Undergrad EPR and Non-Locality - For and Against

[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.

 

[bhobba]

Thank you for the response Bill. This last sentence is my first point of confusion. Your combined state is an extended object with boundaries,

The wavefunction is extended - whether it is an object or not is interpretation dependant. It just encodes probabilities - are actuarial forcasts of life expectancy objects? I am not going to argue either way - but merely point out it is an assumption implied in your language - and we again run into the issue or semantics.

don't think the disagreements are merely semantic

Peter was pointing out what is meant by non-locality is semantic. Is it a violation of he cluster decomposition property, or is it a violation of locality in SR ie influences can travel faster than the speed of light. Note locality in SR can be violated providing you can not use it to sync clocks - otherwise SR falls to pieces. Thats an issue with the modern view of SR as just space-time geometry, rather than how Einstein originally did it with an analysis of clock syntonisation. It's obvious in Einsteins presentation if you can sync clocks, spatially separated, FTL then his arguments do not make sense. The same of course in the modern view - but it is not as obvious. In that approach it boils down to the interpretation of the c that appears in the resulting equations. It is easy to see it is the maximum velocity in any frame - but a more carefull analysis is necessary to see it must be the maximum velocity information can be sent. I often post it but here is the modern approach so you can understand what I am getting at:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

You might like to think about that. If you have difficulty in nutting it out, start a thread in the relativity forum.

Regarding the tracing and other aspects being discussed above, another paper I once posted a lot elucidates what's going on:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

See section 1.2.3. In the example I gave they replace state |a> and |b> with spin up and down. It is shown when observing one particle it acts as if it is in a mixed state. This is the crux of those that use decoherence as at least a partial solution to the measurement problem (some even believe there is no measurement problem to begin with). I will again not argue one way or the other, but it is something to be aware of. Susskind gives a good explanation of this in his excellent book on QM for the layman. Remember though, while written for the layman, it assumes you know calculus. Thats what makes it unique - because math is embraced you do not get watered down half truths, but the real deal. These days, along with Feynman's QED, it is the only lay book I recommend. If you want to study an actual interpretation after reading Susskind, Griffiths (no not that Griffiths who has written widely used textbooks on QM and EM) has kindly made available his textbook on Consistent Histories (CH) for free. I am not saying CH is right or wrong - merely it will acquaint you with the issues:
http://quantum.phys.cmu.edu/CHS/histories.html

Personally, and this is just my opinion, I think CH is just defining your way out of problems instead of facing them head on, but that's just me. It is a perfectly legit interpretation.

Thanks
Bill

 

[Minnesota Joe]

The wavefunction is extended - whether it is an object or not is interpretation dependant. It just encodes probabilities - are actuarial forcasts of life expectancy objects? I am not going to argue either way - but merely point out it is an assumption implied in your language - and we again run into the issue or semantics.

Yes, I shouldn't have used the term 'state', because I didn't mean to take a position on whether or not the wavefunction is "real". The math isn't the phenomenon anyway. The 'object' is whatever it is that is there for Alice and Bob to measure. It is extended in space because Alice and Bob are separated and have something to measure. There are two ends. By referring to it as one object, I was going along with your hypothesis.

Peter was pointing out what is meant by non-locality is semantic. Is it a violation of he cluster decomposition property, or is it a violation of locality in SR ie influences can travel faster than the speed of light.

People use the word 'non-locality' in different ways, yes. But they can't refute the people who argue that EPR-Bell establishes 'non-locality' unless they use the same sense of non-locality as in those arguments.

Here is an example of such a mistake. If I argue, "QM can't be non-local because Alice and Bob can't use entanglement to transmit a message faster than light", then I'm probably the one making a mistake by failing to engage with what physicists mean when they say QM is non-local.

 

[bhobba]

The math isn't the phenomenon anyway.

People like Penrose would challenge that.

We do not know if that something is extended. At some hypothesised sub-quantum level the concepts of extended and place may not even have a meaning This is the whole problem of discussing it in a general way, rather than as part of a well defined interpretation. So pick an interpretation and then we can be more specific.

