Can Special Relativity Explain the Alice and Bob Spin Measurement Paradox?

[DrChinese]

That's because it doesn't matter. Since the measurements are spacelike separated, they commute: their results do not depend on the order in which they are made. Which is good because the order in which they are made is frame dependent.

That is usually taken to mean that there cannot be any cause and effect relationship between them, since any such relationship would require the order of the measurements to be invariant, and it's not.

I agree with your conclusion about commuting measurements. And yet...

When the outcomes DON'T commute in QM: the order of measurements STILL does not demonstrate a cause and effect relationship, and it is quite impossible to prove Alice (measured first*) influenced Bob more than Bob (measuring second*) influences Alice. @RUTA labels this result as "acausal". @Demystifier says there are superluminal influences but there is no possibility of signaling. @vanhees71 believes all quantum action respects c (implying there is a causal direction) [although how this squares with Bell has always been unclear to me, and probably anyone else who cares to probe his perspective].

@malawi_glenn I think you are right: we lost the OP @AndrzejB a while back... It was around the time he stated "if there were signals they would have to be> c which is impossible. Problem is that it is impossible to say which measurement was the cause of the reduction of the wave function."

He's actually correct: There may not be signals >c, but there could be "influences" >c. And it is in fact impossible to say which measurement is the cause of the "wave packet reduction" (assuming that is a physical process). Clearly, these are interpretation dependent; and that should be our answer.*Of course, non-commuting measurements can be performed that are in the same reference frame... and thus would not be frame dependent in determining sequence order. These might or might not be "spacelike" separated (I would prefer the term "spacetime-like" separated here), depending on your perspective on (or definition of) such requirement. The counter-example I would give is measurements on 2 entangled photons that never co-existed (reference available), but are measured sequentially in the same place. There is no way to conclude the first measurement influences the second any more than vice versa - except by assumption. QM is otherwise silent on this point.

 

[vanhees71]

I agree with your conclusion about commuting measurements. And yet...

When the outcomes DON'T commute in QM: the order of measurements STILL does not demonstrate a cause and effect relationship, and it is quite impossible to prove Alice (measured first*) influenced Bob more than Bob (measuring second*) influences Alice. @RUTA labels this result as "acausal". @Demystifier says there are superluminal influences but there is no possibility of signaling. @vanhees71 believes all quantum action respects c (implying there is a causal direction) [although how this squares with Bell has always been unclear to me, and probably anyone else who cares to probe his perspective].

But that's very easily understood: The violation of Bell's inequality is because of the preparation of the system in an entangled state, i.e., the long-ranged correlations are there because of the preparation of the system. No causal influence of A's on B's or B's on A's measurement is necessary to explain it within relativistic local QFT.

The argument is usually the other way around: One says that there cannot be causal influences between the measurements, because the measurement events are space-like separated, i.e., one takes indeed the microcausality condition for be fulfilled in Nature.

 

[DrChinese]

But that's very easily understood: The violation of Bell's inequality is because of the preparation of the system in an entangled state, i.e., the long-ranged correlations are there because of the preparation of the system. No causal influence of A's on B's or B's on A's measurement is necessary to explain it within relativistic local QFT.

The argument is usually the other way around: One says that there cannot be causal influences between the measurements, because the measurement events are space-like separated, i.e., one takes indeed the microcausality condition for be fulfilled in Nature.

What you mean - and I vehemently disagree with - is: "the long-ranged correlations are there because of the [initial local] preparation of the system. Words in brackets added by me to your statement. Of course, the entangled system has spatial (I would call it "spatiotemporal") extent. And all the questions we have pertain to how we get perfect correlations from the expanded system WITHOUT some kind of FTL influence - since the measurements are made independently later (than your locally prepared solution). Since the entangled system itself has spatial extent and is therefore nonlocal from one spot to another, there is something "nonlocal" going on - which is termed "quantum nonlocality" (because we do not further understand the nature of the nonlocality).

For other readers: the statements of vanhees71 are his opinion, and virtually all those studying Bell and QFT do not share his opinion. To date, he has not produced a single quotation from any well respected source echoing his viewpoint - he just says it is "obvious" from QFT. On the other hand, the statements affirming the existence of "quantum nonlocality" are legion. 2022 Nobel winner Zeilinger: "The nonlocality is confirmed by observing a violation of Bell’s inequality by 4.5 standard deviations. Thus, by demonstrating quantum nonlocality for photons that never interacted [and could therefore not have been prepared initially in the synchronized state vanhees71 imagines], our results directly confirm the quantum nature of teleportation."

