I Entanglement swapping, monogamy, and realism

[vanhees71]

In the evolution of the full ensemble, 2&3 are not entangled. Does that mean the BSM has no causal effect on anything?

The "causal effect" is "local", i.e., due to the "local interactions" of these two photons with the polarizing beam splitter and the detectors. Any possible causal effect on the outcome of measurements on photons 1 and/or 4 can only be in the future lightcone of the registration of photons 2&3 in this BSM, i.e., if you do the local measurements on photons 1 and 4 spacelike separated from this BSM there cannot be any causal influence of the BSM on photons 1 and 4 before measured, provided you accept microcausality, which seem to be the case in all scientific papers on Bell-test measurements, particularly when it comes to the discussion about the various loopholes.

 

[martinbn]

So the moral is, a projection can create entanglement when the projector is not separable. I'm sure it can be formulated precisely and proved rigorously as a general theorem, but it looks so intuitive that I don't really feel a need for a precision and proof.

If the projector is a product, then it cannot create entanglement. That is clear. It isnt obvious that not being a product is enough to create entanglement.

 

[Morbert]

Yours is not what I would call a realistic interpretation. "Fundamentally coincidence is the driving factor that allows 1 & 4 to be entangled" doesn't make sense, because the BSM is the driving factor. Each and every BSM results in 1 & 4 entanglement, and that does not occur otherwise

Consider a pair of spacelike separated entangled particles in the state $|\uparrow_A\uparrow_B\rangle + |\downarrow_A\downarrow_B\rangle$. You have particle $A$ and I have $B$. You measure $A$ in the $\{\uparrow, \downarrow\}$ basis and obtain the outcome $\uparrow$, so you know that if I measure $B$, I will obtain the outcome $\uparrow$. My questions to you:

i) If, for the same experimental run (i.e. not merely a new/different run) you had instead not performed a measurement, would I still have been guaranteed to obtain the outcome $\uparrow$?

ii) Is your answer to i) interpretantion-dependent, or enforced by the formalism of QM? Or can QM even concern such questions that are not strictly resolvable by experiment?

 

[vanhees71]

If I'm also allowed to answer:

ad i) No, because all you know for the full ensemble is that your particle is ideally unpolarized. You simply get in 50% of the cases up and in 50% of the cases down (in the usual statistical sense).

ad ii) It may be interpretation dependent. At the end all that counts, however, is what's observed in the lab, and in all such experiments all that's observed are the statistical properties predicted by Q(F)T, as measured on sufficiently large ensembles (for a given level of statistical significance), and that's what the Q(F)T formalism predicts in the minimal statistical interpretation, maybe extended by the POVM formalism when weak measurements are performed or to describe the reality of non-ideal preparation and detection equipment.

As far as the physics is concerned, the minimal statistical interpretation is all that's needed. You don't need additional metaphysical balast, including "state collapse", "many worlds", "de Broglie-Bohm trajectories", and all other kinds of esoterics.

 

[Demystifier]

It isnt obvious that not being a product is enough to create entanglement.

It's not enough.

 

[martinbn]

It's not enough.

So, what you hoped for is not true then?

 

[Morbert]

If I'm also allowed to answer:

ad i) No, because all you know for the full ensemble is that your particle is ideally unpolarized. You simply get in 50% of the cases up and in 50% of the cases down (in the usual statistical sense).

What I'm trying to tease out here is the significance of "counterfactual knowledge". All you know for a given experimental run is that your particle is ideally unpolarized. But for this very specific run, you have some knowledge (your observed outcome) that you can premise some counterfactual reasoning on.

