EPR and Non-Locality - For and Against

[martinbn]

Haha, yes, we have covered this before. In this forum, and you participated in at least some of it (see your post #33).

https://www.physicsforums.com/threa...rpretation-of-quantum-mechanics.989890/page-2

You ask "in what sense"? Per Steven Weinberg, Lectures on Quantum Mechanics, 12.1 Paradoxes of Entanglement (talking about EPR-B):

"There is a troubling weirdness about quantum mechanics. Perhaps its weirdest feature is entanglement, the need to describe even systems that extend over macroscopic distances in ways that are inconsistent with classical ideas. ... Of course, according to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem - it just doesn't change the density matrix."

Of course, you interpreted another statement by Weinberg as implying QM is local (or something that I couldn't agree as saying QM is local). I'd love to an actual quote by Weinberg where he denies quantum non-locality, or otherwise denies the obvious implications of Bell. Since the quote above explicitly says:

According to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem...

Of course, to be fair: there is no apparent direction of the change referred to. It could be in either direction.

To me this is a very sloppy language. The claim is that the measurement here changes the state of the subsystem over there. But what is the state of the system before the measurement? It doesn't make sense to talk about the state of the subsystem (in fact about subsystems) at all. So what state changes!

 

[vanhees71]

Indeed, this apparent problem only occurs if you interpret the collapse of the state as something dynamical really happening in nature, but that's not necessary to assume to use QT. It's also contradicting the very foundations of relativistic LOCAL QFT! There's simply no FTL change on one far distant part of an entangled quantum system due to a local measurement (and all measurements I know of are local) on the other part of it.

 

[RUTA]

It's figured out, how those facts are to be perfectly described, namely by quantum (field) theory, discovered in 1925/26 by Heisenberg, Born, and Jordan.

As I explained many times here, QFT does not resolve the mystery of QM entanglement because QM is QFT for the Bell state phenomena. This is equivalent to saying Newtonian mechanics is special relativity at low velocities. So saying you want to bring QFT to bear on the mystery of QM entanglement is redundant, just like saying you want to bring SR to bear on a mystery of Newtonian mechanics where Newtonian mechanics matches experiment beautifully. If there was a QM prediction that deviated from experiment, then it would perhaps be reasonable to bring the subsuming theory (QFT) to bear on that experiment. But, that's not the case for violations of the Bell inequality to 8 sigma as predicted by QM.

 

[Minnesota Joe]

The experimenters are irrelevant. The particles are entangled - you can't say for sure they exist as separate particles for the idea of locality to even make sense.

Here is the math. Let's say we have two systems that can be in state |a> and |b>. If system 1 is in state |a> and system 2 in state |b> we write this as |a>|b>. Conversely if system 1 is in state |b> and system 2 in state |a> we write it as |b>|a>. By the principle of superposition a possible state of both systems is 1/√2 (|a>|b> + |b>|a>). In such a state what state each system is in, or even if there is still two systems, is unclear - you can only speak with certainty of the combined system 1 and 2. If they have no individuality the idea of signals passing between the two systems does not even make sense.

Thank you for the response Bill. This last sentence is my first point of confusion. Your combined state is an extended object with boundaries, "ends" if you will. We know this because Alice and Bob have something to measure. When those ends reach Alice and Bob, there is distance between the ends since there is separation between Alice and Bob. The idea of a signal passing between two different points in space does make sense.

But as Peter correctly points it is just semantics on what you mean by non-locality.

I don't think the disagreements are merely semantic and I didn't read Peter's comment that way, but dogmatically insisting on our own definitions while ignoring other people's definition can cause us to talk past one another. I hope we are all adults and can provisionally adopt each other's senses of a word for the sake of polite discussion and understanding.

 

[RUTA]

I don't think the disagreements are merely semantic and I didn't read Peter's comment that way, but dogmatically insisting on our own definitions while ignoring other people's definition can cause us to talk past one another. I hope we are all adults and can provisionally adopt each other's senses of a word for the sake of polite discussion and understanding.