Thanks
Bill

 

[Minnesota Joe]

We do not know if that something is extended. At some hypothesised sub-quantum level the concepts of extended and place may not even have a meaning This is the whole problem of discussing it in a general way, rather than as part of a well defined interpretation. So pick an interpretation and then we can be more specific.

Thanks
Bill

That's well above my pay grade. Anyway, if we can't even agree on the EPR setup, I don't think I'd be able to understand your proposed explanation of EPR-Bell non-locality either, but thanks for giving it a go.

 

[PeterDonis]

The 'object' is whatever it is that is there for Alice and Bob to measure. It is extended in space because Alice and Bob are separated and have something to measure.

This does not prove that whatever is there for Alice and Bob to measure is a single extended object. That's one possible interpretation, but not the only one.

 

[vanhees71]

Well, but it's what QT says. In an entangled state, like two photon polarizations which can be measured at far distance, the corresponding correlations which are stronger than any local deterministic theory allows (Bell's inequality) indicate that these two photons are indeed a single extended object. At least they are not separable in Einstein's sense.

 

[PeterDonis]

the corresponding correlations which are stronger than any local deterministic theory allows (Bell's inequality) indicate that these two photons are indeed a single extended object

Again, that's one possible interpretation, but not the only one.

 

[Minnesota Joe]

This does not prove that whatever is there for Alice and Bob to measure is a single extended object. That's one possible interpretation, but not the only one.

I wouldn't use the word 'prove' either. I was trying to follow along with Bill's stipulation that the entangled-pair be treated as a single object in order to understand how that removes quantum non-locality. But the single-object-not-spatially-extended-but-present-in-two-places is where it really goes off the rails for me. I no longer understand enough of what Bill is saying to have confidence that I'd recognize it even if he explained how it removed non-locality in QM. Maybe someday, just not today.

 

[PeterDonis]

I was trying to follow along with Bill's stipulation that the entangled-pair be treated as a single object in order to understand how that removes quantum non-locality.

A particular interpretation can't "remove" anything that's predicted by the basic math of QM. Since the basic math of QM predicts violations of the Bell inequalities, "nonlocality" in that sense is predicted by the basic math and no interpretation can "remove" it.

OTOH, since the basic math of QFT predicts that the cluster decomposition principle is obeyed, "nonlocality" in that sense is not predicted by the basic math and there is no need to "remove" anything in that sense.

 

[Minnesota Joe]

A particular interpretation can't "remove" anything that's predicted by the basic math of QM. Since the basic math of QM predicts violations of the Bell inequalities, "nonlocality" in that sense is predicted by the basic math and no interpretation can "remove" it.

OTOH, since the basic math of QFT predicts that the cluster decomposition principle is obeyed, "nonlocality" in that sense is not predicted by the basic math and there is no need to "remove" anything in that sense.

That is very helpful, and I did pick up some of it in your earlier comments, thank you. One of the great things about this site is that people such as yourself give me new things to read and think about. Your warning about relativistic and non-relativistic explanations of the EPR thought experiment is also much appreciated, albeit jarring because a lot of people talk about that non-relativistically.

 

[DrChinese]

1. 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.

2. 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.

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.

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.

I disagree on a number of points.

1. Relativistic considerations change nothing in a Bell test or any quantum analysis of the context. And as I pointed out multiple times (and you recognized as well), causal direction is by assumption only. If you want to say one occurred first, or the other measurement occurred first, or neither: that's fine by me. There have been plenty of published Bell tests where there was strict Einsteinian locality enforced and never is the outcome any different. All of which show that the "instantaneous" action can be demonstrated to occur arbitrarily quickly, and in arbitrary order as well. And as a matter of fact, measurement can be performed in a frame such that one measurement occurs before the other in all frames. Just have Alice and Bob measure in the same place after Bob's particle makes a side trip somewhere, and returns.

The point is: you really hand wave away that Bob's state is steered by Alice (or vice versa) simply by invoking relativistic considerations. It's circular logic. "Something" occurs that violates relativistic norms of causality and propagation limitations when Alice chooses to measure her entangled particle. Saying it is the "system of 2 particles" which is nonlocal (has spatial extent) changes nothing, and ignores the obvious crucial role of the observers in the process. 2. Weinberg was quoted as the generally accepted view that in a Bell test, something changes instantaneously. And I could quote as many others agreeing as anyone would like, including one from bhobba's first reference in the OP.

