDonis]

His position is "A forward-in-time analysis fails to reproduce the statistics of entanglement swapping experiments."

And, as far as I can tell, there are references on his side of the question, as well as on yours. So again, this is a dispute that's not resolvable here. It depends on how you interpret the interpretation that's being used.

One of the difficulties with QM interpretation discussions is that advocates and critics of particular interpretations often don't even agree on what the interpretations say or how they address particular scenarios. Those are also disputes that aren't resolvable here.

 

[DrChinese]

Have Ma or Zeilinger ever commented on the different interpretations of their experiments? This is not a rhetorical question. I am actually curious.

I looked, not much in the past 20 years. He co-authored this, but it's a survey from 2013:

https://arxiv.org/abs/1301.1069

Edit: shortly after writing this, saw a new survey. It’s in a separate post. Zeilinger does weigh in!

 

[DrChinese]

His position is "A forward-in-time [only] analysis fails to reproduce the statistics of entanglement swapping experiments."

This "quibble" is what is stifling any sort of progress in the discussion. But I will happily move on if I am wrong: @DrChinese , do you in fact accept that a forward-in-time analysis, as an operational "shut up and calculate" application of rules, reproduces the statistics of entanglement-swapping experiments even if you have some objection to interpretations which ascribe ontic significance to this analysis?

I mostly object to ascribing any kind of inferred existence to intermediate unobserved states*, a well-accepted position in the community. I can easily say orthodox QM is forward in time, of course acknowledging generally accepted quantum nonlocality (as mentioned in literally thousands of papers).


*In keeping with Peres.

 

[Sambuco]

And as soon as you ask that question, you've adopted a particular interpretation

The question is valid under any interpretation, and the procedure for obtaining the answer is always the same. Let's see:

- Bohmian mechanics: How can I obtain the conditioned quantum state associated with particle 2 after the effective collapse induced by Alice's measurement on particle 1? By applying the collapse postulate, as explained.

- Zeilinger's information-based interpretation: How can I obtain a quantum state that contains all the information about particle 2, knowing the result of Alice's measurement on particle 1? By applying the collapse postulate, as explained.

- Many worlds: How can I obtain the (Everettian) relative state in the branch corresponding to the result of Alice's measurement on particle 1? By applying the collapse postulate, as explained.

- QBism: How can I obtain the quantum state corresponding to an agent's degree of belief about possible future measurements of particle 2, once he/she obtain information about the outcome of Alice's measurement on particle 1? By applying the collapse postulate, as explained.

- Relational quantum mechanics: How can I obtain the quantum state associated with particle 2, relative to Alice, after she measures particle 1? By applying the collapse postulate, as explained.

What differentiates the various interpretations has to do with the physical meaning associated with this quantum state, as reflected in the way each of them formulates the question.

Lucas.

 

[Sambuco]

Applying the postulate so that it also projects things you didn't measure, if they're entangled with things you did measure, is interpretation dependent.

As I explained in post #116, this is not interpretation-dependent. As the QM textbooks I've mentioned throughout this thread (Zweibach, McIntyre) explain, there is no other way to apply the measurement postulate when dealing with an entangled system that is consistent with experiments. The fact that one of the subsystems has not been measured is explicitly taken into account by using the identity operator on the space associated with that subsystem, as @Morbert wrote in post #106.

Lucas.

 

[Sambuco]

And, as far as I can tell, there are references on his side of the question, as well as on yours.

No, that's not true. No one shared any references that support the position that "A forward-in-time analysis fails to reproduce the statistics of entanglement swapping experiments."

@DrChinese repeatedly argues about the different articles by the Zeilinger's group, but these have nothing to do with this particular issue, as they explicitly use an information-based interpretation and say absolutely nothing about a forward-in-time interpretation.

Lucas.

 

[Sambuco]

You can't speculate on what happens between (or outside of) measurements! How many times has this message been said about QM?

You don't understand that associating a quantum state with a particle is not the same as measuring it.

I mostly object to ascribing any kind of inferred existence to intermediate unobserved states*, a well-accepted position in the community. I can easily say orthodox QM is forward in time, of course acknowledging generally accepted quantum nonlocality (as mentioned in literally thousands of papers).

*In keeping with Peres.

1. It's false that what you say is accepted in the community. QM textbooks (Zweibach, McIntyre) say you're wrong.

2. Again, Peres's quote, "unperformed experiments have no results," refers to measurement results, not quantum states. As I explained in the post #117, the fact that one of the particles hasn't been measured is explicitly taken into account when using the identity operator on the state space associated with that particle.

Lucas.

 

[PeterDonis]

Thread closed for moderation.