We do this in classical scenarios all the time: You are thinking of going for a walk but decide to stay inside. It starts raining. You reason counterfactually that if you had gone for a walk, you would have gotten wet, even though at the beginning of the scenario you didn't know if it would rain.

ad ii) It may be interpretation dependent. At the end all that counts, however, is what's observed in the lab, and in all such experiments all that's observed are the statistical properties predicted by Q(F)T, as measured on sufficiently large ensembles (for a given level of statistical significance), and that's what the Q(F)T formalism predicts in the minimal statistical interpretation, maybe extended by the POVM formalism when weak measurements are performed or to describe the reality of non-ideal preparation and detection equipment.

As far as the physics is concerned, the minimal statistical interpretation is all that's needed. You don't need additional metaphysical balast, including "state collapse", "many worlds", "de Broglie-Bohm trajectories", and all other kinds of esoterics.

The rest of your answer gets closer to what I think is the point of disagreement between you and Dr. Chinese. I think the statistical interpretation discards these kinds of counterfactual scenarios, so that there is no unique answer to i). The significance of your outcome "up" is only the selection of a subensemble of experimental runs, and not some ontological assertion about how the spacelike separated particle would have behaved, contingent on your action. I think this discarding of counterfactual questions as meaningless is how the statistical interpretation stays compatible with locality.

I predict that Dr. Chinese would disagree with the minimalist statistical position, and say that the behaviour of the distant particle (not merely your knowledge of the particle) *is* contingent on whether or not you performed a measurement and observed "up"

[edit] - I'm considering this simple entangled pair because I think it is analogous to the BSM experiment, insofar as there is disagreement about whether the relation between 1 and 4 is contingent on a BSM of 2 and 3

 

[Demystifier]

So, what you hoped for is not true then?

It's true, note that I said "can". Like in "real numbers can have infinite number of non-repeating digits after decimal point".

 

[vanhees71]

What I'm trying to tease out here is the significance of "counterfactual knowledge". All you know for a given experimental run is that your particle is ideally unpolarized. But for this very specific run, you have some knowledge (your observed outcome) that you can premise some counterfactual reasoning on.

There is no "counterfactual knowledge" when you just give the state (in terms of a statistical operator). It describes, how your particle is prepared in each realization of the experiment, defining an "ensemble of equallyt prepared particles". There is no more knowledge than that, and if it's prepared as one particle in a pair of maximally entangled particles, it's perfectly unpolarized.

We do this in classical scenarios all the time: You are thinking of going for a walk but decide to stay inside. It starts raining. You reason counterfactually that if you had gone for a walk, you would have gotten wet, even though at the beginning of the scenario you didn't know if it would rain.

The rest of your answer gets closer to what I think is the point of disagreement between you and Dr. Chinese. I think the statistical interpretation discards these kinds of counterfactual scenarios, so that there is no unique answer to i). The significance of your outcome "up" is only the selection of a subensemble of experimental runs, and not some ontological assertion about how the spacelike separated particle would have behaved, contingent on your action. I think this discarding of counterfactual questions as meaningless is how the statistical interpretation stays compatible with locality.

Physics is about what's observed, and QT with the minimal statistical interpretation used to connect the mathematical formalism with observable facts just tells you about the statistical outcome when measuring what can be measured.

If you measure the spin of a particle in an direction $\vec{n}$, you cannot say anything what would have happened when instead measureing the spin in another direction $\vec{n}'$, which is not collinear to $\vec{n}$. It's simply physically impossible to measure two spin components in different directions. So it's just an empty speculation about something that's not realizable in Nature and thus not part of physics. Indeed this is the merit of the minimal statistical interpretation: It just says what's the meaning of the formalism for real-world observations and not some philosophical (aka esoteric) speculation.

I predict that Dr. Chinese would disagree with the minimalist statistical position, and say that the behaviour of the distant particle (not merely your knowledge of the particle) *is* contingent on whether or not you performed a measurement and observed "up"

[edit] - I'm considering this simple entangled pair because I think it is analogous to the BSM experiment, insofar as there is disagreement about whether the relation between 1 and 4 is contingent on a BSM of 2 and 3

 

[Morbert]

If you measure the spin of a particle in an direction $\vec{n}$, you cannot say anything what would have happened when instead measureing the spin in another direction $\vec{n}'$, which is not collinear to $\vec{n}$.