Exactly. The meaning of a term within a community obtains via de facto consensus. Attempting to idiosyncratically assign a different meaning to the term defeats the point of language as a means of communication. The same holds for any means of communication, you must adhere to convention within the community where you use it: https://www.businessinsider.com/hand-gestures-offensive-different-countries-2018-6

 

[vanhees71]

As I explained many times here, QFT does not resolve the mystery of QM entanglement because QM is QFT for the Bell state phenomena. This is equivalent to saying Newtonian mechanics is special relativity at low velocities. So saying you want to bring QFT to bear on the mystery of QM entanglement is redundant, just like saying you want to bring SR to bear on a mystery of Newtonian mechanics where Newtonian mechanics matches experiment beautifully. If there was a QM prediction that deviated from experiment, then it would perhaps be reasonable to bring the subsuming theory (QFT) to bear on that experiment. But, that's not the case for violations of the Bell inequality to 8 sigma as predicted by QM.

There is no mystery to begin with, and I've no clue, what you mean by "QM is QFT for the Bell state phenomena". QM is a non-relativistic approximation of relativistic QFT. That's all. There is no contradiction between QM and experiment, where it is applicable. There's neither a contradiction between experiment and relativistic QFT.

 

[RUTA]

There is no mystery to begin with, and I've no clue, what you mean by "QM is QFT for the Bell state phenomena". QM is a non-relativistic approximation of relativistic QFT. That's all. There is no contradiction between QM and experiment, where it is applicable. There's neither a contradiction between experiment and relativistic QFT.

QM works beautifully to predict and analyze Bell state phenomena and QM is just the low energy approximation to QFT. So appeals to QFT as resolving any "mystery" associated with Bell state entanglement is vacuous. Whether or not you see anything "mysterious" is irrelevant. If you are going to engage those who do see mystery, then you cannot simply say there is no mystery because QFT is this or that. They already know full well what QFT says about the phenomenon because they know what QM says and, as you agree, QM is QFT when dealing with that experiment.

 

[RUTA]

Here is a relevant quote from Mermin published in Physics Today:

To this moderate point of view I would only add the observation that contemporary physicists come in two varieties.
Type 1 physicists are bothered by EPR and Bell’s theorem.
Type 2 (the majority) are not, but one has to distinguish two subvarieties.
Type 2a physicists explain why they are not bothered. Their explanations tend either to miss the point entirely (like Born’s to Einstein) or to contain physical assertions that can be shown to be false.
Type 2b are not bothered and refuse to explain why. Their position is unassailable. (There is a variant of type 2b who say that Bohr straightened out the whole business, but refuse to explain how.)

 

[Minnesota Joe]

Exactly. The meaning of a term within a community obtains via de facto consensus. Attempting to idiosyncratically assign a different meaning to the term defeats the point of language as a means of communication.

That's half of it, but it cuts both ways. If someone is using 'non-locality' in a way you think is non-standard, it is pointless and disingenuous to pretend they are using it in a way that "obtains via de facto consensus" in order to refute them. You've likely done no such thing.

Besides, different communities in physics might use the same word to mean different things. In that case the dictionary of physics has multiple entries under 'non-locality', one for each sense of the word as it is actually used by physicists.

 

[vanhees71]

I only appeal to relativistic QFT to disprove claims that there's something nonlocal or that there's something "instantaneously caused" by a local measurement on a part of an entangled system as often claimed referring to naive collapse interpretations. You cannot counter such arguments using non-relativistic QM, because in non-relativistic (Galean-Newtonian spacetime) physics nothing prevents the theory predict instantaneous influcences. To the contrary, it's in fact the way how interactions are described (e.g., Newton's theory of the gravitational interaction).