To the OP: there is no paradox. Relativistic QM does not offer a local causal mechanism/explanation for Bell type entanglement, and does not offer an FTL signaling mechanism that would violate relativity. Quantum nonlocality coexists with relativity, they operate in different domains.

I do think we have answered the OP. If we want another go at whether QFT demands local causality, that discussion belongs in the Interpretations subforum.

 

[PeterDonis]

Moderator's note: Thread moved to QM interpretations subforum.

 

[PeterDonis]

Since Alice and Bob case is symmetrical, it cannot be said that the first measurement reduced the wave function

In fact, we cannot even say that "reducing the wave function" happens at all (except as a calculational convenience) unless we adopt an interpretation of QM that includes that. Not all interpretations do.

In other words, how the "paradox" you describe is resolved depends on which interpretation of QM you adopt. That is why this thread has been moved to the interpretations subforum.

 

[bobob]

What you mean - and I vehemently disagree with - is: "the long-ranged correlations are there because of the [initial local] preparation of the system. Words in brackets added by me to your statement. Of course, the entangled system has spatial (I would call it "spatiotemporal") extent. And all the questions we have pertain to how we get perfect correlations from the expanded system WITHOUT some kind of FTL influence - since the measurements are made independently later (than your locally prepared solution).

If the two photons have a spacelike seperation when measured, the two photons were always spacelike seperated. The two photons produced by parametric down conversion have never interacted with each other.

Since the entangled system itself has spatial extent and is therefore nonlocal from one spot to another, there is something "nonlocal" going on - which is termed "quantum nonlocality" (because we do not further understand the nature of the nonlocality).

I think the use of the term "non-local" is not helpful here. It is used inconsistently to mean different things in different articles.

For other readers: the statements of vanhees71 are his opinion, and virtually all those studying Bell and QFT do not share his opinion.
To date, he has not produced a single quotation from any well respected source echoing his viewpoint - he just says it is "obvious" from QFT. On the other hand, the statements affirming the existence of "quantum nonlocality" are legion. 2022 Nobel winner Zeilinger: "The nonlocality is confirmed by observing a violation of Bell’s inequality by 4.5 standard deviations.

Again, I don't think the use of "non-local" here means what you are trying to suggest.

Thus, by demonstrating quantum nonlocality for photons that never interacted...

Why do you think the above implies what you have in brackets below?

[and could therefore not have been prepared initially in the synchronized state vanhees71 imagines],

First, the use of synchronized here doesn't relate to the standard usage (as Einstein used it) of the word in which synchronization takes place via causal processes. The two photons are created with a spacelike seperation, so I don't know what synchronization means in that context.

The following article on parametric down conversion might be interesting:

https://arxiv.org/ftp/arxiv/papers/1809/1809.00127.pdf

To the OP: there is no paradox. Relativistic QM does not offer a local causal mechanism/explanation for Bell type entanglement, and does not offer an FTL signaling mechanism that would violate relativity. Quantum nonlocality coexists with relativity, they operate in different domains.

In an earlier post you mentioned "influences" as different from "cause."
How are those not synonymous here? In Bell's type experiments, the measurements are independant of each other, which by definition means the measurements are not causally connected.

 

[gentzen]

I think the use of the term "non-local" is not helpful here. It is used inconsistently to mean different things in different articles.

Sorry, but I find the sentence from DrChinese perfectly understandable. You are free to suggest a reformulation of his sentence. If it should be indeed more understandable, or at least not significantly less understandable to me, than I could be willing to revise my opinion.
Of course, the word "local" means different things in different contexts. But that does not yet imply any inconsistency, or that the word would be "not helpful".

Again, I don't think the use of "non-local" here means what you are trying to suggest.

Can you enlighten me what DrChinese is trying to suggest, from you point of view?

I am neither a fan of bashing the word "local", nor of concluding wrong things from a statement like "QM is nonlocal". I am especially opposed to conclude the false statement "QM is incompatible with special relativity" from the true statement "QM is nonlocal".

 

[martinbn]

What you mean - and I vehemently disagree with - is: "the long-ranged correlations are there because of the [initial local] preparation of the system. Words in brackets added by me to your statement. ...

