An abstract long-distance correlation experiment

[ddd123]

Inferred but unchecked knowledge does not have to respect causality constraints. I had demonstrated this by reminding us that we can infer what happens inside a black hole where causality forbids that any information leaks out.

I don't see the link with the rest of the post. I understood your point on extended causality, but here you seem to be proposing the old rejection of counterfactual definitess to attempt to recover locality. I'm surely wrong but my impression of your posts is that you go overkill: you only need one of these ideas to explain (away?) the EPR correlations, not all. You've proposed what seemed like (but were not really, at least according to you) superdeterminism, non-realist locality, now a form of non-locality... And you seem to be making a big mix of these without clearly relating them. This is the most confusing aspect for me: I'm sure for you it's all clear and connected but I don't see it.

 

[stevendaryl]

Inferred but unchecked knowledge does not have to respect causality constraints. I had demonstrated this by reminding us that we can infer what happens inside a black hole where causality forbids that any information leaks out.

If I understand what you mean, Bell explicitly allowed for this kind of "inferred knowledge". The causality constraints on such knowledge is that if Alice, making local observations, can infer something about Bob, who is too far away (or inside a black hole, or whatever) to allow information to pass from Bob to Alice, then it must be that Alice's inference depends only on information from the intersection of Alice's and Bob's backwards lightcones. Aren't the inferences about inside a black hole of this type?

 

[A. Neumaier]

Alice's inference depends only on information from the intersection of Alice's and Bob's backwards lightcones. Aren't the inferences about inside a black hole of this type?

Yes. If Norbert's preparation and Bob's settings are agreed beforehand, they are in the past light cone of Norbert, hence in the intersection of the past light cones of Alice and Bob. On the basis of this information and the knowledge of quantum mechanics she can infer (but not observe) Bob's results based on the observation of her own results and the assumed agreement. But she cannot infer Bob's controls (i.e., whether he in fact was able to put the agreed intentions into practice), and hence cannot be sure about what actually happened. Whereas Yvonne doesn't need to draw inferences; she has in her past light cone all information about both the controls used and the observations obtained and can check that the predictions of quantum mechanics came true.

In spite of the observed nonclassical correlations, (extended) causality is nowhere violated. The limit on signal speeds only applies to inferences about the values of controls (e.g., pointer settings) somewhere else from observations here and now, not to inferences about the values of observations depending on these controls! Only the former constitutes an information transfer and hence allows communication. Nothing in the principles of relativity restricts other forms of correlations.

to attempt to recover locality.

I am not attempting to recover locality; see what I wrote at the end of post #210. Instead, I am restoring the compatibility of Bell experiments with causality and relativity by pointing out that the initial assumption in Bell's analysis is unnecessarily strong and not warranted, since there is a proper Lorentz covariant definition of what causality should mean that satisfies all demands I think can reasonably placed on the notion of causality. Nonlocal correlations are not in conflict with extended causality. Thus nonlocal correlations are not a problem for understanding quantum mechanics and its relation to relativity in a rational and intuitive way. At least it doesn't contradict my intuition, and I am sure mine is not so weird that it cannot be learned and defended with rational arguments.

That nonlocal correlations may be an obstacle to a classical interpretation of quantum mechanics is a completely different matter. QM is sufficiently different from CM that one shouldn't expect a simple (e.g., local) such interpretation. In my opinion, Bohmiam mechanics is even more weird than what it tries to replace.

 

[A. Neumaier]

You've proposed what seemed like (but were not really, at least according to you) superdeterminism, non-realist locality

I proposed a deterministic, realist theory of the universe consistent with quantum field theory (to be discussed in the other thread, not here). Quantum field theory is local in the sense of satisfying local commutation relations, i.e., the basic quantum fields can be prepared independently at any finite set of mutually spacelike points. Quantum field theory is nonlocal in Bell's sense since what is (in principle) observable in quantum field theory (and propagates deterministically) are the N-point functions. Unlike classical local fields, the N-point functions are multilocal, encode nonlocal correlations, and exhibit all features familiar from quantum mechanics. It is very unfortunate that the word 'local' has these two very different meanings - but knowing this, the two meanings should not be confused.