I'm not bothered by EPR at all. Why should I be? Bell's theorem is a breakthrough in making the claims of the EPR paper a scientific statement, i.e., something that can be checked by experiment. It rules out all local deterministic HV theories, and all experiments verify QT. For me the case is closed concerning all the confusion with the EPR paper and Bohr's answer to it. Anyway, Einstein didn't like the EPR paper himself and he clarified the point very well himself in a later paper introducing the notion of "inseparability", which is the real issue here.

If it is really the case that "non-locality" means different things in different communities, then one shouldn't use the expression when cross-communicating within differen communities without giving a clear definition of it.

 

[RUTA]

That's half of it, but it cuts both ways. If someone is using 'non-locality' in a way you think is non-standard, it is pointless and disingenuous to pretend they are using it in a way that "obtains via de facto consensus" in order to refute them. You've likely done no such thing.

Besides, different communities in physics might use the same word to mean different things. In that case the dictionary of physics has multiple entries under 'non-locality', one for each sense of the word as it is actually used by physicists.

It would certainly violate the goal of language to pretend they intended to use the term per convention defined by the context (here in talking about Bell state entanglement) when they were in fact violating convention. Communication would be thwarted. The parties involved in a conversation must simply agree on the meaning of the terms being used, lest they violate the first principle of logic, A = A. When the principles of logic are violated, confusion ensues.

 

[RUTA]

I only appeal to relativistic QFT to disprove claims that there's something nonlocal or that there's something "instantaneously caused" by a local measurement on a part of an entangled system as often claimed referring to naive collapse interpretations. You cannot counter such arguments using non-relativistic QM, because in non-relativistic (Galean-Newtonian spacetime) physics nothing prevents the theory predict instantaneous influcences. To the contrary, it's in fact the way how interactions are described (e.g., Newton's theory of the gravitational interaction).

Again, QM is QFT for this experiment so, yes, I can use whatever I like from QM to "explain" the experiment. Indeed, that's exactly what I am doing from the start when I predict violations of the CHSH inequality to the Tsirelson bound using low-energy QFT (aka QM). In order for your analogy with Newtonian gravity to be applicable, you would have to use QFT to predict some violation of the QM prediction. In the case of Newtonian gravity, one would appeal to the appropriate GR solution and show that GR predicts a time delay between changes in the matter configuration and distant "gravitational effects" contra the Newtonian prediction. One does the experiment to verify the GR prediction thus dispelling the "mysterious" but erroneous prediction by Newtonian gravity of instantaneous causation. There is no such QFT intervention for Bell state correlations because we do realize the Tsirelson bound per QM and that alone is what people find "mysterious." So, again, your claim that QFT in any way dispels the mystery of Bell state correlations is vacuous. And, again, whether or not you understand why so many people in foundations find such correlations mysterious is absolutely irrelevant.

 

[PeterDonis]

QM is QFT for this experiment so, yes, I can use whatever I like from QM to "explain" the experiment.

This is not correct as you state it. You can use the math of QM to predict the results of the experiment. But you cannot use an interpretation of QM that is inconsistent with QFT to "explain" the experiment, even if that interpretation is consistent with the math of QM in the non-relativistic approximation. So you can't use "whatever you like" from QM; you can only use the things from QM that remain valid in QFT.

Consider a similar claim for gravity: Newtonian gravity is GR for this experiment (say predicting the orbit of the ISS), so I can use whatever I like from Newtonian gravity to "explain" the experiment. That is not correct. You can predict the orbit of the ISS to very high precision using the math of Newtonian gravity that models it as an instantaneous inverse square law force. But you can't "explain" the orbit of the ISS by saying that gravity "really is" an instantaneous inverse square law force, because in GR, it isn't.

 

[RUTA]

This is not correct as you state it. You can use the math of QM to predict the results of the experiment. But you cannot use an interpretation of QM that is inconsistent with QFT to "explain" the experiment, even if that interpretation is consistent with the math of QM in the non-relativistic approximation. So you can't use "whatever you like" from QM; you can only use the things from QM that remain valid in QFT.

