How do entanglement experiments benefit from QFT (over QM)?

[DrChinese]

Concerning your example it's very simple. You have a spin-entangled state. Both A and B find completely unpolarized particles when measuring their spin. Due to the entanglement, when they compare their measurement protocol (taking carefully appropriate time stamps to know which of each spins are from one and the same entangled pair, they'll find 100% correlation, when measuring in the same direction $\theta$. This is due to the preparation at the very beginning, before any further manipulations where done. It doesn't matter in which temporal order A and B make their measurements. If the measurement events are space-like separated it's for sure that A's measurement cannot have in any causally influenced B's spin nor can B's measurement have in any way causally influenced A's measurement. That's ensured theoretically by the validity of the microcausality property and the only conclusion is that the correlation found is simply due to the preparation in the spin-entangled state in the very beginning.

Here are points of departure:

1. If they evolved independently after state preparation, obviously they could be described by Product State statistics. This is the very definition of a Local Realistic explanation, and therefore flat out prohibited by Bell. Certainly you know all this, so why would you use this explanation?

2. Your explanation does not involve QFT. This same explanation was used in 1935 in EPR. The point of my question, phrased as it was, was to get an explanation of QFT's solution to the issue that works for a simple case (although obviously NOT using local hidden variables, which are excluded), and then you could walk me through how that is extended to a more complex case.

3. You assume: "If the measurement events are space-like separated it's for sure that A's measurement cannot have in any causally influenced B's spin nor can B's measurement have in any way causally influenced A's measurement." This argument is purely tautological, as this is the entire point in question.

In fact. that is almost verbatim what Bell started with and went on to disprove: "The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b." No theory, after Bell, and including QFT, can be local in the manner you describe (no FTL influences), with classic forward in time causality, without being contextual (i.e. observer/measurement dependent) in some non-classical manner. I am hoping you can explain how I am wrong about this point. I am definitely hoping to learn more from you, and if you have any specific quotes, that would be great too. Ah, and I just realized @bhobba shares your position (I'm sure others do too, but I never read them elsewhere).

 

[atyy]

QED is relativistic when everything is treated relativistically, including the electrons. Of course for the local interaction of the em. field with an atom within a solid (i.e., your detector) you don't need the full relativistic treatment. I guess, it's pretty difficult to describe the photoeffect within a fully relativistic model since you need the electron in a bound state being scattered into a continuum state by the interaction with the em. field, and bound states are hard to describe relativistically.

On the other hand, it can be done of course perturbatively too, e.g., for the hydrogen atom neglecting the motion of the proton. Then it boils down to use the Coulomb gauge and use an interaction picture, where $\hat{H}_0$ includes the Coulomb part of the interaction between the nucleus (treated as a fixed center) and the electron. Then you get nice approximate bound and scattering states for this Coulomb problem. The rest can then be done perturbatively in the usual way, leading to utmost precise predictions like the Lamb shift. See Weinberg QT of Fields Vol. I.

Of course you can also use perturbation theory to treat the photoeffect, i.e., the absorption of a photon by some bound state of the hydrogen atom leading to the emission of the photoelectron which can be used to register the photon.

There is have no theory at the moment, which is why most people take the effective field theory point of view of QED - including Weinberg.

 

[DarMM]

There is have no theory at the moment, which is why most people take the effective field theory point of view of QED - including Weinberg.

I would say it's the Landau pole that motivates that more so. There's also no theory for Yang Mills, but the view that it needs an effective field theory treatment isn't as common. QED is usually thought to be trivial due to this pole. Although in my opinion it's a weak argument in light of explicitly constructed models that have a perturbative Landau pole.

 

[atyy]

I would say it's the Landau pole that motivates that more so. There's also no theory for Yang Mills, but the view that it needs an effective field theory treatment isn't as common. QED is usually thought to be trivial due to this pole. Although in my opinion it's a weak argument in light of explicitly constructed models that have a perturbative Landau pole.