As an aside, I think with the minimal statistical interpretation we have an even stronger restriction. If you measure the spin of a particle in a direction $\vec{n}$, you cannot say anything about what would have happened when instead measuring the spin in another direction, collinear or otherwise, even the same direction. Counterfactual statements are thoroughly off limits, and we can only concern ourselves with future measurements on the particle or, in statistical language, subensembles of sequences of measurements, selected by the projectors $P_{\uparrow_\vec{n}}, P_{\downarrow_\vec{n}}$

 

[PeterDonis]

I am using the general realist position that John Bell and Einstein use when they refer to spooky action at a distance.

I'm not sure either Bell or Einstein made the same claims as you are making. That is why you should give a specific reference.

in a realist cause and effect interpretation that I am using it is just the test that reveals the correlation, not what causes the correlation.

If you think either Einstein or Bell made this claim, please give a specific reference. On its face, what you describe here and in the rest of your post looks like a local hidden variable interpretation of the sort that is ruled out by Bell's Theorem.

 

[PeterDonis]

Any possible causal effect on the outcome of measurements on photons 1 and/or 4 can only be in the future lightcone of the registration of photons 2&3 in this BSM, i.e., if you do the local measurements on photons 1 and 4 spacelike separated from this BSM there cannot be any causal influence of the BSM on photons 1 and 4 before measured, provided you accept microcausality

As I commented earlier (in response to someone else, I believe), this leads to what seems like a highly implausible conclusion: that the BSM has a causal effect on photons 1 & 4 only for the case where the BSM is in the past light cone of the 1 & 4 measurements. But both experimental results and the QM math predict the same outcomes regardless of the spacetime relationship of the measurements--whether the BSM is in the past light cone, spacelike separated, or in the future light cone of the 1 & 4 measurements. The simplest conclusion from all this is that, whatever is going on, it's the same for all three of those cases, so if whatever is going on can't be a "causal effect" by whatever definition of "causal effect" you are using, this would be the case when the BSM is in the past light cone of the 1 & 4 measurements, as well as when it is not.

 

[vanhees71]

[EDIT: This is not well formulated, as pointed out in #104; One should never discuss QT in words, only in formulae. See the clarification in #105]

There is no causal effect of the BSM on photons 2&3 on the outcome of measurments on photons 1&4 when the BSM and these measurements are space-like separated. This is a mathematical fact, if you use microcausal QFT, but that's not an implausible conclusion, if you accept that the observed entanglement of 1&4 in the ensemble selected through the BSM on 2&3 is due to the correlations described by the entanglement of the photon pairs 1&2 and 3&4 in the initial state, and that's indeed all what the QFT formalism tells you. So there's no "causation" but "correlation", and there's no implausibility or contradiction whatsoever.

Indeed, in this measurement it doesn't matter, whether the BSM on 2&3 and the measurements on 1&4 are space-like or time-like separated. The only point is that if you make sure that the measurements are space-like separated that there cannot be a causal effect of the BSM on the measurement outcome on 1&4, and this argument you find regularly in experiments with entangled states, and indeed this argument is consistent with the microcausality condition of QFT.

E.g., it was a big breakthrough when Zeilinger et al realized the "teleportation protocol" where this spacelike separation was ensured to exclude some (hidden) causal influences, i.e., excluding the "locality loophole". I think this was in a paper in 1997 or so. In fact it was also realized in Aspects seminal measurements in the early 1980ies. If needed, I can try to find the references.

 

[PeterDonis]

if you accept that the observed entanglement of 1&4 in the ensemble selected through the BSM on 2&3 is due to the correlations described by the entanglement of the photon pairs 1&2 and 3&4 in the initial state, and that's indeed all what the QFT formalism tells you.