Consider a similar claim for gravity: Newtonian gravity is GR for this experiment (say predicting the orbit of the ISS), so I can use whatever I like from Newtonian gravity to "explain" the experiment. That is not correct. You can predict the orbit of the ISS to very high precision using the math of Newtonian gravity that models it as an instantaneous inverse square law force. But you can't "explain" the orbit of the ISS by saying that gravity "really is" an instantaneous inverse square law force, because in GR, it isn't.

Let's follow your analogy and see how it relates to Bell state correlations. What is "mysterious" about Newtonian gravity is its prediction of instantaneous causation. So, you conduct an experiment to see if there is any time delay between gravitational influences and the (distant) ISS. GR says there will be a time delay and Newtonian gravity says there will not be a time delay. What does the experiment find (in analogy with Bell state correlations)? The experiment shows a time delay to 8 sigma, refuting the "mysterious" prediction of Newtonian gravity. What is the analogous situation with Bell state correlations? Local hidden variable theories predict adherence to the CHSH inequality while QFT predicts a violation of the CHSH inequality. The experiment is conducted and we find the CHSH inequality is violated to 8 sigma per the QFT prediction. Unlike the Newtonian gravity/GR "mystery" it is the "mystery" that is actually vindicated in this case. Totally the opposite of your analogy.

 

[DrChinese]

To me this is a very sloppy language. The claim is that the measurement here changes the state of the subsystem over there. But what is the state of the system before the measurement? It doesn't make sense to talk about the state of the subsystem (in fact about subsystems) at all. So what state changes!

Sloppy? Easy to say. It's as descriptive as can be. And I think it summarizes the situation pretty well, which is why I quoted it (the reputation of the author might have also been a factor).

So what state changes? Before there is a measurement, we have an system of 2 photons in an entangled (non-separable) state. After Alice performs a Bell measurement on that system, she has a photon in a known spin state. The remainder of the system, now quite distant and near to Bob, instantaneously changes its state too - also to a known spin state. How is this confusing?

The only question remaining is whether it is Alice's measurement that leads to the state change (causal), or Bob's later measurement that leads to the state change (retrocausal), or both/neither (acausal). RUTA would choose the last of those (acausal). And in fact if you look at the formula* for predicting coincidences, there are only 2 significant variables: the relative angle settings of Alice and Bob. So the coincidence function does not distinguish order, which you could see as a nod to the acausal explanation as much as anything else.*Typically: cos^2(A-B) or sin^2(A-B), depending on entanglement type.

 

[PeterDonis]

GR says there will be a time delay

No, it doesn't, not for this experiment, or for any experiment where the Newtonian approximation is valid. See this classic paper by Carlip:

https://arxiv.org/abs/gr-qc/9909087

 

[RUTA]

No, it doesn't, not for this experiment, or for any experiment where the Newtonian approximation is valid. See this classic paper by Carlip:

https://arxiv.org/abs/gr-qc/9909087

By definition, so that is also not an apt analogy because in our case there are competing predictions.

 

[PeterDonis]

that is also not an apt analogy because in our case there are competing predictions

No, there aren't. The "competing predictions" you refer to are those of local hidden variable theories. But we aren't talking about local hidden variable theories vs. QM. We are talking about QM vs. QFT. We have all agreed that, for the cases in question (Bell-type experiments), QM and QFT make the same predictions. The difference is only in "interpretation"--"interpretations" of QM that aren't consistent with QFT can't be used to "explain" the results of Bell-type experiments, even though non-relativistic QM predicts the same results as QFT does. Just as Newtonian gravity can't be used to "explain" the results of gravity experiments, even in cases where Newtonian gravity and GR make the same predictions.

