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

[atyy]

No.

As a fully relativistic but only approximate QFT, renormalized perturbative QED is perfectly valid and highly accurate (to 12 digits of accuracy). The approximate 2-point functions can be made fully local using Kallen-Lehmann based resummation (which also eliminates the Landau pole). No more is needed for the use in quantum optics.

The main open problem about QED (and other interacting 4D relativistic QFTs) is whether all uncharged n-point functions can be constructed in a way that the Wightman axioms hold. This would give locality for arbitrary n-point functions.

Approximate to what? Could they be approximate to 2-point functions of a non-relativistic theory?

 

[vanhees71]

Thanks for this, very helpful at a number of levels. Some I knew, some I did not. A couple of comments related to your sentences in bold.

1. I am specifically trying to understand how and why you are so focused on QFT as it relates to entanglement, when I don't think it is that critical (if relevant at all). Sure, a better theory is a better theory, and certainly advances are desired. But let's face it: entanglement scenarios (Bell tests for example) do not depend on time ordering or distance, so I don't see why a relativistic theory would be called for unless some additional benefit were derived. That doesn't seem to be the case, ergo my question.

Coming from a different angle: I would assume that a relativistic constraint added to QM would have difficulty explaining how signal locality is achieved, all the while allowing entangled quantum systems to exhibit quantum nonlocality. That seems to be an obvious problem with a theory purporting to respect c from its construction. You have made the case that QFT is consistent and does not have that problem, but I still wonder. I would guess the nonlocality of entanglement is not resolved in QFT; because I have said many times, we wouldn't need interpretations if it were. That would be big news indeed. So yes, I'd like to know if and how QFT explains the mechanism of entanglement better than QM.

(So I don't think I am mixing anything up.)2. And I think this is a significant point of departure between you and I. You are saying there isn't anything occurring FTL in entanglement experiments, because if it did, it would violate relativity - and more specifically relativistic QFT. While I see most entanglement experiments as a demonstration of quantum nonlocality.

I essentially deny that any classically local theory can explain this behavior, while you deny that the quantum nonlocal behavior occurs in the first place. Let me know if I am not representing your position fairly.Next question: Can you explain how perfect correlations occur in entanglement? (For sake of simplicity, can we assume that T1 < T2 < T3 in all reference frames? Let me know if this is not possible.)

a. We have spin entangled A and B, now distant from each other, at T1.
b. I presume you agree that at T1, neither has a well-defined spin.
c. Alice measures A at angle $\theta$ at time T2, giving A a well-defined spin.
d. Bob measures B at angle $\theta$ at time T3, giving B a well-defined spin if it didn't already have one as a result of c. Further, T3 is sufficiently near to time T2 that there is insufficient time for any classical signal to go from A to B.
e. How do Alice and Bob always have anti-correlated results, regardless of choice of $\theta$? One would assume that A and B need some kind of FTL signal, action, mutual rapport or something to accomplish this impressive feat. We know from Bell that it is not due to hidden variables.

Thanks, and this question is not intended to be confrontational. I'd really like to get a better understanding of what QFT says about this, and especially how it differs from QM (as you have said it matters).

I insist on the use of relativistic QFT when relativistic questions are asked, namely how to make the observed "non-locality" of the correlations described by entanglement consistent with the causality structure implied by Minkowski space, i.e., that there must not be faster-than-light causal effects, or in other words, that space-like separated measurement events cannot be causally connected. This is in fact satisfied by stanadard relativistic QFT, implmenting the microcausality feature, which implies Poincare invariance of the S-matrix and the cluster decomposition principle, i.e., precisely what's needed to respect the causal structure of spacetime. You cannot get this with some "addition to non-relativistic QM".

Ad 2) Of course, no classical (deterministic) theory can describe what entanglement within relativistic QFT describes. That's why we do QFT and not classical physics to describe the phenomenon. Why should we use a model that doesn't work?

The entanglement is due to the state preparation process in the very beginning of the experiment. The usual way you get it is through conservation laws from local interactions (in fact in QFT there are only local interactions by construction). E.g., in parametric downconversion you absorb a UV photon from a strong laser field in a birefringent chrystal, which in turn leads to the creation of two photons, obeying energy-momentum and angular-momentum conservation. Thus you get photon pairs that are both momentum and polarization entangled in one of the Bell states like, e.g., the polarization-singlet state,
$$|\Psi \rangle=\frac{1}{2} (\hat{a}^{\dagger} (\vec{p}_1 H) \hat{a}^{\dagger}(\vec{p_2},V) - \hat{a}^{\dagger} (\vec{p}_1 V) \hat{a}^{\dagger}(\vec{p_2},H))|\Omega \rangle,$$
where $|\Omega \rangle$ is the vacuum state of photons. Of course, this is idealized, because momentum eigenstates are no true states, und to have to smear somewhat to get properly normalized wave packets.

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 measurment 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.

 

[A. Neumaier]

Approximate to what? Could they be approximate to 2-point functions of a non-relativistic theory?

Approximate to the nonperturbative 2-point function of a local covariant QFT matching the perturbative QED expansion. Of course, nobody yet knows how to define the latter.

The renormalized perturbative gives only asymptotic series to the n-point functions, and partially summing these series (as is customary) produces not-quite local approximations to what are supposed to be the unknown true local n-point functions. My point was that on the 2-point function level it is known how to make the approximations truly local, whereas it is unknown how to do it in general.

 

[A. Neumaier]

This is in fact satisfied by standard relativistic QFT, implementing the microcausality feature, which implies Poincare invariance of the S-matrix and the cluster decomposition principle

Do you know where there is a proof for that for nonabelian gauge theories? Quarks surely do not satisfy the cluster decomposition principle.

 

[vanhees71]

Agreed. I was just joking. But if we include electrons, then is the theory still relativistic? Don't we run into the problem that there are still no 3+1D interacting relativistic QFTs?

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.

 

[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.