I don't understand. In the initial state there is no correlation between the 1&2 and 3&4 pairs. So how can there be any correlations between 2&3 or 1&4 in the initial state?

 

[vanhees71]

1&2 are in a Bell state as well as 3&4, i.e., each of these pairs is maximally entangled. There are no correlations between 2&3 or 1&4 in the initial state. I haven't claimed anything like that.

Now if you project to a Bell state of 2&3, in the so prepared subensemble 2&3 are fully entangled, because they are prepared to be in a Bell state. Due to the entanglement of 1&2 and 3&4 this implies that for this subensemble also 1&4 are in a Bell state.

It's a easy, although some elaborate calculation, as described by Jennewein et al in

https://arxiv.org/abs/quant-ph/0201134

It's more easily seen in the 2nd-quantization notation. The four Bell states of a photon pair with momentum labels $j$ and $k$ are created from the Vakuum by
$$\hat{\Psi}_{jk}^{\dagger \pm} \rangle=\frac{1}{\sqrt{2}}[\hat{a}^{\dagger}(\vec{p}_j,H) \hat{a}^{\dagger}(\vec{p}_k,V) \pm \hat{a}^{\dagger}(\vec{p}_j,V) \hat{a}^{\dagger}(\vec{p}_k,H)],$$
$$\hat{\Phi}_{jk}^{\dagger \pm} \rangle=\frac{1}{\sqrt{2}}[\hat{a}^{\dagger}(\vec{p}_j,H) \hat{a}^{\dagger}(\vec{p}_k,H) \pm \hat{a}^{\dagger}(\vec{p}_j,V) \hat{a}^{\dagger}(\vec{p}_k,V)].$$
Then the initial four-photon state can then be written in two forms,
$$|\Psi_{1234} \rangle = \hat{\Psi}_{12}^{\dagger -} \hat{\Psi}_{34}^{\dagger-} |\Omega \rangle,$$
but this can as well be written as
$$|\Psi_{1234} \rangle=\frac{1}{2} (\hat{\Psi}_{23}^{\dagger +} \hat{\Psi}_{14}^{\dagger +} - \hat{\Psi}_{23}^{\dagger -} \hat{\Psi}_{14}^{\dagger -}-\hat{\Phi}_{23}^{\dagger +} \hat{\Phi}_{14}^{\dagger +} + \hat{\Phi}_{23}^{\dagger -} \hat{\Phi}_{14}^{\dagger -})|\Omega \rangle.$$
The former notation shows that photon pairs (12) and (34) are each in the polarization-singlet Bell state but (14) and (23), i.e, are uncorrelated.

The latter notation shows that if you project pair (23) to either of the four Bell state the pair (14) must be found in the same Bell state. In Pan et al's work, which we discuss here, (23) has been projected to the polarization-singlet state, and it has been demonstrated that then also the pair (14) is then in the same polarization-singlet state. This happens with probability 1/4.

 

[PeterDonis]

There are no correlations between 2&3 or 1&4 in the initial state. I haven't claimed anything like that.

Yes, you did, in what I already quoted from you:

the observed entanglement of 1&4 in the ensemble selected through the BSM on 2&3 is due to the correlations described by the entanglement of the photon pairs 1&2 and 3&4 in the initial state

This can only explain entanglement between 1 & 4 if there are correlations between 1 & 4 in the initial state. But now you say (correctly) that there aren't.

 

[vanhees71]

Sigh. What I wanted, of course to say, is that the photons in pair (12) and the photons in pair (34) are entangled. One should never use words. Please see #105 for clarification.

 

[PeterDonis]

What I wanted, of course to say, is that the photons in pair (12) and the photons in pair (34) are entangled.

Yes, I agree with that, in the initial state. But what about the final state, after the BSM is done?

 

[vanhees71]

Yes, I agree with that, in the initial state. But what about the final state, after the BSM is done?