Yes, but I don't think considering interactions gives anything beyond the free theory. The free theory is relativistic and rigorous. The interacting theory considerations can either lead to a rigorous relativistic theory, or it could be consistent with a non-relativistic theory from the which the relativistic low energy theory is emergent. In the former case we would reach the same conclusions as for the free theory, in the latter case we would say relativity is not important for foundational considerations.

 

[Demystifier]

Yes, but I don't think considering interactions gives anything beyond the free theory. The free theory is relativistic and rigorous. The interacting theory considerations can either lead to a rigorous relativistic theory, or it could be consistent with a non-relativistic theory from the which the relativistic low energy theory is emergent. In the former case we would reach the same conclusions as for the free theory, in the latter case we would say relativity is not important for foundational considerations.

"I saw from this that to understand quantum field theories I would have to understand quantum field theories on a lattice."
- K. Wilson (Reviews of Modern Physics 55, 583 (1983))

 

[Lord Jestocost]

Both A and B find completely unpolarized particles when measuring their spin. Due to the entanglement, when they compare their measurement protocol (taking carefully appropriate time stamps to know which of each spins are from one and the same entangled pair, they'll find 100% correlation, when measuring in the same direction θ\theta. This is due to the preparation at the very beginning, before any further manipulations where done. [bold by LJ]

Maybe, you overlook something when pointing to the preparation.

J. Bell in “BERTLMANN’S SOCKS AND THE NATURE OF REALITY”:

“Let us summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. But this has implications for non-parallel settings which conflict with those of quantum mechanics. So we cannot dismiss intervention on one side as a causal influence on the other.”

This is commented on https://www.mathpages.com/home/kmath731/kmath731.htm

“Here he is explaining why, if we rule out communication, the perfect anti-correlation at equal angles obliges us to admit that the results are determined in advance, by common cause, i.e., by extra variables. This is not an assumption, it is the only remaining causal option, deduced from the assumption of separability combined with the perfect anti-correlation at equal angles.”

 

[vanhees71]

Here are points of departure:

1. If they evolved independently after state preparation, obviously they could be described by Product State statistics. This is the very definition of a Local Realistic explanation, and therefore flat out prohibited by Bell. Certainly you know all this, so why would you use this explanation?

2. Your explanation does not involve QFT. This same explanation was used in 1935 in EPR. The point of my question, phrased as it was, was to get an explanation of QFT's solution to the issue that works for a simple case (although obviously NOT using local hidden variables, which are excluded), and then you could walk me through how that is extended to a more complex case.

3. You assume: "If the measurement events are space-like separated it's for sure that A's measurement cannot have in any causally influenced B's spin nor can B's measurement have in any way causally influenced A's measurement." This argument is purely tautological, as this is the entire point in question.

In fact. that is almost verbatim what Bell started with and went on to disprove: "The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b." No theory, after Bell, and including QFT, can be local in the manner you describe (no FTL influences), with classic forward in time causality, without being contextual (i.e. observer/measurement dependent) in some non-classical manner. I am hoping you can explain how I am wrong about this point. I am definitely hoping to learn more from you, and if you have any specific quotes, that would be great too. Ah, and I just realized @bhobba shares your position (I'm sure others do too, but I never read them elsewhere).

(1) The state and operators evolve according to the Hamiltonian of the system. If you have free photons the entangled state stays an entangled state and does not change into a product state. How you come to this idea from what I wrote, I don't know.

(2) My explanation does involve QFT. I wrote creation and annihilation operators for photons. The original EPR paper was not about relativistic QT. It was only among the first papers explicitly hinting at what was shortly thereafter called entanglement. The EPR paper is, by the way, much overrated. Einstein himself didn't like it much, because his main point has not been made clear. For him the main quibble was "inseparability" and not "non-locality".

(3) It's not tautological. It's of course the very assumption made to formulate the appropriate QFTs, i.e., those leading to Poincare invariant (co-variant) S-matrices fulfilling the cluster-decomposition principle.