 

[RUTA]

No, there aren't. The "competing predictions" you refer to are those of local hidden variable theories. But we aren't talking about local hidden variable theories vs. QM. We are talking about QM vs. QFT. We have all agreed that, for the cases in question (Bell-type experiments), QM and QFT make the same predictions. The difference is only in "interpretation"--"interpretations" of QM that aren't consistent with QFT can't be used to "explain" the results of Bell-type experiments, even though non-relativistic QM predicts the same results as QFT does. Just as Newtonian gravity can't be used to "explain" the results of gravity experiments, even in cases where Newtonian gravity and GR make the same predictions.

There is no QM vs QFT for this experiment because QM is QFT for this experiment. The only competing prediction is due to local hidden variable theories. So, when comparing theories for the CHSH experiment, we are comparing QFT and hidden variable theories. Appealing to a "QM interpretation" of this experiment is appealing to a "QFT interpretation" of this experiment. There is no distinction, so there is no sense in which "QFT resolves the mystery of the violation of the CHSH inequality created by QM." You have just written, "QFT resolves the mystery of the violation of the CHSH inequality created by QFT."

 

[RUTA]

There is at least one thing meaningful concerning the compatibility of QM and SR that can be said regarding Bell state entanglement and I say it in my Insight:

Of course, we know QM is not Lorentz invariant and so it deviates trivially from SR in that fashion. In order to get QM from Lorentz invariant quantum field theory one needs to make low energy approximations [21, p. 173]. But, the charge of incompatibility based on QM entanglement actually carries serious consequences, because we have experimental evidence confirming the violation of the CHSH inequality per QM entanglement. So, if the violation of the CHSH inequality is in any way inconsistent with SR, then SR is being challenged empirically. By analogy, we know Newtonian mechanics deviates from SR because it is not Lorentz invariant. As a consequence, Newtonian mechanics predicts a very different velocity addition rule, so suppose we found experimentally that velocities do add as predicted by Newtonian mechanics. That would not merely mean that Newtonian mechanics and SR are incompatible, that would mean Newtonian mechanics has been empirically verified while SR has been empirically refuted. So, if one believes the violation of the CHSH inequality is in any way inconsistent with SR, and one believes the experimental evidence is accurate, then one believes SR has been empirically refuted. Clearly that is not the case, so their reconciliation as regards the violation of the CHSH inequality must certainly obtain in some fashion and here we see how the principle of NPRF does the job.

I'm sure NPRF isn't unique in this respect

 

[PeterDonis]

Appealing to a "QM interpretation" of this experiment is appealing to a "QFT interpretation" of this experiment.

You apparently aren't even reading my posts. We can't have a conversation if you don't read what I'm saying.

 

[RUTA]

You apparently aren't even reading my posts. We can't have a conversation if you don't read what I'm saying.

Haha, you and I almost always talk past one another. I'm not sure why that is because we are both very conventional physicists.

 

[martinbn]

Sloppy? Easy to say. It's as descriptive as can be. And I think it summarizes the situation pretty well, which is why I quoted it (the reputation of the author might have also been a factor).

So what state changes? Before there is a measurement, we have an system of 2 photons in an entangled (non-separable) state. After Alice performs a Bell measurement on that system, she has a photon in a known spin state. The remainder of the system, now quite distant and near to Bob, instantaneously changes its state too - also to a known spin state. How is this confusing?

The only question remaining is whether it is Alice's measurement that leads to the state change (causal), or Bob's later measurement that leads to the state change (retrocausal), or both/neither (acausal). RUTA would choose the last of those (acausal). And in fact if you look at the formula* for predicting coincidences, there are only 2 significant variables: the relative angle settings of Alice and Bob. So the coincidence function does not distinguish order, which you could see as a nod to the acausal explanation as much as anything else.*Typically: cos^2(A-B) or sin^2(A-B), depending on entanglement type.

The confusing part is where you say that the remainder of the system, at Bob, insantaneuosly changes its state. What was its state before that?