After you project (23) in one of the four Bell states, (14) must necessarily be in the same Bell state (see #105). I think nobody disagrees with this.

The point, however, is that this is not due to some "spooky interaction at a distance" between the spacelike separated BSM projection measurement on (23) and photons 1 and 4 but simply due to the correlations due to entanglement of pair (12) and the entanglement of (34) in the initial state (of course (14) and (23) are not entangled in the initial state).

 

[PeterDonis]

After you project (23) in one of the four Bell states, (14) must necessarily be in the same Bell state (see #105). I think nobody disagrees with this.

Nobody disagrees with the math, but I think there is considerable disagreement on how to interpret it.

simply due to the correlations due to entanglement of pair (12) and the entanglement of (34) in the initial state

But how does this work? The math doesn't say. If you are satisfied with just pointing at the math and leaving any question the math doesn't answer unanswered, that's fine. But many people aren't; that's why this thread exists. And it doesn't seem like that's the position you're taking anyway: you're asserting what I quoted above as an explanation; you're not saying that no explanation is required at all.

On its face, it seems like you are describing a local hidden variable model of the kind that is ruled out by Bell's Theorem.

 

[DrChinese]

Consider a pair of spacelike separated entangled particles in the state $|\uparrow_A\uparrow_B\rangle + |\downarrow_A\downarrow_B\rangle$. You have particle $A$ and I have $B$. You measure $A$ in the $\{\uparrow, \downarrow\}$ basis and obtain the outcome $\uparrow$, so you know that if I measure $B$, I will obtain the outcome $\uparrow$. My questions to you:

i) If, for the same experimental run (i.e. not merely a new/different run) you had instead not performed a measurement, would I still have been guaranteed to obtain the outcome $\uparrow$?

ii) Is your answer to i) interpretantion-dependent, or enforced by the formalism of QM? Or can QM even concern such questions that are not strictly resolvable by experiment?

I would agree with @vanhees71 :

i) No, because all you know for the full ensemble is that your particle is ideally unpolarized. You simply get in 50% of the cases up and in 50% of the cases down (in the usual statistical sense).

DrC: You must look at the full initial and final contexts. The general rule is not to ascribe a specific value to an unmeasured observable.

ii) It may be interpretation dependent. ...

There are interpretations that answer i. differently. A true realistic interpretation would say there is a specific value independent of the act of measurement, even if it is unknowable in principle.

 

[kurt101]

I'm not sure either Bell or Einstein made the same claims as you are making. That is why you should give a specific reference.

What I meant is that Bell or Einstein, used the phrasing of action at a distance in their papers. For example Bell uses it in his BERTLMANN'S SOCKS AND THE NATURE OF REALITY paper: https://hal.science/jpa-00220688/document

If you think either Einstein or Bell made this claim, please give a specific reference.

I don't.

On its face, what you describe here and in the rest of your post looks like a local hidden variable interpretation of the sort that is ruled out by Bell's Theorem.

I am NOT describing a local hidden variable theory. The action that I am using is the spooky action at a distance like Bell uses in his BERTLMANN'S SOCKS AND THE NATURE OF REALITY paper: https://hal.science/jpa-00220688/document.

 

[PeterDonis]

What I meant is that Bell or Einstein, used the phrasing of action at a distance in their papers.

That's just a phrasing to describe the issue. It doesn't describe any particular interpretation.

I am NOT describing a local hidden variable theory.

Then I have no idea what "realist" interpretation you think you are using or what you think it says. All you are doing is describing the issue under discussion. That is pointless; the discussion is not about describing the issue, it's about what possible resolutions of it might be.

 

[DrChinese]

1. After you project (23) in one of the four Bell states, (14) must necessarily be in the same Bell state (see #105). I think nobody disagrees with this.

2. The point, however, is that this is ... simply due to the correlations due to entanglement of pair (12) and the entanglement of (34) in the initial state (of course (14) and (23) are not entangled in the initial state).