Weinberg: "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."

Boughn: "Now suppose that the spin of particle 1 is measured with a Stern-Gerlach apparatus oriented in the ˆz direction and is determined to be ↑. The usual statement is that such a measurement instantaneously collapses the wave function of particle 2 such that Ψ(2) = |2, ↓> in the ˆz direction."

To the extent that QFT denies this, it is inconsistent with hundreds of Bell-type experiments - which is why these quotes are out there. And as I have asked many times, I have yet to see any quote from a suitable source that says anything different that what these 2 say. (It would be nice to see something that directly contradicts, not something that must be interpreted by someone else to make the point.) 3. Boughn then goes on to say: "Even if one defines state in such a way that it is changed in the above scenario, the notion of a cause offers little in the way of explanation if no physical model of the cause is offered. "

Apparently, nothing can happen unless a cause is identified. Woe be to acausal theories! Or maybe he means: we'll just ignore that something happens nonlocally if we can't explain it to everyone's satisfaction; i.e. we'll just call it local anyway and go home.

As I said before: if it looks like a duck, and quacks like a duck: it's quantum nonlocal.

---------------------------------------------------------------------------------

Of course, there are interpretations - such as Relational BlockWorld (RBW) - that feature strict Einsteinian locality (nothing is directly FTL) but sacrifice other classical features (such as causality) to achieve a mechanism/description of quantum nonlocality. I wonder if some of the folks here should give that a second look. That is, if you deny Bohmian-type nonlocality. Our fellow PFer @RUTA has co-authored a book* on the subject:

Beyond the Dynamical Universe *Hopefully I will get a commission on all the copies he sells from my plug.

 

[PeterDonis]

Relativistic considerations change nothing in a Bell test or any quantum analysis of the context.

I agree that they don't for me. I'm not sure that's true for you, given the claims you are making about what happens to the the "state" of Bob's particle when Alice makes a measurement. Those claims seem inconsistent with relativity to me. Note carefully that I am not saying the predictions of QM are inconsistent with relativity; they are obviously not. I am saying the claims you are making, which are claims about a particular interpretation of QM that you are using, seem inconsistent with relativity to me.

If you want to say one occurred first, or the other measurement occurred first, or neither: that's fine by me.

How do you reconcile this with your claim that Alice's measurement instantaneously "changes" the "state" of Bob's particle? I don't see how you can.

you really hand wave away that Bob's state is steered by Alice

I'm not the one that is hand-waving about the "state" of Bob's particle. You are, by repeatedly ignoring questions you have been asked about exactly what you mean by such a "state", and how you justify your claim that this "state" changes when Alice makes her measurement. I challenge you to justify that claim by specifying exactly what "change" occurs to the "state" of Bob's particle when Alice makes her measurement, and then showing how this is consistent with relativity.

To the extent that QFT denies this, it is inconsistent with hundreds of Bell-type experiments

I disagree. It is only inconsistent with your interpretation of what is happening in those experiments.

I have yet to see any quote from a suitable source that says anything different that what these 2 say.

I do not see the point of appealing to authority in this discussion. You are making a claim that the "state" of Bob's particle "changes" instantaneously when Alice makes her measurement. You should be able to justify that claim without appealing to authority. And those who disagree with it should be able to justify their disagreement without appealing to authority. I have already tried to do that regarding my disagreement, by pointing out that there is an obvious interpretation of "state" (density matrix) according to which the "state" of Bob's particle does not change at all when Alice makes her measurement. You have yet to respond to this statement of mine. I wish you would.

 

[DrChinese]

In an entangled state, like two photon polarizations which can be measured at far distance, the corresponding correlations which are stronger than any local deterministic theory allows (Bell's inequality) indicate that these two photons are indeed a single extended object. At least they are not separable in Einstein's sense.

1. If those 2 photons are distinguishable, and can be individually manipulated - and still remain polarization entangled: are they 1 quantum object or 2? Obviously, what I am mentioning occurs in many Bell-type tests. The entangled photons can be of different frequencies, for example, and even from different sources. I don't think anything important changes by going down the "one system of 2 particles" path.