 

[vanhees71]

Again, QM is QFT for this experiment so, yes, I can use whatever I like from QM to "explain" the experiment. Indeed, that's exactly what I am doing from the start when I predict violations of the CHSH inequality to the Tsirelson bound using low-energy QFT (aka QM). In order for your analogy with Newtonian gravity to be applicable, you would have to use QFT to predict some violation of the QM prediction. In the case of Newtonian gravity, one would appeal to the appropriate GR solution and show that GR predicts a time delay between changes in the matter configuration and distant "gravitational effects" contra the Newtonian prediction. One does the experiment to verify the GR prediction thus dispelling the "mysterious" but erroneous prediction by Newtonian gravity of instantaneous causation. There is no such QFT intervention for Bell state correlations because we do realize the Tsirelson bound per QM and that alone is what people find "mysterious." So, again, your claim that QFT in any way dispels the mystery of Bell state correlations is vacuous. And, again, whether or not you understand why so many people in foundations find such correlations mysterious is absolutely irrelevant.

For which experiment? The Bell experiment with polarization-entangled photons is for sure not describable by QM but only by QED, i.e., relativistic QFT. QM is based on actions at a distance and thus by construction violates Einstein causality. It's no argument against the fact that there is a QT obeying Einstein causality, which is local relativistic QFT.

 

[vanhees71]

No, there aren't. The "competing predictions" you refer to are those of local hidden variable theories. But we aren't talking about local hidden variable theories vs. QM. We are talking about QM vs. QFT.

But you can't use QM, where it's not applicable, and you can't use it particularly for answering the question whether there are non-local interactions or not. By definition in QM the interactions are instantaneous as in classical Newtonian mechanics, and that's why QM is only applicable, where non-relativistic approximations are valid. As in classical electrodynamics of course quasistationary approximations violate locality because you neglect retardation effects and you cannot conclude from that approximation that there's non-locality in classical electrodynamics, you cannot claim there are actions at a distance by the argument that you use an approximation assuming such interactions. The point is that local relativistic QFT shows that QT is compatible with Einstein causality. You simply cannot disprove this by using a non-relativistic approximation.

 

[Tendex]

Let's follow your analogy and see how it relates to Bell state correlations. What is "mysterious" about Newtonian gravity is its prediction of instantaneous causation. So, you conduct an experiment to see if there is any time delay between gravitational influences and the (distant) ISS. GR says there will be a time delay and Newtonian gravity says there will not be a time delay. What does the experiment find (in analogy with Bell state correlations)? The experiment shows a time delay to 8 sigma, refuting the "mysterious" prediction of Newtonian gravity. What is the analogous situation with Bell state correlations? Local hidden variable theories predict adherence to the CHSH inequality while QFT predicts a violation of the CHSH inequality. The experiment is conducted and we find the CHSH inequality is violated to 8 sigma per the QFT prediction. Unlike the Newtonian gravity/GR "mystery" it is the "mystery" that is actually vindicated in this case. Totally the opposite of your analogy.

This way of using the analogy makes no sense at all to me, it reads like purely misleading sophistry. How can a "mistery" be at once vindicated and solved by the QFT prediction(and claiming at the same time QFT doesn't solve it)? And on top of it you get to asign the vindication or refutation of the "mistery" to analogous outcomes in the gravitational and quantum case as you see fit.

 

[DrChinese]

The confusing part is where you say that the remainder of the system, at Bob, instantaneously changes its state. What was its state before that?

It was a part of a 2 photon state/system*. Later, its entangled observable takes on a specific value depending on the nature of the measurement on the partner particle. I'd call that a change of state. I don't know when it changed exactly, but it definitely changes. Before is different than after. Agree?*Actually, that's only true for the photon observables that are entangled (say spin). The "rest" of the quantum particle is separable and can be identified and manipulated as an independent object. An example would be routing the photon through optical fiber.