 

[stevendaryl]

Yes. If Norbert's preparation and Bob's settings are agreed beforehand, they are in the past light cone of Norbert, hence in the intersection of the past light cones of Alice and Bob. On the basis of this information and the knowledge of quantum mechanics she can infer (but not observe) Bob's results based on the observation of her own results and the assumed agreement.

I don't think there is any difficulty in understanding how Alice's observations can tell her something about Bob's situation far away (or inside a black hole). Bell's "Bertlmann's socks" example is of this type of inference. However, in similar non-quantum cases, the information that Alice gets through observation already existed in the intersection of Alice's and Bob's backwards light cones. In the case of QM, the information seems to come into existence through the act of observation itself. You seem to be saying that you think that's true in the quantum case, too, but I think that is not the mainstream view of QM.

 

[Mentz114]

I don't think there is any difficulty in understanding how Alice's observations can tell her something about Bob's situation far away (or inside a black hole). Bell's "Bertlmann's socks" example is of this type of inference. However, in similar non-quantum cases, the information that Alice gets through observation already existed in the intersection of Alice's and Bob's backwards light cones. In the case of QM, the information seems to come into existence through the act of observation itself. You seem to be saying that you think that's true in the quantum case, too, but I think that is not the mainstream view of QM.

If I understand the problem correctly then this is the logic

1. Alice's detector interacts with the left photon
2. Bob's detector interacts with the right photon

Later when the humans compare results they infer that Bob's result is correlated with Alice's, which is problematic.

The problem is because they assume that '... detector interacts with the ... photon' means 'detector clicked'. This seems to be unjustified.

If that assumption is relaxed then there is no theoretical proof or experimental support that the two detectors did not 'click' until the event lies in Bob and Alice's past light-cone. Before that we cannot say anything about the order.

 

[A. Neumaier]

In the case of QM, the information seems to come into existence through the act of observation itself. You seem to be saying that you think that's true in the quantum case, too, but I think that is not the mainstream view of QM.

I would say that the two mainstream views are the Copenhagen interpretation and the ensemble interpretation.

In the Copenhagen interpretation, the individual system has no definite properties before it is observed. This is possible only if the observation creates the properties. How else could this statement be interpreted?

In the ensemble interpretation, one is silent about the properties of the individual systems and only talks about the prepared and observed properties of the ensemble. In this case, the observations are properties of the measurement devices alone, and become properties of the ensemble only when averaged over a large number of observations. (In our nonlocal experiment, only when Yvonne creates the statistics!)

In both mainstream views, therefore, the information comes into existence through the act of observation. (Except that expositions of both views generally prefer to be vague about this.)

 

[stevendaryl]

If I understand the problem correctly then this is the logic

1. Alice's detector interacts with the left photon
2. Bob's detector interacts with the right photon

Later when the humans compare results they infer that Bob's result is correlated with Alice's, which is problematic.

The problem is because they assume that '... detector interacts with the ... photon' means 'detector clicked'. This seems to be unjustified.

If that assumption is relaxed then there is no theoretical proof or experimental support that the two detectors did not 'click' until the event lies in Bob and Alice's past light-cone. Before that we cannot say anything about the order.

Are you talking about the possibility that neither Alice nor Bob has an actual result until some future time when the results can be compared? (That's sort of the many-worlds approach, if I understand you correctly.)

 

[Mentz114]

Are you talking about the possibility that neither Alice nor Bob has an actual result until some future time when the results can be compared? (That's sort of the many-worlds approach, if I understand you correctly.)

Postponed into the future by just enough time to allow Bob and Alice to be in causa contact.

If we regard coincidences to be the only observables and put an electronic coincidence counter between Bob and Alice, it can onlt register after a signal has traveled from B abd A. So the data does not exist until B and A are in contact.

QED ?

 

[A. Neumaier]

after a signal has traveled from B abd A. So the data does not exist until B and A are in contact.

after half the time if the coincidence detector is placed halfway between them.