An extended system of 2 particles, interacts with 2 distant observers
-------vs--------
2 particles entangled on 1 or more bases, interact with 2 distant observers

FAPP: Same problem as we started with.

2. And all that commentary about "stronger correlations than any local deterministic theory allows" gets us nothing. We're not talking about local deterministic theories, so that's irrelevant. We are discussing the presence of quantum nonlocality in QFT. When there are 100% correlations in Bell tests, this is not something that occurs by coincidence, as you imply. Out of many (infinite?) possible measurement/result pairs, all of them will follow the appropriate conservation rules AND can also be made to violate Bell tests.

There is some type of selection occurring, and it is observer dependent. Obviously.

 

[DrChinese]

I agree that they don't for me. I'm not sure that's true for you, given the claims you are making about what happens to the the "state" of Bob's particle when Alice makes a measurement. Those claims seem inconsistent with relativity to me. Note carefully that I am not saying the predictions of QM are inconsistent with relativity; they are obviously not. I am saying the claims you are making, which are claims about a particular interpretation of QM that you are using, seem inconsistent with relativity to me.

How do you reconcile this with your claim that Alice's measurement instantaneously "changes" the "state" of Bob's particle? I don't see how you can.

...

I do not see the point of appealing to authority in this discussion.

Well, it is normal in PF to cite generally accepted science in support of a position. Which I have. I get that we are in the Interpretations section, so things are looser here (as should be). But it stings a bit to provide appropriate support for a position, just to have that dismissed by calling it an "appeal to authority". If his position is wrong, fine, but I am missing the better explanation.

My position is there is quantum nonlocality, as the Weinberg quote indicates. I quoted him hoping that his words wouldn't be semantically ripped to pieces. Well, that hasn't worked so well for me... so far.

 

[DrChinese]

You are making a claim that the "state" of Bob's particle "changes" instantaneously when Alice makes her measurement. You should be able to justify that claim without appealing to authority. ... You have yet to respond to this statement of mine. I wish you would.

I did, specifically:
Now suppose that the spin of particle 1 is measured with a Stern-Gerlach apparatus oriented in the ˆz direction and is determined to be ↑. The usual statement is that such a measurement instantaneously collapses the wave function of particle 2 such that Ψ(2) = |2, ↓> in the ˆz direction."

This is the same example given everywhere, with only minor differences. That being: before Alice performs a measurement, Bob was NOT in a specific state that could be predicted. And only after Alice selects the nature of her measurement, does Bob then acquire a specific basis for a specific observable that can predicted with 100% certainty. Why on Earth would that "coincide" unless there is a causal relationship with what measurement spacelike separated Alice performs?

Since this is what happens in actual experiments, that should be proof enough.

 

[PeterDonis]

it is normal in PF to cite generally accepted science in support of a position. Which I have.

This is the QM interpretations forum; there is no "generally accepted science" on QM interpretations. There are only various opinions. That's a major reason why this forum was spun off from the regular QM forum.

it stings a bit to provide appropriate support for a position, just to have that dismissed by calling it an "appeal to authority".

You have not given any reference that answers the question I asked about what "state" means, or that responds to the point I made about the density matrix for Bob's particle not changing when Alice makes her measurement. Nor, as I have pointed out, should you need to.

You have also not addressed the point I made about the ordering of the measurements: that if the measurements are spacelike separated, which one comes first is frame-dependent, so there is no valid grounds for treating Alice's measurement as the one that "causes" whatever "change" you think
instantaneously happens.

Basically, what I see you doing is adopting a particular interpretation and failing to acknowledge any issues with it that anyone else points out. And then wondering why you are getting pushback.

My position is there is quantum nonlocality, as the Weinberg quote indicates. I quoted him hoping that his words wouldn't be semantically ripped to pieces.

I don't understand why you would hope that, given that it has already been pointed out in this thread, several times, that the term "quantum locality" has multiple possible meanings. So if you just help yourself to one meaning in this thread and talk as though it's the only possible one, you should expect exactly what you've gotten.

only after Alice selects the nature of her measurement, does Bob then acquire a specific basis for a specific observable that can predicted with 100% certainty.

