How measurement in the double slit experiment affects result

[atyy]

Now to the argument that it's not the state preparation which determines the outcome of measurements. This is pretty absurd, or do I misunderstand this statement completely? Even in classical physics, of course the preparation of an experiment determines the outcome of measurements. This is trivial, isn't it? The difference in quantum theory is that there are indetermined observables even when we know the exact (pure) state of the system, as with our entangled photon pair.

In both classical and quantum physics, there is the possibility that the state preparation and measurement procedure determines the outcome.

Another way to see the problem is that even if one says that state preparation determines measurement outcomes, the problem is that the quantum formalism says that measurement is a form of state preparation. If there an initial state preparation, followed by measurement A, followed by measurement B, there is more than one state preparation procedure, so it is unclear which state preparation procedure is the "cause" for the outcome of measurement B.

If I prepare photons in the described polarization-entangled state, quantum theory predicts the probabilistic properties of measurements of the single photons' polarizations uniquely, including correlations of (independent and local) measurements by Alice and Bob, when they compare their measurement protocols, provided the measurements are accurate enough in time resolution to be able to always associate the photons belonging to one entangled pair. Of course, the polarization state of both photons is maximally indetermined, but for each measurement of the polarization of Alice's and Bob's photons, we can predict the corresponding conditional probabilities. The same holds for the prediction of the interference pattern, which reflects the probabilities to detect photons on the screen behind the double slit, and as far as I know these probabilistic predictions of QT are very well (i.e., with very high statistical significance) agreeing with the findings in experiments. Why then, can't I then conclude that it is simply the preparation in this entangled state by parametric down conversion that determines the (probabilistic) behavior predicted by QT and confirmed by experiment? If I can't, I don't know, how to make sense of the notion of states in quantum theory at all, but also this contradicts the experience that we very well know how to use quantum theory to describe the empirical findings when performing such experiments.

Yes, quantum mechanics works. The question is whether quantum mechanics respects Einstein causality. Let me try to extract what I think is the essence of the Cavalcanti and Lal paper. The two important definitions are:

(RCC) Relativistic causality: the cause of an event is in the past light cone of the event
(FP) Common cause of a correlation: if z is the common cause of a correlation between A and B, then P(A,B|z) = P(A|z)P(B|z)

It can be shown that Bell's local causality, which is understood to be equivalent to Einstein Causality, is essentially RCC + FP. Quantum mechanics does not obey local causality, so either RCC or FP or both must be rejected. Presumably we are trying to keep RCC, since that is essential for Einstein Causality. If we reject FP, then correlations cannot have a common cause. It may be possible to redefine what it means for a correlation to have a common cause, but FP is the definition of common cause for all classical causality including Einstein Causality, so if you redefine common cause, one would be redefining Einstein causality.

I would say that in a minimal interpretation, relativistic quantum mechanics does not need Einstein Causality for correlations. Only signal locality is needed, ie. classical information cannot travel faster than light. The requirement that spacelike separated observables commute is closer to signal locality, because measurement of an observable is something that extracts a classical outcome from a quantum state.

 

[vanhees71]

Yes, quantum mechanics works. The question is whether quantum mechanics respects Einstein causality. Let me try to extract what I think is the essence of the Cavalcanti and Lal paper. The two important definitions are:

(RCC) Relativistic causality: the cause of an event is in the past light cone of the event
(FP) Common cause of a correlation: if z is the common cause of a correlation between A and B, then P(A,B|z) = P(A|z)P(B|z)

It can be shown that Bell's local causality, which is understood to be equivalent to Einstein Causality, is essentially RCC + FP. Quantum mechanics does not obey local causality, so either RCC or FP or both must be rejected. Presumably we are trying to keep RCC, since that is essential for Einstein Causality. If we reject FP, then correlations cannot have a common cause. It may be possible to redefine what it means for a correlation to have a common cause, but FP is the definition of common cause for all classical causality including Einstein Causality, so if you redefine common cause, one would be redefining Einstein causality.

I would say that in a minimal interpretation, relativistic quantum mechanics does not need Einstein Causality for correlations. Only signal locality is needed, ie. classical information cannot travel faster than light. The requirement that spacelike separated observables commute is closer to signal locality, because measurement of an observable is something that extracts a classical outcome from a quantum state.

Microcausal local relativistic QFTs imply the linked-cluster theorem, according to which local far-distant experiments appear uncorrelated. Thus, indeed you always need a classical information exchange after doing the experiments as between Alice and Bob in our example to "erase" the (putative) which-way information of the photons. So (RCC) is fulfilled by such theories at least in this weak form. I don't see, why (FP) is in any way necessary for the consistency of physics to hold. So I've no problem to give it up, and indeed quantum theory and the outcome of measurements checking the Bell or CHSH inequality, which base on (RCC+FP), which at the same time confirm Q(F)T, show that this is what one has to do to be in accordance with these empirical facts. To give up RCC is no option, because then you'd give up causality, which is the very reason why physics is possible at all. Of course, you can argue that nature may be such that natural sciences are impossible by first principle, but this seems not to be the case either since natural sciences are pretty successful in their description of the world around us.