1. Agreed by me.

2. What does this even mean? What correlations? You agree that (14) are NOT entangled in the initial state (good, we agree). And all of them (in the ideal case) are entangled in one of the 4 Bell states in the final state (even if that particular state is unknown).

I have said this before: Certainly there is nothing that connects the successful swap to any change in the statistical relationship of the (14) pairs in *your* reading of the experiment. But we are talking about perfect correlations and violation of Bell inequalities here. According to your reading, EVERY entangled pair anywhere in the universe at any time could be shown to have the same Bell correlations with (12) or (34) - and each other. Because in your mind, those correlations are present (pre-existing) in any 2 entangled pairs - they are just waiting to be uncovered. (Since of course, nothing actual happens/changes with a BSM - in your worldview).

How do you make any physical sense of that? Any 2 entangled pairs anywhere have these hidden correlations, waiting to be revealed? Are you really saying that?

 

[mattt]

1. Agreed by me.

2. What does this even mean? What correlations? You agree that (14) are NOT entangled in the initial state (good, we agree). And all of them (in the ideal case) are entangled in one of the 4 Bell states in the final state (even if that particular state is unknown).

I have said this before: Certainly there is nothing that connects the successful swap to any change in the statistical relationship of the (14) pairs in *your* reading of the experiment. But we are talking about perfect correlations and violation of Bell inequalities here. According to your reading, EVERY entangled pair anywhere in the universe at any time could be shown to have the same Bell correlations with (12) or (34) - and each other. Because in your mind, those correlations are present (pre-existing) in any 2 entangled pairs - they are just waiting to be uncovered. (Since of course, nothing actual happens/changes with a BSM - in your worldview).

How do you make any physical sense of that? Any 2 entangled pairs anywhere have these hidden correlations, waiting to be revealed? Are you really saying that?

Yes, he will accept that (because the mathematical analysis will be identical for (1,2)×(3,4) than for (1,2)×(5,6) or any other entangled pair ( (7,8) , (9,10), ... ) created independently anywhere, anytime.

There will be maximally entangled subensembles (1,4) ( or (1,6), or (1,8).... depending on what projection to a BSM State we make with what pairs (2,3) (or (2,5), or (2,7)....) respectively.

He just accepts it as a given (because the mathematics of QM says that) and I think he doesn't need any "more profound" explanation.

In my case, I'm still thinking about it...

 

[kurt101]

Then I have no idea what "realist" interpretation you think you are using or what you think it says. All you are doing is describing the issue under discussion. That is pointless; the discussion is not about describing the issue, it's about what possible resolutions of it might be.

I am trying to get closure on this statement from @DrChinese who said my previous statement "Fundamentally coincidence is the driver factor that allows 1 & 4 to be entangled" doesn't make sense because BSM is the driving factor. I am trying to clarify my statement and I want to know if we understand each other.

Yours is not what I would call a realistic interpretation. "Fundamentally coincidence is the driving factor that allows 1 & 4 to be entangled" doesn't make sense, because the BSM is the driving factor. Each and every BSM results in 1 & 4 entanglement, and that does not occur otherwise.

I am using a very vanilla cause and effect realist interpretation and applying it to the case where the BSM test is done after the measurement of 1 and 4. @DrChinese says the BSM test results in 1 & 4 entanglement, but my interpretation is that the actions prior to the BSM test is what leads to the entanglement.

Here is how I describe this case from the realist perspective:
Measuring the polarization of photon 1 makes the polarizations states of 1 & 2 different. Measuring the polarization of photon 4 makes the polarization states of 3 & 4 different. When photons 2 and 3 are identical in almost all properties including polarization, the BSM test will determine they are indistinguishable and this indicates that the measurements of 1 & 4 are maximally entangled.