 

[Mentz114]

after half the time if the coincidence detector is placed halfway between them.

Whoops. Thank you.

 

[stevendaryl]

Postponed into the future by just enough time to allow Bob and Alice to be in causa contact.

Just for clarification, in the time period between Alice's measurement and the time when she receives confirmation from Bob, does Alice not have a definite result? She's in some kind of mixed, or superposed state?

 

[Mentz114]

It seems not, because I've ruled out detector clicks as observables. So the channel that informs has to be a quantum channel (?).

[edit : A and B could be in mixed states as you suggest. Need more thought]

This looks fairly non-realistc but the 2-point photon correlation has nothing to say about that.

I'm painting pictures here. Maybe a model will emerge so numbers can be calculated.

(I'm also reading Ballentine on the KS theorem so my education is incomplete).

 

[A. Neumaier]

in the time period between Alice's measurement and the time when she receives confirmation from Bob, does Alice not have a definite result? She's in some kind of mixed, or superposed state?

According to Bohr (cited in post #197), one has to consider the experiment as a whole to get a consistent quantum interpretation in the most orthodox sense. Thus the answer depends on how one dissects the universe into system and environment, just as in the old analysis about Wigner's[/PLAIN] friend.

To avoid problems of Schroedinger cat type, we may assume that Alice is simply modeled as the pair of (pionter setting,color of light) in Alice's device, and similar for Bob. Yvonne is modeled in the Cartesian product by a state in the tensor product.

From the perspective of Alice, the experiment is concluded when she gets her result, and Bob's result (which she is not observing but only inferring) is not part of the setting. As a consequence, the system is in a definite state as far as Alice is concerned and Bob is in a superposition of possible pairs (pointer setting, light color). Unless Alice assumes that Bob could keep any prior agreements and uses a reduced system description that breaks Bob's superposition.

On the other hand, from the perspective of Yvonne (the coincidence counter), the experiment is concluded only when she gets her coincident result, and before that both Alice and Bob are in a superposition as obtained from the unitary dynamics prepared by Norbert.

Thus what is definite depends on which problem description is being employed - as in any stochastic description of a system.

Indeed, this is in many ways analogous (though different in detail) to what one finds in the interpretation of a classical experiment involving throwing a sequence of labelled dice. We may consider the experiment to be performed by Alice who hides the dice thrown under a piece of cloth; later Yvonne comes and lifts the cloth slowly so that one number after the other appears.

To Alice, all dice are known and the system is in a pure state with definite outcomes. To Yvonne, no definite outcome exists initially, and her system is in a mixture of all possible sequences. As she lifts the veil from the first die, her system collapses into an eigenstate of the first die, and only a mixture of the sequences with fixed first entry results, etc. until at the end, when the veil is completely removed, her system state is collapsed to a pure state with the same definite outvcomes as that known by Alice long before.

 

[strangerep]

[...] extended causality [...]

What you seem to be rediscovering/reinventing overlaps with Mermin's interpretation of QM: that (fundamentally) only correlations have physical reality. Also with Rovelli's ideas on Relational QM, which he already noted is sufficient to banish some of the confusion that arises when QM confronts Relativity. (I can dig out references if you don't already have them.)

I don't have a problem with any of that, since that's more-or-less how Bell-type puzzles were solved long ago: through understanding that correlation is not causation (though it may masquerade as such).

But I think your term "extended causality" might be misunderstood, since it's really (iiuc) about the causality features associated with nonlocal coherence (and hence nonlocal correlations). To me, this is all about time evolution of (in general, spacelike-) extended N-point correlation functions -- which is fine.

To turn these vague ideas into a proper theory, I guess you intend to use something like the Wightman reconstruction theorem to recover operator-valued distributions (quantum fields) from a suitable set of correlation functions?

 

[Mentz114]

According to Bohr (cited in post #197), one has to consider the experiment as a whole to get a consistent quantum interpretation in the most orthodox sense. Thus the answer depends on how one dissects the universe into system and environment, just as in the old analysis about Wigner's[/PLAIN] friend.