 

[billschnieder]

(FP) Common cause of a correlation: if z is the common cause of a correlation between A and B, then P(A,B|z) = P(A|z)P(B|z)

With post-processing, P(A,B|z) = P(A|z)P(B|z) is wrong even in classical probability, since the only B outcomes used are then onces which have been filtered according to Alice's outcomes, it should be P(A,B|z) = P(A|z)P(B|Az). So there should be no problem rejecting FP without fanfare.

 

[atyy]

Microcausal local relativistic QFTs imply the linked-cluster theorem, according to which local far-distant experiments appear uncorrelated. Thus, indeed you always need a classical information exchange after doing the experiments as between Alice and Bob in our example to "erase" the (putative) which-way information of the photons. So (RCC) is fulfilled by such theories at least in this weak form. I don't see, why (FP) is in any way necessary for the consistency of physics to hold. So I've no problem to give it up, and indeed quantum theory and the outcome of measurements checking the Bell or CHSH inequality, which base on (RCC+FP), which at the same time confirm Q(F)T, show that this is what one has to do to be in accordance with these empirical facts.

Yes, it is fine to keep RCC without FP. The linked-cluster theorem and commutation of spacelike separated observables are all about RCC without FP. It means that the probabilities of outcomes of local measurements don't depend on distant measurement choices and outcomes, and that classical information cannot be communicated faster than light. However giving up FP also means that the nonlocal correlations do not have any local common cause, because FP is the usual definition of what it means for correlations to have a common cause. Because Einstein Causality is usually associated with EPR, Einstein Causality usually means RCC+FP, so if one means RCC without FP, people usually say signal locality or commutation of spacelike separated observables. The term "RCC" itself may be a bit confusing, because it sometimes means Einstein Causality, but it is also commonly used to mean signal locality. For example, Popescu and Rohrlich http://arxiv.org/abs/quant-ph/9508009 use the term "relativistic causality" to mean signal locality.

(Actually, there is an even finer distinction going at least back to Bell that I've ignored, but that Cavalcanti and Wiseman mention in http://arxiv.org/abs/0911.2504.)

To give up RCC is no option, because then you'd give up causality, which is the very reason why physics is possible at all. Of course, you can argue that nature may be such that natural sciences are impossible by first principle, but this seems not to be the case either since natural sciences are pretty successful in their description of the world around us.

I think this is beyond a minimal interpretation. If there is a non-perturbative theory of quantum gravity, then spacetime itself may be emergent and RCC may be emergent, so that RCC is not fundamental. Certainly it seems very hard to do physics without some notion of locality, so that the big picture can be built up from small pictures, and we can have predictions for the small picture without knowing the big picture, and Weinberg does say this in his books. However, while agreeing with him that it is difficult, I think I wouldn't go all the way to impossible, at least not yet.

Also, one of the beautiful things about the quantum formalism is that for any choice of inertial frame, once we take a classical/quantum cut so that the wave function is not real, we can take the wave function as FAPP real, and we can give up RCC and take FP so that the correlations are FAPP explained by the quantum state and measurement choice. So quantum theory at the top level has RCC-FP, but FAPP it has FP-RCC, and we can use both to help our intuition and get correct predictions.

 

[atyy]

With post-processing, P(A,B|z) = P(A|z)P(B|z) is wrong even in classical probability, since the only B outcomes used are then onces which have been filtered according to Alice's outcomes, it should be P(A,B|z) = P(A|z)P(B|Az). So there should be no problem rejecting FP without fanfare.

One can reject FP. Indeed, in general P(A,B|z) = P(A|z)P(B|A,z) in classical probability. However, in such a case, one cannot call z the sole cause of B, because A is also potentially a cause or correlated with a cause that is independent of z. Also, Einstein Causality usually means classical relativistic causality so it includes FP. Of course, everything is fine if another less common definition of Einstein Causality is used.

 

[billschnieder]

However, in such a case, one cannot call z the sole cause of B, because A is also potentially a cause or correlated with a cause that is independent of z.

Right, that is what post-processing means.

Also, Einstein Causality usually means classical relativistic causality so it includes FP.

Nope, Einstein Causality only implies FP if there is no post-processing. Even in classical physics, FP is wrong when we have post-processing. See for example the very simple Bernouli's Urn example in Jaynes' paper. FP fails woefully there, even though it is obviously Einstein Causal. Einstein Causality is fully consistent with a rejection of FP while post-processing, so there is no conflict and no need to modify the definition of Einstein Causality.

 

[atyy]

Nope, Einstein Causality only implies FP if there is no post-processing. Even in classical physics, FP is wrong when we have post-processing. See for example the very simple Bernouli's Urn example in Jaynes' paper. FP fails woefully there, even though it is obviously Einstein Causal. Einstein Causality is fully consistent with a rejection of FP while post-processing, so there is no conflict and no need to modify the definition of Einstein Causality.