I don't understand why you disagree with that! Surely the state the system is in is due to the preparation. The state contains all the information about the measurement outcomes. All predictions are based on it and the experiments confirm them.

 

[martinbn]

Nevertheless, relativistic spacetimes admit a causality structure (at least locally), and you can always choose your time-like coordinate such that the causal ordering is as usual, i.e., if two events have a cause and effect relation you can always make the time-like coordinate such that the event at the smaller time coordinate must be the cause.

Coming back to this, which of course is true. The point that I was trying to make was different. Given an event A, all other events can be divided into those in the future of A, in the past of A, and the rest. You can also choose a time coordinate, which gives a label to all events. Then all events can be divided into those with time coordinate bigger than that of A, smaller than that of A or equal to that of A. In classical physics these two divisions are the same (or at least they can be, it depends on how you choose the time parameter). In relativity they are definitely not the same. My statement is that often in the Bell type discussion people forget that. In classical physics if an event B has time coordinate bigger than that of A, then B is in the causal future of A and can be influenced by A. In relativity if B has bigger time coordinate it doesn't mean that it is in the causal future of A. But in these discussions some people try to use that as one of their steps in their arguments to conclude that there are possible influences from A to B.

 

[vanhees71]

What you mean - and I vehemently disagree with - is: "the long-ranged correlations are there because of the [initial local] preparation of the system. Words in brackets added by me to your statement. Of course, the entangled system has spatial (I would call it "spatiotemporal") extent. And all the questions we have pertain to how we get perfect correlations from the expanded system WITHOUT some kind of FTL influence - since the measurements are made independently later (than your locally prepared solution). Since the entangled system itself has spatial extent and is therefore nonlocal from one spot to another, there is something "nonlocal" going on - which is termed "quantum nonlocality" (because we do not further understand the nature of the nonlocality).

There is no FTL influence. The correlations are there due to the preparation made before the measurements. Of course the entangled state has spatial extent, because photons are not localizable at all.

Now we entering the endless debate about locality, and I use locality always in the sense it's understood in the relativistic-QFT community, i.e., a local QFT is a QFT, where the Hamilton density is a function of the field operators and their derivatives at one spacetimepoint and field operators representing local observables, among them the Hamilton density (energy density), commute at space-like separated arguments. This excludes the posibility of faster-than-light causal influences.

There are long-ranged correlations, i.e., observables on a quantum system taken at far-distant places can be strongly correlated although the observables are maximally uncertain due to the preparation of the system. That's what's described by entanglement.

The alleged tension between locality (in the above precise mathematical sense) and long-range correlations are thus not there in relativistic local QFTs, and these theories are in accordance with all observations.

For other readers: the statements of vanhees71 are his opinion, and virtually all those studying Bell and QFT do not share his opinion. To date, he has not produced a single quotation from any well respected source echoing his viewpoint - he just says it is "obvious" from QFT. On the other hand, the statements affirming the existence of "quantum nonlocality" are legion. 2022 Nobel winner Zeilinger: "The nonlocality is confirmed by observing a violation of Bell’s inequality by 4.5 standard deviations. Thus, by demonstrating quantum nonlocality for photons that never interacted [and could therefore not have been prepared initially in the synchronized state vanhees71 imagines], our results directly confirm the quantum nature of teleportation."

Here, Zeilinger uses another notion of locality than that used in relativistic QFT. If you read Zeilinger's scientific papers, it's pretty clear that he is pretty much a follower of the standard Copenhagen interpretation. That "locality" is used with different meanings in different scientific communities is not my fault!

To the OP: there is no paradox. Relativistic QM does not offer a local causal mechanism/explanation for Bell type entanglement, and does not offer an FTL signaling mechanism that would violate relativity. Quantum nonlocality coexists with relativity, they operate in different domains.

I do think we have answered the OP. If we want another go at whether QFT demands local causality, that discussion belongs in the Interpretations subforum.

Now you precisely say, what I'm saying, i.e., you are contradicting yourself. Since this thread is now in the interpretation subforum, I refrain from further following it.

 

[gentzen]

That "locality" is used with different meanings in different scientific communities is not my fault!

Fully agreed. And it is not a problem anyway, in my opinion. Locality is a general concept, not a technical term.

Since this thread is now in the interpretation subforum, I refrain from further following it.