While we are talking about coincidences - is there a distinction between classical coincidences and quantum coincidences ?

Ballentine says that the probability of two detectors at $x_1,x_2$ will both register is proportional to the second order two photon correlation $G^{(2)}(x_1,x_2;x_1,x_2) = C^4 2\left(1 + \cos\left[ (k_1-k_2)\cdot (x_1-x_2) \right] \right)$

Can we deduce from this that $G^{(2)}(x_1,x_1;x_1,x_1) + G^{(2)}(x_2,x_2;x_2,x_2) \geq G^{(2)}(x_1,x_2;x_1,x_2)$ ?

I'm not sure if what I've written is meaningful.

 

[zonde]

What you seem to be rediscovering/reinventing overlaps with Mermin's interpretation of QM: that (fundamentally) only correlations have physical reality.

As I see, idea that only correlations have physical reality does not quite help.
Consider setup where Alice and Bob makes two copies of their results and send them to two distant Yvonnes so that the moment when Yvonnes receive both results they are spacelike separated (they are on a line that is perpendicular to the line connecting Alice and Bob). And considering that QM predictions are probabilistic two correlation results could have slightly different results if they are determined independently from quantum (non factual) detection records.

 

[strangerep]

As I see, idea that only correlations have physical reality does not quite help.
Consider setup where Alice and Bob makes two copies of their results and send them to two distant Yvonnes so that the moment when Yvonnes receive both results they are spacelike separated (they are on a line that is perpendicular to the line connecting Alice and Bob).

I don't understand where your Yvonnes are. To be spacelike separated, I would have thought they'd be on line "parallel" to the line connecting Alice and Bob.

And considering that QM predictions are probabilistic two correlation results could have slightly different results if they are determined independently from quantum (non factual) detection records.

I must be missing something. I don't understand the significance of this sentence.

 

[zonde]

I don't understand where your Yvonnes are. To be spacelike separated, I would have thought they'd be on line "parallel" to the line connecting Alice and Bob.

Imagine square. Alice and Bob are at two opposite vertices and two Yvonnes are at other two. When Alice and Bob sends their results to any Yvonne both messages are received at the same time.

I must be missing something. I don't understand the significance of this sentence.

If Alice s and Bob's results are not factual but instead are in some kind of quantum superposition then predictions for correlations are determined only when coincidence "measurement" is made, right?

 

[A. Neumaier]

I can dig out references if you don't already have them.

Yes, please; things are easier to discuss if the background is fixed.

that (fundamentally) only correlations have physical reality.

Slightly more, namely all N-point functions. (Correlations are 2-pooint functions.) This is indeed what emerges once one considers relativistic quantum field theory as fundamental, where the correlations contain everything that makes contact with reality. Related is

the Wightman reconstruction theorem to recover operator-valued distributions (quantum fields) from a suitable set of correlation functions

The fact

that correlation is not causation

is another related, purely classical piece of understanding, obtained (at least in the Wikipedia account of it) under informal assumptions. What emerged from the present discussion goes beyond the informal stage by giving a clear, scientifically checkable criterion for causation, a better word for ''an infomation transfer'' in the following statement:

The limit on signal speeds only applies to inferences about the values of controls (e.g., pointer settings) somewhere else from observations here and now, not to inferences about the values of observations depending on these controls! Only the former constitutes an information transfer and hence allows communication.

your term "extended causality" might be misunderstood, since it's really (iiuc) about the causality features associated with nonlocal coherence (and hence nonlocal correlations).

I deliberately chose the words ''extended'' and ''separable'' rather than ''nonlocal'' and ''local'' in my formalization of the two forms of causality since the term ''(non)local'' is ambiguous and gives rise to additional misunderstandings:

Quantum field theory is local in the sense of satisfying local commutation relations, i.e., the basic quantum fields can be prepared independently at any finite set of mutually spacelike points. Quantum field theory is nonlocal in Bell's sense since what is (in principle) observable in quantum field theory (and propagates deterministically) are the N-point functions.