And here is how I describe this case differently than @DrChinese
The BSM test is what reveals the correlation, not what causes the correlation. All the actions that happen prior to the BSM test being performed is what causes the correlation between 1 & 4. If you choose not to do the BSM test, the correlation between 1 & 4 is still there, you just don't have a BSM test to select it from your measurement data.

So now that I have clarified my perspective. Is my perspective an acceptable one to hold? And if it is not acceptable, what is wrong with it?

 

[PeterDonis]

Measuring the polarization of photon 1 makes the polarizations states of 1 & 2 different. Measuring the polarization of photon 4 makes the polarization states of 3 & 4 different.

This is "realist", but it isn't local, because 1 & 2 are spatially separated when photon 1 is measured, and 3 & 4 are spatially separated when photon 4 is measured. So this is a nonlocal "action at a distance" model. You might be satisfied with that, but the others that have been objecting to the interpretation @DrChinese has been using won't be; they have been trying to defend a local interpretation, where there is no "action at a distance" even when particles are entangled, so measuring photon 1 can't change anything about photon 2, and measuring photon 4 can't change anything about photon 3.

 

[DrChinese]

I am using a very vanilla cause and effect realist interpretation and applying it to the case where the BSM test is done after the measurement of 1 and 4. @DrChinese says the BSM test results in 1 & 4 entanglement, but my interpretation is that the actions prior to the BSM test is what leads to the entanglement.

Here is how I describe this case from the realist perspective:
Measuring the polarization of photon 1 makes the polarizations states of 1 & 2 different. Measuring the polarization of photon 4 makes the polarization states of 3 & 4 different. When photons 2 and 3 are identical in almost all properties including polarization, the BSM test will determine they are indistinguishable and this indicates that the measurements of 1 & 4 are maximally entangled.

And here is how I describe this case differently than @DrChinese
The BSM test is what reveals the correlation, not what causes the correlation. All the actions that happen prior to the BSM test being performed is what causes the correlation between 1 & 4. If you choose not to do the BSM test, the correlation between 1 & 4 is still there, you just don't have a BSM test to select it from your measurement data.

If you assume Causality (as @vanhees71 does, for example), then naturally your explanation will center on what happens first. It does lead to awkward explanations (as the before/after scenarios will not be consistent).

Also, as @PeterDonis points out in post #117, your explanation is nonlocal - which is fine. QM is "quantum nonlocal." However, the usual point is to maintain Einsteinian causality in which no effect can occur outside of a light cone. So there is that.

 

[kurt101]

It can't reveal any correlation between 1 & 4 that existed before, because there is no correlation between 1 & 4 that existed before. That's obvious from the initial state that was prepared.

The initial state that 1 & 2 were prepared in and 3 & 4 were prepared in are changed prior to when the BSM test is performed. So it is not obvious to me that 1 & 4 were not changed to a maximally entangled state prior to the BSM test.

This is "realist", but it isn't local, because 1 & 2 are spatially separated when photon 1 is measured, and 3 & 4 are spatially separated when photon 4 is measured. So this is a nonlocal "action at a distance" model. You might be satisfied with that,

Yes, I am satisfied with this nonlocal "action" at a distance model.

but the others that have been objecting to the interpretation @DrChinese has been using won't be; they have been trying to defend a local interpretation, where there is no "action at a distance" even when particles are entangled, so measuring photon 1 can't change anything about photon 2, and measuring photon 4 can't change anything about photon 3.

So you are saying @DrChinese and I are not really in any disagreement? I mean we probably have some disagreements in our preferred interpretation (assuming he has one), but that set aside, are you saying he is not saying my interpretation and perspective are not allowed?

 

[PeterDonis]

The initial state that 1 & 2 were prepared in and 3 & 4 were prepared in are changed prior to when the BSM test is performed.

I deleted the post you are quoting here.

I am satisfied with this nonlocal "action" at a distance model.

Ok.

So you are saying @DrChinese and I are not really in any disagreement?

Not if you're OK with nonlocal action at a distance. See his post #118.