Again: QFT is local in the interactions, but still enabling the inseparability of far-distant parts of quantum systems through entanglement. That's what's built in in the very beginning. Bell defines local deterministic hidden-variable models showing that these must obey the Bell inequalities, which are violated by all QTs (relativistic as well as non-relativistic). Relativistic QFT is local in the interactions but not deterministic, i.e., it violates the Bell inequalities in a way which is consistent with relativistic causality principles. All very accurate Bell tests confirm the predictions of Q(F)T, not the predictions of local deterministic hidden-variable theories. It's the great merit of Bell's idea to make in this way a before purely philosophical question scientific in the sense that the hypotheses (local deterministic HV theories versus relativistic microcausal QFT) can be objectively tested. The local deterministic HV theories are disproven by the corresponding experiments, while the predicts of relativistic microcausal QFT are confirmed. That's why the standard interpretation is that local deterministic HV theories are ruled out, and QFT is the correct description.

 

[vanhees71]

Maybe, you overlook something when pointing to the preparation.

J. Bell in “BERTLMANN’S SOCKS AND THE NATURE OF REALITY”:

“Let us summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. But this has implications for non-parallel settings which conflict with those of quantum mechanics. So we cannot dismiss intervention on one side as a causal influence on the other.”

This is commented on https://www.mathpages.com/home/kmath731/kmath731.htm

“Here he is explaining why, if we rule out communication, the perfect anti-correlation at equal angles obliges us to admit that the results are determined in advance, by common cause, i.e., by extra variables. This is not an assumption, it is the only remaining causal option, deduced from the assumption of separability combined with the perfect anti-correlation at equal angles.”

The entangled state predicts the probabilities for the outcome of measurements. Each of the local observers can of course freely choose their local experimental setup, and the entangled state describes all correlations the preparation in this state implies. All these predictions are confirmed by very accurate experiments today, including the violation of Bell's inequality but confirming the prediction of this violation by QT precisely.

For me this implies clearly that all there is is the quantum state, and the prepation in the entangled state is the only cause for the correlations it describes. The single outcomes are maximally indetermined, but there's no other needs to describe the correlations accurately than the QT formalism itself. The conclusion that there must be hidden variables making a deterministic local world view consistent with these results is disproven by these experiments. There's only QT, and one must accept the irreducible randomness of nature or find a new non-local determinsitic theory which is conistent with both these findings and with Einstein causality, i.e., it must be at least as successful and consistent as relativistic QFT is. Obviously up to today nobody has found such a theory.

As long as this is the case we have to live with QFT, and indeed QFT is not contradicting any empirical findings. So there's no need for a new theory from this point of view. A real physical problem is the lack of understanding of gravity, and that may be even related to these questions of entanglement, correlations, locality and all that.

 

[DarMM]

Yes, but I don't think considering interactions gives anything beyond the free theory. The free theory is relativistic and rigorous. The interacting theory considerations can either lead to a rigorous relativistic theory, or it could be consistent with a non-relativistic theory from the which the relativistic low energy theory is emergent. In the former case we would reach the same conclusions as for the free theory, in the latter case we would say relativity is not important for foundational considerations.

I agree in the case of classifying mechanisms for entanglement. For other foundational issues I would say it does matter since it changes the structure of the state space quite a bit. Although I realize your remarks were only about entanglement mechanisms.

 

[bhobba]

I am definitely hoping to learn more from you, and if you have any specific quotes, that would be great too. Ah, and I just realized @bhobba shares your position (I'm sure others do too, but I never read them elsewhere).

I was unsure whether to reply here because both Vanhees and Dr Chinese are two of my favorite posters. I have posted my view on EPR many times. It is a minority view. It disputes nothing in Bells work who I consider a physicist on a par with the greats like Fermi, Feynman etc. It's just a different way of looking at it.