 

[vanhees71]

Well, when A meausures the polarization of her photon and takes note of the result, she changes the state. B doesn't change his description, because he doesn't know about what A measured.

I don't know what you mean by your remark labelled with a *. A complete state of two entangled photons is of course given by something like (for simplicity I take momentum-helicity single-photon states; it's of course understood that for a true state you have to integrate over the momentum weighted with some square-integrable function to get a true state, but that's not important for the argument):
$$|\Psi \rangle=\frac{1}{\sqrt{2}} [\hat{a}^{\dagger}(\vec{p}_1,1) \hat{a}^{\dagger}(\vec{p}_2,-1) - \hat{a}^{\dagger}(\vec{p}_1,-1) \hat{a}^{\dagger}(\vec{p}_2,1)] |\Omega \rangle.$$
I don't know what you mean by "the rest of the quantum particle is separable". This state is maximally entangled (in other words it's a Bell state). So it's not separable wrt. any single-photon basis.

 

[martinbn]

It was a part of a 2 photon state/system*. Later, its entangled observable takes on a specific value depending on the nature of the measurement on the partner particle. I'd call that a change of state. I don't know when it changed exactly, but it definitely changes. Before is different than after. Agree?*Actually, that's only true for the photon observables that are entangled (say spin). The "rest" of the quantum particle is separable and can be identified and manipulated as an independent object. An example would be routing the photon through optical fiber.

Well, no, no agree. Before any of the two makes a measurment you cannot talk about two subsystems, nor about the state of each subsystem. So it is still confusing.

Here is the question again if the system is in the state $\frac1{\sqrt{2}} \left(|01\rangle - |10\rangle\right)$, before Alice or Bob measure, what is the state of the part that is at Bob's? If Alice measures and gets outcome $1$, then the part at Bob's is in state $|0\rangle$. And the statement is that it has changed instantaneously. What was it before that? $|\psi\rangle = ?$

 

[PeterDonis]

if the system is in the state $\frac1{\sqrt{2}} \left(|01\rangle - |10\rangle\right)$, before Alice or Bob measure, what is the state of the part that is at Bob's?

The answer, of course, is that there is no such state; Bob's part of the system does not have a well-defined quantum state. The only thing it has that is well-defined is a reduced density matrix, obtained by tracing over Alice's part of the system. And this density matrix does not change when Alice makes her measurement.

I'd call that a change of state.

How, then, would you respond to my statements above, which are just clarifying the point that @martinbn has been making?

 

[vanhees71]

Well, no, no agree. Before any of the two makes a measurment you cannot talk about two subsystems, nor about the state of each subsystem. So it is still confusing.

Here is the question again if the system is in the state $\frac1{\sqrt{2}} \left(|01\rangle - |10\rangle\right)$, before Alice or Bob measure, what is the state of the part that is at Bob's? If Alice measures and gets outcome $1$, then the part at Bob's is in state $|0\rangle$. And the statement is that it has changed instantaneously. What was it before that? $|\psi\rangle = ?$

The state of the parts is given by the partial trace over the other part of the state, which is
$$\hat{\rho}=\frac{1}{2} (|01 \rangle-|10 \rangle)(\langle 01 |-\langle 10|).$$
The state for B's spin then is
$$\hat{\rho}_B=\mathrm{Tr}_{\text{A}} \hat{\rho} = \sum_{j,j',k=0}^1 |j \rangle \langle j' \langle j,k|\hat{\rho}|j',k \rangle = \frac{1}{2} (|0 \rangle \langle 0| + |1 \rangle \langle 1|)=\frac{1}{2} \hat{1}.$$
This describes the full ensemble of spins prepared in this specific state.