Yes, post-processing is needed for A or B to find out the a Bell inequality, and the time at which the post-processing is carried out means that no superluminal communication of classical information is needed for A or B to discover the Bell inequality violation. The question is whether A or B add an inference step to the post-processing and conclude that the violation occurred at spacelike separation. Usually "reality" is accepted, the violation is inferred to have occurred at spacelike separation. By Einstein Causality, one usually means that this inference step is added to the post-processing so that Einstein Causality is ruled out by a Bell inequality violation. If the inference is not taken, and only the post-processing is performed, then one can have violation of the Bell inequalities and a modified form of Einstein Causality, because although there is a violation of the Bell inequalities, the violation did not occur at spacelike separation. This is uncontroversial and agreed on by Bell himself, and indeed by EPR themselves. However, because EPR favoured doing the post-processing and adding the inference about spacelike separation, the usual definition of Einstein Causality includes the additional inference. Again, if all you are saying is that the post-processing is taken, but not the inference, that is not controversial, except for what one might mean by Einstein Causality.

 

[billschnieder]

But the inequalities assume FP, -- i.e. no post-processing. You cannot then use their violation in the presence of post-processing to reject or modify Einstein causality, which is fully consistent with FP when no postprocessing is done, and also fully consistent with the rejection of FP when post-processing is done. For that, you need a violation in the absence of postprocessing. All experiments to date have used postprocessing.

Remember that EPR was always about the "real physical situation", which is unaffected by " inference".

 

[atyy]

But the inequalities assume FP, -- i.e. no post-processing. You cannot then use their violation in the presence of post-processing to reject or modify Einstein causality, which is fully consistent with FP when no postprocessing is done, and also fully consistent with the rejection of FP when post-processing is done. For that, you need a violation in the absence of postprocessing. All experiments to date have used postprocessing.

Remember that EPR was always about the "real physical situation", which is unaffected by " inference".

FP assumes post-processing, but that the post-processing does not prevent you from making the inference about the real physical situation, in particular that the correlations did occur at spacelike separation.

Actual experiments are a different matter, and you can certainly find loopholes. However, what is being discussed is the prediction of quantum mechanics that if the measurement choices and outcomes are real, then a violation of a Bell inequality at spacelike separation is the real physical situation.

 

[billschnieder]

FP assumes post-processing, but that the post-processing does not prevent you from making the inference about the real physical situation

I have to disagree. P(A,B|z) = P(A|z)P(B|z) implies that P(B|z) = P(B|Az). The expression P(A,B|z) = P(A|z)P(B|z) is only ever an accurate probability expression if and only if P(B|z) = P(B|Az). But the reverse is not true. In classical probability P(A,B|z) = P(A|z)P(B|Az) is always accurate, but P(A,B|z) = P(A|z)P(B|z) is only accurate when P(B|z) = P(B|Az) or P(A|z) = P(A|Bz). Therefore if you obtain P(B|z) =/= P(B|Az) that tells you that P(A,B|z) =/= P(A|z)P(B|z) and therefore FP must be rejected. It tells you nothing about Einstein Causality.

The type of post-processing we are talking about here is specifically the type in which the results of one side, are used to filter the results of the other. If the post-processing does not change the results then post-processing is not necessary. In other words, if P(A|z) = P(A|Bz), then why post-process in the first place? We know from the delayed choice experiments that post-processing does indeed change the results ie, P(A|z) =/= P(A|Bz) and FP must be rejected, with zero impact on Einstein Causality. It is very difficult to accept this if you believe P(B|z) =/= P(B|Az) necessarily implies physical influence that is why Jaynes' Bernoulli urn example is so important. It removes all doubt that such a view is wrong.

However, what is being discussed is the prediction of quantum mechanics that if the measurement choices and outcomes are real, then a violation of a Bell inequality at spacelike separation is the real physical situation.

Yes, QM simply predicts certain correlations which have been confirmed experimentally, but all the experiments involve post-processing. Bell used FP (without post-processing) to derive inequalities which were violated by experiments involving post-processing. The real physical situation produced the clicks on the detectors, then you added post-processing to the results (after the fact, long after the real-physical situation had done its thing) and obtained the correlations. If the post-processing is irrelevant to the results, then you can simply not do it and show that the violation is still there. You do not need a new experiment, or new data why not use the existing data without post-processing? Unless the post-processing is such an important component of the definition of the problem that it is impossible to avoid it?

​

 

[Ken G]

Ok, then give the description if the quantum-erasure experiment within classical electromagnetism. I don't think that this is possible.

Give me some time to write the paper, then I'll return to this. It sounds like it's worth that effort.

 

[atyy]

Give me some time to write the paper, then I'll return to this. It sounds like it's worth that effort.

But didn't you say that the usual quantum eraser does not violate a Bell inequality? If so, then it's not that surprising if it has a local classical explanation?

Maybe you can try this version, where they violate a Bell inequality (but not sure about spacelike separation): http://arxiv.org/abs/1205.4926 :D Bonus: they start off with wave-particle duality

That paper references http://arxiv.org/abs/1206.4348 which also has a Bell inequality violation.

 

[Ken G]

But didn't you say that the usual quantum eraser does not violate a Bell inequality? If so, then it's not that surprising if it has a local classical explanation?

I don't remember saying anything about Bell inequalities, but that is certainly an interesting tack to take.

Maybe you can try this version, where they violate a Bell inequality (but not sure about spacelike separation): http://arxiv.org/abs/1205.4926 :D Bonus: they start off with wave-particle duality

Yes, they like the particle/wave language for describing the interference patterns. Personally, I think it's more insightful to recognize that waves do all that stuff, so the "duality" is that there's not really a distinction.