Wow, this sounds to me like you are intentionally bringing up interpretational issues in answers to beginners questions. The corresponding "irony" was already pointed out earlier in this thread:

This, perhaps, is a meta-postulate, that is, a postulate that lies behind "ordinary" postulates. If so, then it belongs to meta-physics, rather than "ordinary" physics. But I know that you don't have a high opinion on meta-physics, so it's a bit ironical that you put such a strong emphasis on a postulate that seems to be a meta-postulate.

Then it belongs to philosophy of science, not to physics proper. But physics, as the most fundamental science, often has aspirations to explain some general scientific principles from more fundamental physics principles.

I guess your reasoning is that other answers already brought it up, and therefore you were kind of forced to react. But I think the deeper issue for you is about how to teach and explain relativistic QT. You somehow believe that teaching QFT right from the start is the only valid answer:

Now the only successful relativistic QT is local (sic!) relativistic QFT, which is constructed such that the causality structure of special relativistic spacetime is fulfilled.

 

[vanhees71]

Fully agreed. And it is not a problem anyway, in my opinion. Locality is a general concept, not a technical term.Wow, this sounds to me like you are intentionally bringing up interpretational issues in answers to beginners questions. The corresponding "irony" was already pointed out earlier in this thread:

This is not an interpretational issue. It's a mathematical issue. Relativistic QFT in its usual form as a local QFT excludes faster-than-light propagation of causal effects/signals. That's not an interpretational but a mathematical fact. Of course we use it to construct the "right" relativistic QTs, because we want to be able to interpret the formalism physically, and physics in the form we know it, implies causality! If you call this an interpretational issue, fine with me.

I guess your reasoning is that other answers already brought it up, and therefore you were kind of forced to react. But I think the deeper issue for you is about how to teach and explain relativistic QT. You somehow believe that teaching QFT right from the start is the only valid answer:

Indeed this horse is beaten to death in this forum, and that's why I don't need to repeat these mathematical arguments again and again.

 

[DrChinese]

1. There is no FTL influence. The correlations are there due to the preparation made before the measurements.

2. Of course the entangled state has spatial extent, because photons are not localizable at all.

3. Here, Zeilinger uses another notion of locality than that used in relativistic QFT. If you read Zeilinger's scientific papers...

1. As I have pointed out a zillion times, the entanglement can be created AFTER Bell measurements are performed. That shows how absurd your argument is.

There is no experimental evidence that indicates that the quantum world respects local causality. And I don't know of any respected author in the field that would agree with you on this point.2. The component photons in actual Bell experiments are localizable to relatively small sections of spacetime. True, they are not exact point particles in the usual sense. But that is NOT the spatial extent I am referring to.

A biphoton has spatial (actually spatiotemporal) extent as its path is shaped by the experimenter on its way to Alice (in one place) and Bob (in another). This is the spacelike separation. Somehow the biphoton is able to "collapse" into 2 separable photons that are consistent with joint measurements by Alice and distant Bob, but are NOT consistent with independent (and therefore separable) measurements by Alice and distant Bob. That's the quantum nonlocality Zeilinger refers to.3. And again, no quotes to support your position. Your quotes are always: a) trust me as I quote myself; or b) read every book or paper ever written, and trust me, there's a quote somewhere. A call for a relevant quote should not go unanswered in PF, and you get away with it far too often.

-DrC

 

[vanhees71]

ad 1) I have repeatedly argued that also entanglement swapping doesn't imply any non-local causal influences. The entanglement swapping is by selecting events based on measurements on entangled systems, i.e., the entanglement of the corresponding subensembles is as well explained by the entanglement of the original systems, and this entanglement was due to the preparation of these systems.

I don't know, what you'd accept as empirical evidence for the locality of interactions. The point is that with local relativistic QFT we have a theory, where all interactions are local, and today there's not a single experiment violating the predictions of local relativistic QFT, i.e., all phenomena can explained with this kind of theory, which is consistent with the relativistic causality structure of spacetime.

ad 2) Now you contradict yourself. In your posting before you emphasized the finite extension of the "wave packets". Now you make a point about the localization of the photons. Indeed what's "localized" are the detection events at A's and B's detectors, and these can indeed by space-like separated, which excludes a causal influence of one of these events on the other, and this assumption is usually made by all experimenters performing such experiments, and this is indeed justified, because these experiments are in accordance with local relativistic QFT! If you deny the validity of the locality (microcausality) principle, you also deny the validity of this argument, which for sure is not denied in all papers on the subject I'm aware of.