First, as can be seen in Charter 3 of Ballentine ordinary QM (ie Schrodinger's Equation etc) are derived from the assumption of the Galilean Transformation which automatically implies non-locality is possible. Of course that changes Bell in no way but does put non-locality in a different light - if there is non-locality its not really against QM like some seem to think. To further investigate the issue of locality in QM you really need QFT. But in QFT locality is replaced by the cluster decomposition property:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/
In that principle to avoid possible problems IMHO its best to avoid correlated systems from discussions about locality in the first place. So my view is while Bell's Theorem is both interesting and true its not something people should worry about. You simply say including correlations in locality discussions makes QFT harder than it needs to be, and IMHO its already hard enough, then move on,

Just to be sure my position is understood - in discussions on locality you really need QFT. But including correlations in that, while allowable, complicates things. Bell would have known this, but chose to investigate including it. Others however did not seem to cotton onto one can take the position its not something you really need to worry about in issues of locality - and I personally do not.

Thanks
Bill

 

[DrChinese]

(1) The state and operators evolve according to the Hamiltonian of the system. If you have free photons the entangled state stays an entangled state and does not change into a product state. How you come to this idea from what I wrote, I don't know.

QFT is local in the interactions, but still enabling the inseparability of far-distant parts of quantum systems through entanglement.

I guess it's best to do this an idea at a time.

You said earlier on the one hand: that entangled pairs evolve such that neither it affected by a measurement of the other. To me, that says they evolve independently. Any pair of anything that evolve causally independently of each other would have Product State statistics, and could not have Entangled State statistics.

On the other hand: you just stated that the distant subsystems are inseparable (which of course I agree with). There is no useful meaning to your description of that single entangled system as "inseparable" unless a measurement on one component of the system affects another component of that system (regardless of actual mechanism). Of course, we call that effect "quantum nonlocality" and it cannot be limited to a forward looking light cone (as you imply).

So how are distant parts of an entangled system considered inseparable, while measurements on those parts are made locally without some kind of distant impact? Bell has something to say about that, and you seem to skip past that at every turn.

 

[DrChinese]

I was unsure whether to reply here because both Vanhees and DrChinese are two of my favorite posters.

Before I dig into the meat of your post, I'd like to address your kind comment.

I am not asking anyone to take sides with me against vanhees71, and I certainly respect almost everything vanhees71 adds to this forum. While his and my interactions of late seem acrimonious on some levels, I can assure you that I am truly interested in hearing the other side of opinions, viewpoints, perspectives, etc. I am perfectly happy to adjust my own perspective as I gain new knowledge. Please don't feel you need to sugarcoat anything on my behalf.

 

[bhobba]

So how are distant parts of an entangled system considered inseparable, while measurements on those parts are made locally without some kind of distant impact? Bell has something to say about that, and you seem to skip past that at every turn.

Its in the fact the observable of one part of an entangled system is a more complicated thing than a single non-entangled system.

Thanks
Bill

 

[A. Neumaier]

I guess it's best to do this an idea at a time.

You said earlier on the one hand: that entangled pairs evolve such that neither it affected by a measurement of the other. To me, that says they evolve independently. Any pair of anything that evolve causally independently of each other would have Product State statistics, and could not have Entangled State statistics.

On the other hand: you just stated that the distant subsystems are inseparable (which of course I agree with). There is no useful meaning to your description of that single entangled system as "inseparable" unless a measurement on one component of the system affects another component of that system (regardless of actual mechanism). Of course, we call that effect "quantum nonlocality" and it cannot be limited to a forward looking light cone (as you imply).

So how are distant parts of an entangled system considered inseparable, while measurements on those parts are made locally without some kind of distant impact? Bell has something to say about that, and you seem to skip past that at every turn.

Its inaccurate to talk about a pair of photons traveling. What travels is a single quantun system in an entangled 2-photon state. In QFT it is impossible to separate this system into two photons. This is called inseparability.

 

[bhobba]

Please don't feel you need to sugarcoat anything on my behalf.

I wasn't being 'kind' just telling the truth.

Many people here, including yourself and Vanhees know more physics than I do. I am sorry, when discussing physics with these people I am 'cautious' about what I say, which may come across as sugar-coating - its not something I can easily stop doing.