That paper references http://arxiv.org/abs/1206.4348 which also has a Bell inequality violation.

Thanks for those references, it will be interesting to ponder what is the appropriate classical analog to those Bell inequality violations. Note that by "classical analog" I certainly do not mean "locally real particle treatment" or "local hidden variable treatments", those are classical particle analogs. I'm talking about a classical wave analog.

 

[atyy]

I don't remember saying anything about Bell inequalities, but that is certainly an interesting tack to take.

I thought that was the point you were making in post #23 when you said "Yet the correlations are not surprising when they have a "Bertlmann's socks" flavor (which your correlations did by the way, that's a detail that needs to be fixed up but it's not essential)." But maybe you were referring to a different scenario. To be honest, I just presumed without evidence that the usual delayed choice has no Bell inequality violation, since otherwise the more recent versions wouldn't make the point of adding the violation. I suppose another consideration is that although there is no Bell inequality violation, the Wigner function may not be positive. If the Wigner function is positive, then I think one can have a noncontextual local classical model, but if the Wigner function is not positive, then I think that although a local model is not ruled out, it will have to be contextual. On the other hand, the Wigner function is not the unique function whose marginals are the quantum probabilities, and in special cases one can construct another joint distribution that is positive, even if the Wigner function is not.

 

[Ken G]

I thought that was the point you were making in post #23 when you said "Yet the correlations are not surprising when they have a "Bertlmann's socks" flavor (which your correlations did by the way, that's a detail that needs to be fixed up but it's not essential)."

Ah, I see what you mean. I was talking about the mathematical description given by vanhees71, not necessarily about quantum erasure experiments writ large. I haven't really thought about whether quantum erasure is a Bell-type violation, but those articles you cited certainly clarify that question. I didn't think the issue was essential-- I suspected the analysis by vanhees71 could be generalized to Bell-type violations, but maybe there is some important wrinkle that distinguishes the classes.

To be honest, I just presumed without evidence that the usual delayed choice has no Bell inequality violation, since otherwise the more recent versions wouldn't make the point of adding the violation.

Yes, I see what you are saying now, and indeed this might be an important difference when it comes to looking for classical analogs.

I suppose another consideration is that although there is no Bell inequality violation, the Wigner function may not be positive. If the Wigner function is positive, then I think one can have a noncontextual local classical model, but if the Wigner function is not positive, then I think that although a local model is not ruled out, it will have to be contextual.

The classical analogs I mean are not local, they are wavelike, by which I mean they can involve interferences in two-point correlations that are sensitive to the history of the entire system. It is my contention that "quantum weirdness" lives in the idea that if you have a quantum, you should have attributes "carried with" that quantum, i.e., local realism, and so any two-point correlations must be correlations between two sets of information independently associated with the different quanta. We never think that should be true of waves, so the issue might not even come up. It's food for thought, if there is a classical-wave analog to Bell inequality violations.

So I think this may be a different issue. On the other hand, the Wigner function is not the unique function whose marginals are the quantum probabilities, and in special cases one can construct another joint distribution that is positive, even if the Wigner function is not.

The importance of the Wigner function is more food for thought-- these are all potentially important issues to ponder, I cannot tell at this stage what the classical importance of these are but it should be included in the landscape of classical analogs.

 

[vanhees71]

Sure, with such a setup you can also do Bell inequality violation tests. Isn't the famous CHSH paper about such an experiment with a set of different relative orientations between Alice's and Bob's polarizer? One should note that nothing changes concerning the interpretation within the minimal interpretation, and I still think my treatment sticks to the minimal interpretation, particularly because, nowhere one needs to argue with a "collapse" as a physical process.

 

[Cthugha]

Ok, then give the description if the quantum-erasure experiment within classical electromagnetism. I don't think that this is possible.

The standard DCQE experiment uses entangled photons and thus cannot be explained using classical electromagnetism. However, you just need correlation, but not necessarily quantum correlation to demonstrate DCQE. An example for a classical version of DCQE is given e.g. in T. Peng, et al., "Delayed-Choice Quantum Eraser with Thermal Light" Phys. Rev. Lett. 112, 180401 (2014).

 

[Ken G]

The standard DCQE experiment uses entangled photons and thus cannot be explained using classical electromagnetism. However, you just need correlation, but not necessarily quantum correlation to demonstrate DCQE. An example for a classical version of DCQE is given e.g. in T. Peng, et al., "Delayed-Choice Quantum Eraser with Thermal Light" Phys. Rev. Lett. 112, 180401 (2014).

Thanks for that, you may have saved me a lot of work, though I'm disappointed it has been done! Though not surprised.

 

[vanhees71]

The standard DCQE experiment uses entangled photons and thus cannot be explained using classical electromagnetism. However, you just need correlation, but not necessarily quantum correlation to demonstrate DCQE. An example for a classical version of DCQE is given e.g. in T. Peng, et al., "Delayed-Choice Quantum Eraser with Thermal Light" Phys. Rev. Lett. 112, 180401 (2014).

Thanks a lot for pointing us to this very exciting paper. It made a great read last night (although I lack some sleep now :-)). It's very well understandable. Here's the link to the paper.

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.180401

Unfortunately I couldn't find a link to a free preprint. Unfortunately the quantum opticians seem not to send everything to the arXiv :-(.