 

[stevendaryl]

What you seem to be rediscovering/reinventing overlaps with Mermin's interpretation of QM: that (fundamentally) only correlations have physical reality. Also with Rovelli's ideas on Relational QM, which he already noted is sufficient to banish some of the confusion that arises when QM confronts Relativity. (I can dig out references if you don't already have them.

I'll look those up. But is there a pithy way to say what it means that only correlations have physical reality? Does that mean that Alice's result (heads up, or whatever it is) isn't real, only the fact that her result is correlated with Bob's (equally unreal) result?

 

[A. Neumaier]

means that only correlations have physical reality? Does that mean that Alice's result (heads up, or whatever it is) isn't real, only the fact that her result is correlated with Bob's (equally unreal) result?

No. It means (in quantum mechanics) that everything has meaning only relative to an observer and its (the observer may be a machine) way of defining what the system under study is. The context and the framework it is considered in defines (also classically) what observations mean and how they are related to predictions.

 

[ddd123]

No. It means (in quantum mechanics) that everything has meaning only relative to an observer and its (the observer may be a machine) way of defining what the system under study is. The context and the framework it is considered in defines (also classically) what observations mean and how they are related to predictions.

That doesn't seem very "realist". The Einsteinian spacetime was supposed to be a block universe after all, and your definition of extended causality should still work with that.

 

[A. Neumaier]

That doesn't seem very "realist". The Einsteinian spacetime was supposed to be a block universe after all, and your definition of extended causality should still work with that.

Yes, with extended causality and a quantum field view of what is real one can (in my view) maintain a realist picture. What I had described was the more orthodox view since stevendaryl prefers explanations to be mainstream, it seems.

 

[ddd123]

Ok, I know I'm not so knowledgeable but I'm making these comments since you want to write an Insights article aimed at people like me, so that I could be able to follow it.

 

[A. Neumaier]

since you want to write an Insights article aimed at people like me

Yes; I am a bit behind; too many things want to be done at the same time. But I should have it ready by the end of the month.

 

[strangerep]

That doesn't seem very "realist". [...]

Heh, it's relational...

 

[strangerep]

[References...] Yes, please; [...]

(1) N. David Mermin, The Ithaca Interpretation of Quantum Mechanics,
Available here.

Some material in his acknowledgment section points to further (older) references:

I first encountered the view that correlations are fundamental and irreducible when I heard it advocated as the proper way to think about Einstein–Podolsky–Rosen correlations, in talks by Paul Teller and Arthur Fine.12 It did not then occur to me that this might be the proper way to think about much more general correlations.13 Nor did it occur to me that objective reality might consist only of correlations until I heard Lee Smolin14 sketch an approach to quantum mechanics that treated symmetrically a physical system and the world external to that physical system. Shortly thereafter I received a paper from Carlo Rovelli,15 arguing from a very different point of view that quantum states were nothing more than expressions of relations between subsystems. A similar point of view toward quantum states goes at least back to Everett’s original “relative–state” formulation of quantum mechanics 16 before it was swept off into the many–worlds extravaganza. I acquired the notion that certain density matrices were just as fundamental and irreducible as pure states from Rudolf Peierls, who insisted to me several years ago that the proper conclusion to draw from EPR was not non-locality, but the absence of any objective difference between mixtures of photons with random 0-90 degree polarizations, or random 45-135 degree polarizations. After the Bielefeld conference I had an instructive e-mail argument with Tim Maudlin about this point, and about some analysis by Sandu Popescu18 that confirmed my growing suspicion that conventional views about density matrices and “quantum non-locality” were inadequate.

(2) N. David Mermin, What is quantum mechanics trying to tell us?
Available here.

This paper also mentions Wooter's thm, or what Mermin calls the "SSC" thm (Sufficiency of Subsystem Correlations).
It only occurred to me yesterday, that this serves a similar purpose in Mermin's (ordinary QM) context that the Wightman reconstruction thm might serve in the current context.