Thanks
Bill

 

[DrChinese]

Its inaccurate to talk about a pair of photons traveling. What travels is a single quantun system in an entangled 2-photon state. In QFT it is impossible to separate this system into two photons. This is called inseparability.

I couldn't agree more. Although it's common practice to reference each as subsystems (or components) simply for shorthand purposes (since they eventually result in 2 particles).

However, you eventually have the combined system breaking out into what becomes 2 independent single particle systems (for example an entangled pair of electrons becomes 2 unentangled electrons). We don't know exactly when or how that happens (from experimental considerations), just that at some later time, that's what we find.

[entangled system with particle number=2] -> [independent particle A] + [independent particle B]

But while it is an inseparable system: it has both spatial and/or temporal extent... and therefore it should not be thought of as a localized quantum object. And clearly, the nature of an observation on one of the components somehow affects the other - or vice versa. Or it is mutual. I don't know. But clearly trying to describe it initially as 2 independent components can't be right (as you rightfully object); and trying to describe the correlated results as independently arrived at also can't be right (as Bell would object).

So I again ask: if we start with an entangled system which has spatial extent, and we measure one of the components A: how does the other B come into being with some observable strongly correlated to the A component?

And of course, I am asking how QFT would handle that, as vanhees71 asserts it offers an explicit local mechanism. (And I don't think it does, because of Bell.)

 

[bhobba]

Its inaccurate to talk about a pair of photons traveling. What travels is a single quantun system in an entangled 2-photon state. In QFT it is impossible to separate this system into two photons. This is called inseparability.

Its responsible for why its not like the classical green and red slip discussion in articles on EPR. The slips are always separate objects - in QM if entangled that's not true - they are inseparable, but of course you can still observe each part - but the observable is different to the observable if that part was a single system - it acts on the whole entangled system. Its also the usual starting point of discussions on decoherence even though by itself is not quite what we think of as decoherence which usually includes an environment as well.

Thanks
Bill

 

[DarMM]

Well in a sense inseperability isn't that odd or shocking. Classical statistical theories have inseparability as well since in general the distribution for two observables does not factor, i.e. $p(a,b) \neq p(a)p(b)$. However pure states would always factor.

If the classical theory has an epistemic limit then we would have the interesting feature that there can be pure states do not factor, just like quantum theory.

Thus inseparability is not unique to QM.

It's really the violation of the CHSH inequalities (or generalizations thereof) by a subset of entangled states that's the "shocking" part of QM.

 

[bhobba]

So I again ask: if we start with an entangled system which has spatial extent, and we measure one of the components A: how does the other B come into being with some observable strongly correlated to the A component?

That's axiom 1 in Ballentine. Why is the outcome an eigenvalue, and why is it the particular eigenvalue that is observed. We do not know, or even if its an in issue to worry about. By construction the particular observation of this single system is |a>|b> or |b>|a>. How the entangled system is prepared ensures |a> and |b> are correlated,

As I have mentioned my view is correlated systems is difficult to include in discussions of locality because by construction they always have a certain relationship.

Thanks
Bill

 

[DrChinese]

As I have mentioned my view is correlated systems is difficult to include in discussions of locality because by construction they always have a certain relationship.

No issue there. And I would call that relationship "quantum nonlocal". It certainly shouldn't be called "local" (or anything that implies that c is respected in the process of the entangled system evolving into 2 independent particles in a Product State). Obviously, the distance between a) the measurement that terminates the entanglement; and b) the other now independent partner; is too great for that.

 

[A. Neumaier]

No issue there. And I would call that relationship "quantum nonlocal". It certainly shouldn't be called "local" (or anything that implies that c is respected in the process of the entangled system evolving into 2 independent particles in a Product State). Obviously, the distance between a) the measurement that terminates the entanglement; and b) the other now independent partner; is too great for that.

The 2-particle systen is already nonlocal, so it shouldn't be surprising that it generates nonlocal effects. The intuitive problems come solely from treating the system as two separate entities - which it never is. Only the recorded events are separate things.