Now comes my question. Can we let this through as a proof for the claim that delayed-choice (postselection) experiments can be explained by classical electromagnetics? My answer is no!

The modeling given in the paper is very clearly using the quantum properties of the quantized radiation field. The source is modeled as a (quasi-)thermal source via the superposition of coherent states with random-phase averaging. Then single photons are detected at D0. Looking at all photons, registered there one sees only the interferrence pattern of the single slit, because the two slits are separated by a distance larger than the coherence length of the source at the slits.

Now the experiment is driven further by using the clever Mach-Zehnder like beam splitters by making coincidence experiments, i.e., one looks at the two-photon correlation function for photons at D0 and one of the other detectors. Unfortunately there seem to be some typos in the text, mixing up the detectors D1,...,D4 somewhat. The labeling of the plots in Figs. 2 and 3 are, of course, correct. Measuring the coincident detection of a photon at D0 and D1 and filtering such as to register only really coincident photon events, i.e., such "picked up" by D0 and $\mathrm{D}\alpha$ ($\alpha \in \{1,2,3,4 \}$) from two wave trains within the coherent state coming from the same time $t_0$ as encoded in the electric-field operator in Eq. (5)-(7). Then the corresponding two-photon correlation function given by Eq. (8) is measured. For the QFTlers among us: That's nothing else than the appropriate two-photon Wightman function for the number operators of photons at D0 and $\mathrm{D}\alpha$.

Now the setup is such that if you have a coincident detection of two photons at D0 and D4 you know that the photon registered by D4 must have gone through slit B (i.e., you have which-way information). From the incoherence of the wave trains emitted from slits A and B, then necessarily also the photon registered at D0 must have come from slit B, and thus when looking only on such coincident two-photon events these photons registiered by D0 only show the single-slit refraction pattern (Fig. 2 only shows the main maximum) as expected since due to the filtering process with help of the photon registered at D4 we have gained which-way information concerning the photon registered at D0. In the same way one deduces that one also sees only the single-slit interference pattern when using the coincident two-photon appearance at detectors D0 and D3.

On the other hand when looking for coincident two-photon events at D0 and D1, we cannot decide through which slit the photon at D1 has run and thus also not for the coincidently registered photon at D0. As the calculation and also experiment shows, then one observes the double-slit interference pattern (of course with the single-slit pattern as envelope). Correspondingly one sees also the double-slit interference pattern when using the coincident two-photon appearance at D0 and D2.

Thus, the final statements in the paper, where the math is discussed, is correct. There's something mixed up in the description directly following Eq. (1), which is of course a simple typo.

As this analysis shows, again this experiment detects two-photon Fock states. The difference to the above discussed quantum eraser experiment is that not entangled photon pairs where prepared but a quasi-thermal source with a cleverly chosen geometrical setup concerning the coherence length and the distance of the double slit. Nevertheless, the "delayed erasure" [1] of the which-way information and the observed appearance of the double-slit interference pattern for the appropriately chosen subensembles is only possible within the quantum picture of the radiation field. I don't see, how you can describe these coincidences within classical Maxwell theory. This is closely related to the Hanbury-Brown and Twiss effect (HBT) and its explanation by Glauber et al.

[*] It's a "delayed choice" through "postselection", whether you want which-way information or the double-slit interference pattern, because the photon at D0 is detected significantly relative to the "rise time" of 1 ns of the photo diodes before (5ns delay) the one at $\mathrm{D}\alpha$. Thus, the photon at D0 is absorbed significantly before we decide which photon subensemble we chose (i.e., one leading to which-way information or one "erasing" it).

Again, according to my understanding of the minimal interpretation the corresponding observations are due to the preparation of the "pseudo thermal" radiation field at the very beginning, i.e., by shining a laser on the "ground glass". There's no retrocausal collapse of the photon detected at D0 by registering the photon at the detector $\mathrm{D} \alpha$. The observation or non-observation of the double-slit interference pattern in the respective choice of coincidence measurement, within this (ensemble) representation, is thus not due to retrocausal manipulation of the physical state of the observed system. Of course, also here we implicitly assume that "Einstein causality" is correct, i.e., that the photons travel with the speed of light and that the detectors are thus uncorrelated, i.e., that there is no faster-than light "communication" between the detectors. Of course, one cannot strictly prove this by this experiment. So there seems to be still a loophole for metaphysicists who like to give up Einstein causality in favor of what they call "realistic" (or better "ontological") interpretation of quantum states. I'm more on the conservative side and prefer to assume that the space-time structure of (at least special) relativity to be valid :-).

The whole experiment is a "delayed choice" experiment, because the path length difference between the photon detected at

 

[atyy]

I think it should be made clear (if I undrerstand both correctly) that vanhees71 and billschneider are not saying the same thing.

billschneider, citing Jaynes, claims the fundamental logic of the Bell inequalities is wrong, and that local realism or Einstein Causality in the usual sense is consistent with quantum mechanics.

vanhees71 is only claiming a weakened form of Einstein Causality, in which RCC is preserved but FP is given up so that correlations do not have a common cause explanation.