If A measures her spin and she gets 1, then she assigns the new state $|10 \rangle$ to this partial ensemble, and indeed when A and B exchange there measurement protocols they'll realize that for that partial ensemble, i.e., for the ensemble selected by A's measurement result 1, indeed Bob always measured 0. That's all. There's nothing weird or faster than light or whatever. One simply has to take the probabilistic meaning of states seriously and not add some vague ideas about what quantum states describe to it or think there's a collapse of the state. It's just probabilities and nothing else. There's nothing enigmatic about the fact that selecting a subensemble from a full ensemble due to observations has a different statistics from the full ensemble.

 

[PeterDonis]

The state of the parts is given by the partial trace over the other part of the state, which is

...a density matrix, not a state vector. And, as I noted in post #65, this density matrix does not change when Alice makes her measurement. Bob's density matrix only changes when he makes his measurement.

 

[vanhees71]

Of course, it's a general state, not a pure one. I should have added that for me the state is represented always by a statistical operator, i.e., in the beginning the state is $\hat{\rho}=|\Psi \rangle \langle \Psi|$., not by a state ket in the case of a pure state.

It's a typical feature of entanglement that the reduced state of one part of a system prepared in an entangled (pure) state is a proper mixture, not a pure state. The partial trace (the reduced density matrix for B's particles) describes what Bob observes on the full ensemble. It tells you that he sees "unpolarized particles" (maybe the most perfect realization of an ensemble of unpolarized particles one can think of).

I hope I made my interpretation of what's sloppily called "collapse" clear: It's simply the selection of a partial ensemble dependent on the outcome of Alice's measurement, and this partial ensemble has different statistical properties. It is described by the pure state $|01 \rangle$ and the unique feature of such a "separable state" is that of course the reduced density matrix in this case is the projector $|1 \rangle \langle 1|$, i.e., a pure state.

 

[DrChinese]

How, then, would you respond to my statements above, which are just clarifying the point that @martinbn has been making?

...

Bob's density matrix only changes when he makes his measurement.

Well, Bob's particle was neither spin up or spin down before Alice executes a measurement (per Bell). After that, it is definitely either up or down, and can be so predicted. Ergo, it changed at some point - some might call that instantaneous collapse. Of course, we are assuming some kind of causal order when we say that. These assumptions might not be justified.

IIRC: Weinberg says Bob's state vector changes upon Alice's measurement, but not his density matrix.

 

[PeterDonis]

Bob's particle was neither spin up or spin down before Alice executes a measurement (per Bell). After that, it is definitely either up or down, and can be so predicted

This is a non-relativistic interpretation. But that's not the only possible interpretation. At the very least, a relativistic interpretation would not claim that either measurement happened before the other, since they are spacelike separated. That being the case, I don't see how a relativistic interpretation could claim that either measurement caused a change of state of the other particle.

Also, since you say that something "changes" with Bob's particle when Alice makes her measurement, you are using an interpretation where "state" means "state vector", or at least something related to some state vector (since Bob's particle by itself does not have a well-defined state vector at all before measurement). As has already been pointed out, the density matrix for Bob's particle does not change when Alice makes her measurement; it only changes when Bob makes his measurement. So an interpretation that used "state" to mean "density matrix" would say that Alice's measurement doesn't change anything about Bob's particle; only Bob's measurement does.

Of course, we are assuming some kind of causal order when we say that. These assumptions might not be justified.

Indeed not, if the measurement events are spacelike separated. But, as you have yourself pointed out in other threads, the QM prediction for this scenario actually is the same regardless of whether the measurements are spacelike, timelike, or null separated. So it seems like it would be nice to have a single unified account of what is going on in such a scenario that doesn't require any assumptions about causal order.

Weinberg says Bob's state vector changes upon Alice's measurement, but not his density matrix.

If "state vector changes" is meant literally, it can't be true, since Bob's particle doesn't even have a well-defined state vector before measurement. But Weinberg might have simply meant "doesn't have a well-defined state vector before measurement, but does afterwards". That, of course, still leaves the interpretation issue that I described above.