 

[DennisN]

Interesting discussion going on here!

The intuitive problems come solely from treating the system as two separate entities - which it never is. Only the recorded events are separate things.

With "recorded events" I assume you mean when the detectors detect the events, or? If so, is an entangled photon pair (system) a nonseparate entity after one (or the other) photon passes a polarizer? I'm a bit confused .

 

[DrChinese]

Interesting discussion going on here!

With "recorded events" I assume you mean when the detectors detect the events, or? If so, is an entangled photon pair (system) a nonseparate entity after one (or the other) photon passes a polarizer? I'm a bit confused .

That is a tough question to answer. The general thinking has long been that polarizer outputs (for A) could be recombined to restore the original entangled system (of A+B). And regardless of that, it is not clear whether the OTHER part of the entangled system (B) changes when a final measurement is made on A or only when B itself is measured. I think all of that is interpretation dependent, lacking experimental clarity.

 

[DrChinese]

A previous reference posted by someone related to this thread (I forget who) says:

Relativistic causality =
No signaling = "...the local probability distributions of one experimenter (marginal probabilities) are independent of another experimenter’s choices."

Their definition more or less matches the microcausality of vanhees71. And they reference:

https://arxiv.org/abs/quant-ph/9508009Daniel Rohrlich and Sandu Popescu (1995)

"Quantum mechanics and relativistic causality together imply nonlocality: nonlocal correlations (that violate the CHSH inequality) and nonlocal equations of motion (the Aharonov-Bohm effect) "

So this is what I deduce from above:

a) We have a theory (QFT) that embeds relativistic causality (no signaling) explicitly.
b) There is (traditional) quantum nonlocality within that theory, as relates entanglement and some other effects.

The result is a theory that respects "no signaling" but reproduces the Entangled State statistics of QM. That would explain (to some extent) why vanhees71 insists there is microcausality in QFT, but why I insist that quantum nonlocality is a generally accepted feature of generally accepted quantum theories. You could even say we are both correct.

 

[A. Neumaier]

A previous reference posted by someone related to this thread (I forget who) says:

Relativistic causality =
No signaling = "...the local probability distributions of one experimenter (marginal probabilities) are independent of another experimenter’s choices."

Their definition more or less matches the microcausality of vanhees71. And they reference:

https://arxiv.org/abs/quant-ph/9508009Daniel Rohrlich and Sandu Popescu (1995)

"Quantum mechanics and relativistic causality together imply nonlocality: nonlocal correlations (that violate the CHSH inequality) and nonlocal equations of motion (the Aharonov-Bohm effect) "

So this is what I deduce from above:

a) We have a theory (QFT) that embeds relativistic causality (no signaling) explicitly.
b) There is (traditional) quantum nonlocality within that theory, as relates entanglement and some other effects.

The result is a theory that respects "no signaling" but reproduces the Entangled State statistics of QM. That would explain (to some extent) why vanhees71 insists there is microcausality in QFT, but why I insist that quantum nonlocality is a generally accepted feature of generally accepted quantum theories. You could even say we are both correct.

If quantum nonlocality is defined as the possibility of violation of Bell inequalities then causality and quantum nonlocality coexist in relativistic QFT.

 

[A. Neumaier]

That is a tough question to answer. The general thinking has long been that polarizer outputs (for A) could be recombined to restore the original entangled system (of A+B). And regardless of that, it is not clear whether the OTHER part of the entangled system (B) changes when a final measurement is made on A or only when B itself is measured. I think all of that is interpretation dependent, lacking experimental clarity.

A polarizer is a dissipative instrument, hence such a recombination is impossible. A recombination is in principle possible, however, for passing a Stern-Gerlach magnet, which is a unitary process.

 

[A. Neumaier]

Interesting discussion going on here!

With "recorded events" I assume you mean when the detectors detect the events, or? If so, is an entangled photon pair (system) a nonseparate entity after one (or the other) photon passes a polarizer? I'm a bit confused .

Yes, events are detection events. What happens at an event is interpretation dependent.