 

[Ken G]

I would also point out that having a "classical analog" is not making the claim that everything can be explained without quantum mechanics. It just means that it is untrue to claim some phenomenon had no classical analog, i.e., that there is no classical version of a similar phenomenon. A good example is quantum chaos, where the wavefunction takes on a different character in systems that exhibit classical chaos. We don't say the existence of classical chaos means you don't need a wavefunction to describe that system. Still, having said that, I have a slightly different classical analog in mind, and I'm not sure about the Bell ramifications. Questions about wave vs. particle behavior are a bit different from Bell violations.

 

[vanhees71]

I think it should be made clear (if I undrerstand both correctly) that vanhees71 and billschneider are not saying the same thing.

billschneider, citing Jaynes, claims the fundamental logic of the Bell inequalities is wrong, and that local realism or Einstein Causality in the usual sense is consistent with quantum mechanics.

vanhees71 is only claiming a weakened form of Einstein Causality, in which RCC is preserved but FP is given up so that correlations do not have a common cause explanation.

I think you understood me right, but I don't see, where Einstein Causality is weakened. In my understanding of the statistical interpretation, there is no faster-than-light signal necessary to explain the outcome of the delayed-choice experiments in accordance with quantum mechanics, and I still hold to my opinion that the common-cause explanation for this phenomenon is the entanglement of the photons for the eraser. Also in the delayed-choice experiment by Peng and all there is no superluminal (or even retrocausal) action at a distance. The two-photon correlations there are also due to the preparation procedure encoded by the description given in the paper.

I'd still be glad about comments about whether my understanding of the Peng paper is correct (at least on the physics level; of course there seem to be subtle or even big differences among us concerning the metaphysical implications, which however should be left out of the discussion as long as the physics is absolutely clarified).

 

[atyy]

I think you understood me right, but I don't see, where Einstein Causality is weakened. In my understanding of the statistical interpretation, there is no faster-than-light signal necessary to explain the outcome of the delayed-choice experiments in accordance with quantum mechanics, and I still hold to my opinion that the common-cause explanation for this phenomenon is the entanglement of the photons for the eraser. Also in the delayed-choice experiment by Peng and all there is no superluminal (or even retrocausal) action at a distance. The two-photon correlations there are also due to the preparation procedure encoded by the description given in the paper.

Because of the EPR paper, Einstein Causality usually means RCS + FP, so if one rejects FP, Einstein Causality is weakened (by definition).

Also, throughout classical physics, FP is the definition of common cause. For example, in biology the framework of Bayesian networks is quite common, and FP is the definition of common cause in Bayesian networks. So if FP is rejected, there is no notion of common cause, unless one uses a new definition, which would be ok. But the question is what new definition of common cause are you using? Actually, the Cavalcanti and Lal paper http://arxiv.org/abs/1311.6852 is interesting because it discusses a proposal by Leifer and Spekkens http://arxiv.org/abs/1107.5849 to define a new notion of common cause, so that there is a modified Einstein Causality in which one keeps RCS and a more general notion of common cause.

Edit: In my previous posts I used "RCC", which is a transcription error of mine from Cavalcanti and Lal's terminology, so here I use "RCS" instead for "relativistic causal structure".

 

[vanhees71]

I see, but I don't think that EPR is consistent with the modern findings concerning the predictions of quantum theory in the connection with entanglement as is precisely the topic of the EPR paper. So you cannot keep both assumptions, which you call RCS and FP. I don't see, why one should have to keep FP for any reason. For me it contradicts the fundamental principles of quantum theory, which where tested very thoroughly with all these experiments. As bhobba likes to quote, quantum theory just introduces a way to consistently describe the probabilistic behavior of nature, which is to our best knowledge today an observed fact. This doesn't exclude the possibility that one finds another more comprehensive deterministic theory, which then most probably will be even weirder than quantum theory itself from a metaphysical point of view. but physics (particularly quantum theory) teaches us that nature behaves is she behaves and doesn't care too much about our metaphysical convenience ;-)). I'll have a look at the papers later.

 

[atyy]

I see, but I don't think that EPR is consistent with the modern findings concerning the predictions of quantum theory in the connection with entanglement as is precisely the topic of the EPR paper. So you cannot keep both assumptions, which you call RCS and FP.

Yes, I mentioned EPR only because "Einstein Causality" will usually be understood to mean what EPR advocated, which was RCS + FP, which cannot both be kept.

I don't see, why one should have to keep FP for any reason. For me it contradicts the fundamental principles of quantum theory, which where tested very thoroughly with all these experiments.

Yes, it's fine to remove FP. But since FP is the old definition of common cause, one needs a new definition if one wants to say that the entangled state is a common cause.

 

[vanhees71]

Hm, I don't know, how to formalize my statement. Just in plain words, I think the quantum mechanical states, represented by the statistical operator in the formalism (which is by definition a trace-class positive semidefinite self-adjoint operator with trace 1; a state is pure if and only if it's a projection operator), describe the known properties of the system under consideration. It's objectively related to a single system through an equivalence class of preparation procedures but, even when we have full knowledge about the quantum system, i.e., if a complete set of compatible observables is determined through the preparation procedure and thus the state is a pure state, we have only probabilistic knowledge about the outcomes of measurements of the observables possible for this system. To test the corresponding predictions about such meaasurements one thus always needs a suffuciently large ensemble of independently prepared systems.