But Bob doesn't know this basis until after he gets the information from Alice's measurement. Which he can't get before he makes his own if the measurements are spacelike separated. So I don't see how this supports your claim that Alice's measurement instantaneously changes the state of Bob's particle.

this is what happens in actual experiments

No. What happens in actual experiments is that Alice makes a measurement, Bob makes a measurement, and when we collect the data, we find that the correlations between the results violate the Bell inequalities.

All this stuff about instantaneous changes of state only happens in your interpretation. You cannot just help yourself to the claim that whatever your intepretation says happens in reality, actually happens in reality. But that's what you are doing.

 

[vanhees71]

A particular interpretation can't "remove" anything that's predicted by the basic math of QM. Since the basic math of QM predicts violations of the Bell inequalities, "nonlocality" in that sense is predicted by the basic math and no interpretation can "remove" it.

Exactly! It's an interpretation-independent statement, and it's "nonlocality" in the sense of "inseparability"!

 

[vanhees71]

1. If those 2 photons are distinguishable, and can be individually manipulated - and still remain polarization entangled: are they 1 quantum object or 2? Obviously, what I am mentioning occurs in many Bell-type tests. The entangled photons can be of different frequencies, for example, and even from different sources. I don't think anything important changes by going down the "one system of 2 particles" path.

Of course, they can be individually manipulated, because the valid theory to describe them, QED, is a local (sic!) relativistic QFT and the interaction with the measurement device are local. The photons are indistinguishable always. That's forgotten, because people usually write only the polarization part. Doing a complete calculation (which is not more difficult than the shortcut one) shows that photons are indistinguishable. The photons are distinguished by the different momenta they have, but in an entangled state they are not individuals but you have to consider the two-photon state as a whole. They are only separated when A or (and) B make a local single-photon measurement (and take note of the measurement outcome). This "collapse" is purely epistemic in this minimal interpretation, and the appeal of this minimal interpretation is that there's no conflict with the very foundations of QFT (locality of interactions) but still describing the established properties of "inseparability" described by entangled states.

An extended system of 2 particles, interacts with 2 distant observers
-------vs--------
2 particles entangled on 1 or more bases, interact with 2 distant observers

FAPP: Same problem as we started with.

2. And all that commentary about "stronger correlations than any local deterministic theory allows" gets us nothing. We're not talking about local deterministic theories, so that's irrelevant. We are discussing the presence of quantum nonlocality in QFT. When there are 100% correlations in Bell tests, this is not something that occurs by coincidence, as you imply. Out of many (infinite?) possible measurement/result pairs, all of them will follow the appropriate conservation rules AND can also be made to violate Bell tests.

There is some type of selection occurring, and it is observer dependent. Obviously.

The only thing I like to stress is that one should not talk about nonlocality in the context of QFT which are local by construction. It's simply confusing language. Physicists should have a clear language and leave the confusion to the philosophers who make a living out of confusing the issues so that they can write tons of papers debating these confusions without reaching any solution forever!

 

[Morbert]

As an aside, I think the Bertlmann's socks example helps illustrate the underlying assumptions at play in the different interpretations.

In both classical and quantum theories, a system can be characterised by a set of observables $\{f\}$ and a state $S$. Also in both cases, the observables can be considered as elements of an algebra $\mathcal{A}$, and the state as a linear functional on $\mathcal{A}$ that returns an expectation value $S(f)$ for each observable $f$, or equivalently, returns a probability $S(Q)$ for each proposition $Q$ about the system.

For a classical theory, @DrChinese would presumably invoke a further constraint: $S$ is only an objectively real state if the variance of $f$ with respect to $S$ is 0 for all $f$. I.e. if the state ascribes no uncertainty to any observable. And for any proposition $Q$ about the system, we must have $S(Q) = 0$ or $S(Q) = 1$. This extra condition is not (cannot be) applied in a quantum theoretic context. He might consider $S$ to be an objectively real quantum state even if $0 < S(Q) < 1$.