In interpretations where the state represents knowledge, different observers continue with different states. For the analysis of the complete nonlocal experiment, the perspective of the observer having the complete information is relevant. It's view of the state involves nonlocal information in its past light cone only, hence is fully compatible with relativity.

In the Bohmian interpretation, nothing at all happens to the state when a detectors detects an event. The detector simply records a particle at its position.

 

[Cthugha]

However, you eventually have the combined system breaking out into what becomes 2 independent single particle systems (for example an entangled pair of electrons becomes 2 unentangled electrons). We don't know exactly when or how that happens (from experimental considerations), just that at some later time, that's what we find.

[entangled system with particle number=2] -> [independent particle A] + [independent particle B]

Personally, I find this an odd way of labeling it. You have a spatially extended field and a measurement puts it into an eigenstate corresponding to the measurement. This is not really different for entanglement compared to standard qm in spatially extended systems. If you have a spatially extended wavefunction for an electron, which spans from here to the moon and perform a measurement on it and find it here on earth, you also immediately know that the probability to detect it on the moon at the same time will be 0. Here, you also can assume non-local influences if you consider the wavefunction to be an real or you can assume that the wavefunction is a bookkeeping device representing knowledge that is not "real" and do not need non-local influences. These basic options do not change when considering entanglement.

For some reason some people started calling any violation of Bell inequalities non-locality at some point, which is somewhere between odd and unwarranted because it favors one of this alternatives over the other without any experimental evidence. From my point of view, it is perfectly okay to claim that inside a realist interpretation, violation of Bell inequalities equate non-locality, but people rarely care to mention that this logical step depends on the interpretation used.

 

[vanhees71]

I agree in the case of classifying mechanisms for entanglement. For other foundational issues I would say it does matter since it changes the structure of the state space quite a bit. Although I realize your remarks were only about entanglement mechanisms.

What do you mean by "mechanisms for entanglement"? It's all explained by QT, and there are several ways to prepare entangled states (of course you have to mention which observables are entangled to be concrete).

One example is the preparation of entangled states via local interactions (and all intereactions are local within relativistic QFT!): E.g., in the original Michelson Morley experiment the decay of an unstable "particle" into two particles leads to the creation of an (asymptotic free) two-particle state, where energies, momenta, and angular momenta/spin are entangled due to the validity of conservation laws.

More common today are the ubuiquitously used biphotons produced via parametric down conversion, where again the same principle of dynamically generated entangled state holds.

Another way is "entanglement swapping". Here you prepare two independent entangled systems (e.g., two biphotons) and perform a filter measurement on partial systems of each of these systems. The subensemble(s) passing the filter(s) are entangled, and indeed here far distant parts of the two systems that have never been in any causal contact with each other are entangled, but the selection of the subensemble is due to bringing two independent local measurement processes in coincidence. Also here no violations of relativsitic causality is needed to explain the correlations encoded in the descxription by entangled state: Everything is due to the initial preparation in (partially) entangled states.

I guess, there might be more prepration procedures for entangled states, which is how I'd translate the sloppy term "mechanism for entanglement" into more precise language, but as long as all results are consistent with relativistic QFT there's no faster-than-light causal effects necessary to explain them.

 

[vanhees71]

Before I dig into the meat of your post, I'd like to address your kind comment.

I am not asking anyone to take sides with me against vanhees71, and I certainly respect almost everything vanhees71 adds to this forum. While his and my interactions of late seem acrimonious on some levels, I can assure you that I am truly interested in hearing the other side of opinions, viewpoints, perspectives, etc. I am perfectly happy to adjust my own perspective as I gain new knowledge. Please don't feel you need to sugarcoat anything on my behalf.

I've no problems with this. Only claiming, another poster provides "minority opinions" goes too far, particularly given the fact that your conclusion of acausality and non-locality based on an alternative model (local deterministic hidden-variable theory a la Bell) which is, according to the opinion of the vast majority of physicists working in the field, disproven with the plethora of Bell tests having been performed (and nearly every day you find new papers on this elucidating various aspects of the issue). That's why my answers also got sharper with the time, but indeed it's all about understanding the science!