Among the many predictions of quantum theory are also the non-local correlations known as "entanglement", which are found contradicting local deterministic (hidden-variable) theories by Bell's and related theorems. What's now the "cause" for these "non-classically strong" correlations? In the above picture about states, it's the preparation procedure in such an "entangled state", and in all cases, known to me, (including the gedanken experiment described in the original EPR paper) these preparations are due to local manipulations on particles or photons, which then evolve for some "long" time such that subsystems can be measured at far distant (again local) experiments. The correlations due to entanglement are there for the whole time, from the very first preparation procedure. The measurements on the photons by Alice and Bob in the eraser experiment or the coincident-photon-apir countings in the above discussed experiment by Peng et all are local and can be thus, i.e., due to the locality of the interaction between each of the photons with the corresponding detector, done at space-like separated space-time regions and thus are (due to the microcausality of QED) not causally mutually affecting the far-distant photons measured in coincidence. I'm not aware of any test of these issues, where this explanation with local microcausal relativistic QFT fails, and thus I think there's no problem with causality. As demonstrated in my summaries of the two experiments above, there's no need for a collapse interpretation, and thus no need to assume a faster-than-light manipulation of a far-distant object or even a "retrocausal action at a distance". One must clearly distinguish between interactions and correlations. The former are always local by construction of the standard relativistic QFTs; the latter can refer to far-distant objects and are thus non-local. The locality of the interactions, i.e., microcausality, guarantees the consistency of the S-matrix with relativistic covariance, unitarity, and causality.

 

[atyy]

What's now the "cause" for these "non-classically strong" correlations? In the above picture about states, it's the preparation procedure in such an "entangled state", and in all cases, known to me, (including the gedanken experiment described in the original EPR paper) these preparations are due to local manipulations on particles or photons, which then evolve for some "long" time such that subsystems can be measured at far distant (again local) experiments.

The locality of the interactions, i.e., microcausality, guarantees the consistency of the S-matrix with relativistic covariance, unitarity, and causality.

I read the rest of the post too, but I think the key issues are:
(A) Do cluster decomposition and microcausality have anything to say about the entangled state as the "cause" of the nonlocal correlations?
(B) If the entangled state is a "cause" is it a local cause?

Let me try to address (B) first. I need to think more about (A).

Let's work in a frame in which Alice and Bob measure simultaneously, so the observable measured is the tensor product of two local spacelike-separated observables. Let's use the Heisenberg picture so the initial entangled state does not evolve, but the operators do. In the Heisenberg picture, the field operator has an equation of motion that has the same form as the classical relativistic equation, except that it is an operator, so there is a good argument that the field dynamics obey local causality or Einstein causality. That leaves the initial state. I'm not sure it's the only cause, but even if it is, is the initial state a local cause?

(1) First the initial state is in Hilbert space, so it is not obviously local or associated with any point in spacetime. To avoid this we can try to
(2) Associate the initial state with the location of the preparation procedure. But if we do this, the state does not evolve, so when the measurement is made, if the preparation and measurement are spacelike separated, then the measurement outcome will depend nonlocally on the state at a spacelike location. To avoid this we can try to
(3) Associate the initial state with the entire initial spacelike slice, or put a copy of the state at every location on the intial spacelike slice. But if we do this, the preparation procedure itself is nonlocal, since the local preparation procedure is affecting the entire spacelike slice.

The basic reason I don't think the state can be a local cause is that for the state to be a cause, we have to treat it as real (FAPP). But if we treat it as real, then in a frame in which the measurements are not simultaneous, the state for the later measurement will be caused by the earlier measurement and collapse which is manifestly nonlocal. Going to a frame in which the measurements are simultaneous hides the nonlocality, but cannot make it go away.

 

[atyy]

Regarding (A), here is a discussion that says cluster decomposition does not apply for entangled initial states: https://www.physicsforums.com/threads/cluster-decomposition-and-epr-correlations.409861/#post-2773606 (especially posts #4 by humanino and #7 by Demystifier).

As for microcausality, what it says is that the measurement of one local observable cannot affect the measurement of a different spacelike-separated local observable. This is a requirement for no superluminal signalling of classical information. This is about the causes of local events. It does not say anything about the cause of nonlocal correlations.

 

[vanhees71]

I've the impression we have just a different language again. So I think we have to clarify what we mean by "cause" first. Two events a causally connected if one event necessarily leads to the other event. Now the fundamental time arrow is defined via causality, i.e., it parametrizes the order of causal events and by convention an event A can only be the cause of an event B when A happens before B.

In relativistic physics this implies that two causally connected events must be time-like or light-like relative to each other, because otherwise the statement that A causes B would become observer dependent, i.e. the causality relation, defined by time order, would not be invariant under proper orthochronous Lorentz transformations (the proper orthochronous Lorentz group is the symmetry group underlying the structure of special relativistic spacetime).