Say Alice and Bob both possesses one of Bertlmann's matching socks. Before Alice observes the colour of her sock, she assigns the sock system a state $S$ such that\begin{eqnarray*}
S(\mathrm{red}_A,\mathrm{red}_B) = S(\mathrm{blue}_A,\mathrm{blue}_B) = 0.5
\end{eqnarray*} I.e. A state that assigns the probability of 0.5 to the proposition that Alice's and Bob's respective socks are red or blue. If Alice observes the colour of her sock to be red, the state instantaneously changes to $S'$ such that\begin{eqnarray*}
S'(\mathrm{red}_A,\mathrm{red}_B) &=& 1\\
S'(\mathrm{blue}_A,\mathrm{blue}_B) &=&0
\end{eqnarray*}An instantaneous change across an extended system? Nonlocality!

@DrChinese might say "aha, but $S$ was not an objectively real state. The system was actually in the objectively real state $S'$ all along and Alice merely learned of the true state by inferring it from her observation, so there was no real change in state, and no nonlocality."

His antirealist interlocutor would say "neither $S$ nor $S'$ were objectively real states. They exist locally in Alice's head and codify her expectations and probabilities for observables and propositions relevant to the system."

 

[DrChinese]

Say Alice and Bob both possesses one of Bertlmann's matching socks. Before Alice observes the colour of her sock, she assigns the sock system a state $S$ such that\begin{eqnarray*}
S(\mathrm{red}_A,\mathrm{red}_B) = S(\mathrm{blue}_A,\mathrm{blue}_B) = 0.5
\end{eqnarray*} I.e. A state that assigns the probability of 0.5 to the proposition that Alice's and Bob's respective socks are red or blue. If Alice observes the colour of her sock to be red, the state instantaneously changes to $S'$ such that\begin{eqnarray*}
S'(\mathrm{red}_A,\mathrm{red}_B) &=& 1\\
S'(\mathrm{blue}_A,\mathrm{blue}_B) &=&0
\end{eqnarray*}An instantaneous change across an extended system? Nonlocality!

@DrChinese might say "aha, but $S$ was not an objectively real state. The system was actually in the objectively real state $S'$ all along and Alice merely learned of the true state by inferring it from her observation, so there was no real change in state, and no nonlocality."

His antirealist interlocutor would say "neither $S$ nor $S'$ were objectively real states. They exist locally in Alice's head and codify her expectations and probabilities for observables and propositions relevant to the system."

1. Agreed, your example is half of the equation we want to explain. That is, the perfect correlations. These correspond to EPR's "elements of reality", the definition of which I have no objection to. That being: if an observable can be predicted with 100% certainty, then there is an element of reality to that observable.

The antirealist says that there is ONLY reality to those observables that can be simultaneously predicted. After Alice's measurement, that is exactly 1 (Bob's). EPR (being realists) assumed that all possible observables were simultaneous elements of reality, a greater assumption. (And an assumption that proved unwarranted.) I (as an antirealist) wouldn't personally argue that the antirealist does not believe in quantum nonlocality. I would simply say that there are a variety of options that exist as "outs". They could be nonlocal too. They certainly "appear" nonlocal, hence why it is called "quantum non-locality". In my book, it should be called "quantum non-reality" instead. But hey, that's just me. Ultimately, they are the same thing. 2. The other half is the Bell issue. Clearly, Bob's outcome cannot be randomly independent of the choice of measurement by Alice. If Bob's outcome were fully independent: Bell inequalities would not be violated, and quantum predictions would be wrong. There MUST be some channel of some kind of communication, influence, selection or otherwise between Alice's setting or particle, and Bob's setting or particle. That being the mystery "channel" we seek to solve. That mystery is precisely what is described by my Weinberg and Boughn quotes, and this is generally accepted by virtually all writers on the subject - and should not need any defense in this thread. I have yet to see a single quote to the contrary, except by PF members quoting themselves.3. So as I see it: we are trying to explain how QFT handles this as a mechanism. And if correctness (or not) of the cluster decomposition property is relevant, great, but experimental considerations don't go out the door just because someone is enamored of theory. I get that QFT makes the correct mathematical predictions, but so did QM from the better part of a century ago. So what can QFT add to this mystery, if anything? As RUTA already pointed out, there seems to be nothing added to the description by QFT. For spin entanglement of photons: matches=cos^2(A-B)