The experiments are also independent, as has been demonstrated by randomly choosing the observable measured at A's and B's place independently, again in a way, where relativistic causality excludes a mutual causal influence of one of these choices on the other.

3) As I said before, any paper I know, take the locality assumption as an argument rather than denying it. I think this is once more a misunderstanding, because you don't accept the precise definition of locality as used in relativistic QFT, but I defined precisely what I mean by locality, namely the validity of the microcausality condition for local observables.

 

[StevieTNZ]

Now you precisely say, what I'm saying, i.e., you are contradicting yourself. Since this thread is now in the interpretation subforum, I refrain from further following it.

So are you, by continuing to post in this thread.

 

[martinbn]

1. As I have pointed out a zillion times, the entanglement can be created AFTER Bell measurements are performed. That shows how absurd your argument is.

Correct me if I am wrong but some entanglement is created before the measurements. You cannot have all entanglement created after the measurements. And all swapping happens through local interactions. There is no swapping at a distance, is there?

 

[vanhees71]

Precisely that's my point!

 

[DrChinese]

Correct me if I am wrong but some entanglement is created before the measurements. You cannot have all entanglement created after the measurements. And all swapping happens through local interactions. There is no swapping at a distance, is there?

There is no requirement that the entangled system being tested (via a Bell test) be created before the swap (which creates the entanglement). The decision to do that can be done after the measurements. The swap can be done anywhere, and need not be close (local) to Alice or Bob's measurements. Yes, you are correct that there is some entanglement created before the swap - and keep in mind that the later swap also creates the final entanglement in an apparently retrocausal manner. An entangled system operates in spacetime that has no classical analogy. Alice can observe her particle before Bob's is ever created, and before a swap occurs. How can you begin to describe that in classical terms?

The thing to remember, when considering swapped entanglement experiments, is that the Bell statistics are respected regardless of ordering. Nothing changes when sequence changes, which you would absolutely expect (that it would change) if we were witnessing local causality (which was ruled out by Bell of course).

In any Bell test on a stream of biphotons (created by any means, and regardless of whether post-selection occurs), I can tell Alice and Bob to test polarization at any angle across 360 degrees (essentially a large/infinite number of possibilities). After the swap, we will see perfect correlations (a signature of entanglement) - despite the fact that Alice's portion of the biphoton never interacted in any manner with Bob's portion of the biphoton. The ONLY interaction that occurs is where the swap occurs, which is distant to both Alice and Bob. How is it that these perfect correlations ONLY occur when a swap occurs, despite the swap being distant? Oh, and AFTER the component photons observed have had a change to interact in the beam splitter (in the Bell State Measurement device). Because their interaction is an absolute requirement for us to see the perfect correlations elsewhere! If you sent those same 2 component photons through the BSM in manner in which they DON'T meet, then even when you get the same triggers in the BSM there is no entanglement (and therefore no perfect correlations).

Anyone who claims that post-selection changes the situation (as I have described above) is flat out wrong. The only requirement for swapping is that the component photons arrive together within a narrow time window - something that is a requirement for all Bell tests. And having this interaction occur AFTER the perfect correlations are already recorded proves that local causality cannot be present - and therefore cannot be a feature of QFT. Or any other theory, as we already knew post-Bell.

 

[vanhees71]

This is all clear, but indeed the point is that for entanglement swapping you need two entangled pairs prepared before all the manipulations for swapping are done. After the swapping you have entangled two photons that have never been in causal contact through local measurements.

 

[kurt101]

How can you begin to describe that in classical terms?

I think there is a simple classical explanation that preserves causality with the entanglement swapping experiment.

The entanglement swapping experiment case where the BSM test is done after the measurements can be thought of as the inverse of the basic EPR experiment. In the basic EPR experiment (like Alain Aspect 1983) the two photons are in the same state when they are created at the SPDC and then the "action" that changes the photon states happens afterwards. In the entanglement swapping experiment, in the case where the BSM test is done after the measurements, you are doing the inverse; the "action" happens first when the measurements are done and then the BSM test happens after when you are looking for the condition where the photons are in the same (or perpendicular) state.

In other words, with this explanation, it is the symmetry in the entanglement swapping experiment that tricks you into thinking that true entanglement swapping is happening in all cases, but it does not actually happen in the case where the BSM test is done last.