 

[DarMM]

What do you mean by "mechanisms for entanglement"?

Explanations for what is occurring to generate the correlations in entangled particles as classified by which assumption of Bell's theorem they reject. It has nothing to do with you are discussing, i.e. preparations of entangled states and thus isn't a "sloppy term" for that concept.

local deterministic hidden-variable theory

I think it's pretty clear @DrChinese isn't saying that.

 

[vanhees71]

I guess it's best to do this an idea at a time.

You said earlier on the one hand: that entangled pairs evolve such that neither it affected by a measurement of the other. To me, that says they evolve independently. Any pair of anything that evolve causally independently of each other would have Product State statistics, and could not have Entangled State statistics.

On the other hand: you just stated that the distant subsystems are inseparable (which of course I agree with). There is no useful meaning to your description of that single entangled system as "inseparable" unless a measurement on one component of the system affects another component of that system (regardless of actual mechanism). Of course, we call that effect "quantum nonlocality" and it cannot be limited to a forward looking light cone (as you imply).

So how are distant parts of an entangled system considered inseparable, while measurements on those parts are made locally without some kind of distant impact? Bell has something to say about that, and you seem to skip past that at every turn.

The distant parts are inseparable due to the preparation in an entangled state. The correlations are implied by this initial (!) state preparation and not caused by local measurements on one part.

Bell has discovered a way to check the question, whether there are local deterministic hidden-variable theories that can explain the observed facts we are discussing here. The important point is that this entire class leads to a conclusion, Bell's inequality, which contradicts the predictions of QT. Thus you can check one theory against the other with objective experiments, and all experiments done so far with an astonishing precision and statistical significance (since both the HV theory and QT make probabilistic statements, you need statistical significance) disprove the local deterministic HV theories and confirm standard Q(F)T. The very construction of standard relativistic QFT rules out that there is the possibility of causal effects between space-like separated measurements, i.e., non-local interactions.

I prefer to use clear language, and I use Einstein's term, because it's more precise: There are correlations between measurement outcomes on far-distant parts of entangled systems. This is inseparability. There are no non-local interactions in standard relativistic QFT by construction. In this sense this theory is local. There's no contradiction in these two statements.

Bell was ingenious in inventing this possibility to check vague metaphysical or even philosophical issues. There's no question about this. I must admit, however, that I find his writing not always very clear, and I prefer to stick to the experimental papers which clearly state what was how prepared and what was measured and what came out of these measurements.

 

[vanhees71]

Explanations for what is occurring to generate the correlations in entangled particles as classified by which assumption of Bell's theorem they reject. It has nothing to do with you are discussing, i.e. preparations of entangled states and thus isn't a "sloppy term" for that concept.

Then I don't understand what you mean by "mechanisms" at all. Entanglement is a property of quantum states. Quantum states describe preparation procedures (in a broad sense of course). So all there is necessary to understand entanglement is to understand how entanglement comes about. I've just given some (for sure not exhaustive) examples. If it's not answering your question about "mechanisms of entanglement", I didn't understand what you mean by "mechanism".

 

[DarMM]

Then I don't understand what you mean by "mechanisms" at all. Entanglement is a property of quantum states. Quantum states describe preparation procedures (in a broad sense of course). So all there is necessary to understand entanglement is to understand how entanglement comes about. I've just given some (for sure not exhaustive) examples. If it's not answering your question about "mechanisms of entanglement", I didn't understand what you mean by "mechanism".

I didn't have a question about entanglement, all the stuff in your post is known to me.

I'm referring to what physical fact/explanation is responsible for the breaking of the CHSH inequalities, a fairly standard topic in Quantum Foundations.

 

[vanhees71]

And your answer to that question is? Isn't it just a general consequence of the standard formalism? Physicswise there's no quibble in the standard minimal statistical interpretation (often called "orthodox interpretation" to distinguish it from several other flavors of Copenhagen interpretations).