This implies that the natural laws, describing the dynamics of systems through equations of motion, should also be causal in the sense that interactions between distant subsystems, affecting changes of one subsystem due to the interaction with the other. So far, on a fundamental level, this is realized by the field picture. In classical physics this means that the equations of motion of particles are described as mediated through fields, which obey equations of motion that are formulated in terms of causal laws, which excludes (at least to experience from model building so far) tachyonic field equations (free tachyonic fields can be interpreted in a way fulfilling the causality constraint for their propagation, but this has not been achieved for interacting tachyonic fields and tachyonic fields interacting with particles). The forces in the equation of motion of the particles are local functions of the particle's space-time coordinate and its time derivatives, and the field-equations of motion have source terms due to the presence of particles which admit causal (retarded) solutions. On the classical level, however, there is a tremendous self-consistency problem. Even the most simple case of electromagnetics of point particles is intrinsically inconsistent or at least only solvable in an approximate sense (see, F. Rohrlich, Classical charged particles).

In quantum theory these ideas are transferred to the ideas of local microcausal quantum field theories, from which the causality of observable quantities can be deduced (it's a sufficient condition for that, whether it's necessary I'm not clear about; so far I haven't seen a formal proof of this, but FAPP we can constrain our discussion to such local microcausal QFTs because all practically relevant theories, including the Standard Model of elementary particle physics, is of this kind).

This also implies the linked-cluster principle, which states that local (local here means local in both space and time of course) observations (and so far all our observations are quite local, made with measurement apparati in the lab which always have finite spatial extent) are uncorrelated if the observations are space-like separated. There is no restriction on the states in which the observed (sub)systems are prepared. Also if there is entanglement as in our quantum-eraser example, there is no way to find out about this entanglement with local observations. Alice and Bob, making local polarization measurements about photons from a parametric-down conversion "preparation". They simply find unpolarized photons. There's no way for Alice (Bob) to tell that her (his) photon is part of an entangled pair. To figure this out they have to compare their measurement protocols, which they have made such as that they are able to know which photons belong to one pair. That's done by properly keeping track about the time of their measurements, i.e., the ensemble of entangled photon pairs must be timewise separated enough such that within their time-measurement accuracy (limited by the dead time of their photon detectors) they can clearly resolve which photon pair comes from the common preparation as an entangled pair by parametric downconversion. Then they find out about the correlations encoded in the formalism by the description as a two-photon state for which the polarization states of the single photons is entangled. Thus the "cause" for the correlation lies in the preparation of the two-photon state in this entangled state, i.e., in the preparation procedure at the very beginning, i.e., causally (!) before either Bob or Alice measure the polarization state of their photon.

Now to the Heisenberg picture. Of course, it's clear that the choice of the picture of time evolution is totally unimportant. The outcome is always the same in each picture. In the Heisenberg picture the state (statistical operator for pure or mixed states) is time-independent. But then the operators, describing observables and thus their corresponding (generalized) eigenstates, carry the full time evolution with the full Hamiltonian (including the interaction part). For the Schrödinger picture it's the opposite, i.e., the stat. op. carries the full time evolution and the observables are described by time-independent operators. For the general Dirac picture you split the time-dependence among the stat. op. and the operators describing observables. Among all pictures you change with unitary transformations. So the probabilities for Alice and Bob to find one of the photons in the entangled pair in a certain polarization state at their place at a certain time are of course the same in all pictures. So the answer to the question, whether "the state is the cause for the correlations" cannot depend on the choice of the picture of time evolution. This is so by construction: QT is invariant under changes of the picture of time evolution (of course, here I ignore all formal problems in connection with Haag's theorem concerning the interaction picture used to define perturbative QFT).

However, it depends somewhat on the metaphysical interpretation of "state". I think to define the meaning of the notion of "states" in QT is the key for all these debates and misunderstandings in such debates. Of course, physicswise a state is not "a selfadjoint normalized trace-class operator in Hilbert space". This is the mathematical description of it within the theory. Physical notions must be defined as statements about objectively observable facts. That's why in my understanding, the physical definition of "state" is that it is an equivalence class of preparation procedures. E.g., in a Stern-Gerlach experiment a silver atom is in the state with spin up in $z$ direction in the sense that I've let it go through an inhomogeneous magnetic field such that I can (with practically arbitrary accuracy) be sure that silver atoms are separated according to the two different spin states and that I can filter out the unwanted spin-down beam. For Alice and Bob in the quantum-eraser experiment the state is given by the parametric-down conversion setup: You shine a laser beam on the appropriate birefringent chrystal and just consider the polarization-entangled photons. This ensures, as proven empirically (with practically arbitrarily high accuracy), that you have photon pairs showing the correlations described by the corresponding statistical operators (or rays in Hilbert space for this case of a pure state). In this sense, I say the "quantum correlations are caused by the preparation in this particular state".

 

[atyy]

I've the impression we have just a different language again. So I think we have to clarify what we mean by "cause" first. Two events a causally connected if one event necessarily leads to the other event.

Let's try to define this mathematically. Let's suppose that there are only 3 events u,v,w. If u is the cause of w, then P(w|u,v) = P(w|u), otherwise u does not necessarily lead to w, since changing v can influence the distribution of w.

Let's consider a simple case without spatially separated measurements, where A is Alice's outcome, a is Alice's measurement setting, and z is the preparation procedure. In general, P(A|a,z) will not be P(A|z) so z is not the cause of A. The preparation procedure is not the cause of the measurement outcome, because the outcome also depends on the measurement setting. Using this definition of cause, the preparation procedure and measurement setting together are the cause of the outcome.