(3) C. Rovelli, Relational Quantum Mechanics,
Available here.

There are some more recent related papers by Rovelli, e.g.,

(4) C. Rovelli, Relative information at the foundation of physics,
Available here.

 

[stevendaryl]

What you seem to be rediscovering/reinventing overlaps with Mermin's interpretation of QM: that (fundamentally) only correlations have physical reality. Also with Rovelli's ideas on Relational QM, which he already noted is sufficient to banish some of the confusion that arises when QM confronts Relativity. (I can dig out references if you don't already have them.)

I took a look at Mermin's paper "Ithaca Interpretation of Quantum Mechanics" http://arxiv.org/abs/quant-ph/9609013, and I really wanted to like it, being an Ithacan myself (I wonder whether Mermin still lives here). I really liked his 6 "Desiderata for an interpretation of quantum mechanics", because, other than number 6 (I'm not exactly sure what objective probability means), they're exactly what I'd want for an interpretation of quantum mechanics:

1. Is unambiguous about objective reality.
2. Uses no prior concept of measurement.
3. Applies to individual systems.
4. Applies to (small) isolated systems.
5. Satisfies generalized Einstein–locality.
6. Rests on prior concept of objective probability.

However, I still don't understand what his interpretation really is, or how it applies in the most interesting case--EPR.

 

[ddd123]

Same here also for Rovelli's interpretation. I read the EPR explanation on wikipedia and elsewhere but they're all so cryptic.

 

[strangerep]

[...]
However, I still don't understand what his interpretation really is, or how it applies in the most interesting case--EPR.

IIUC, it's still only an interpretation. The idea is that correlations are what's physically real. Then, since the correlata are unphysical, it's a red herring that they "seem" to influence each other superluminally. One should instead concentrate on how correlations evolve.

But like all interpretations, one's tummy is left feeling insufficiently fed. Afaict, there's not really any new tangible physics there -- just a different way of thinking about things that (hopefully) banishes some of the older philosophical puzzles.

I wonder whether Mermin still lives here [Ithaca]

His webpage at Cornell University still seems active, though he retired 10 yrs ago. I was interested to see that the leading quote on his webpage (from 1931) is relevant to this thread:

"Quantum mechanics forbids statements about the object. It deals only with the object-subject relation." — Schroedinger to Sommerfeld, 1931.

Apparently Mermin is also responsible for the "shut up and calculate" phrase.

 

[Mentz114]

That's very interesting, are there explicit constructions?

You asked about this a long time ago and I found this paper (*).

Instead of polarisers the theory and experiment uses phase plates('parity rotators'). This means they are looking for correlations in the spatial domain and they map the infinite dimensional position space into 2D parity space so the CHSH inequality can be realized. The important thing is that the correlations are explicitly non-local as shown in equation (2).

I see this as possible support for the change in the correlations ( ie probabilities of coincidences) at phase-velocity.
Or perhaps I'm just out-of-phase on this.

(*)
Experimental Violation of Bell’s Inequality in Spatial-Parity Space
Timothy Yarnall, Ayman F. Abouraddy,Bahaa E. A. Saleh, Malvin C. Teich
http://arxiv.org/pdf/0708.0653.pdf

We report the first experimental violation of Bell’s inequality in the spatial domain using the
Einstein–Podolsky–Rosen state. Two-photon states generated via optical spontaneous parametric
downconversion are shown to be entangled in the parity of their one-dimensional transverse spatial
profile. Superpositions of Bell states are prepared by manipulation of the optical pump’s transverse
spatial parity—a classical parameter. The Bell-operator measurements are made possible by devising
simple optical arrangements that perform rotations in the one-dimensional spatial-parity space of
each photon of an entangled pair and projective measurements onto a basis of even–odd functions.
A Bell-operator value of 2.389 ± 0.016 is recorded, a violation of the inequality by more than 24
standard deviations

 

[edguy99]

.. Does this help?

Sure does, Thanks a lot.

Sorry for slow response, I was out of internet access for 2 weeks. :)