A Hidden Assumptions in Bell's Theorem?

[kurt101]

Please start a separate thread if you want to delve further into this.

Ok, I may do that.

 

[Jarvis323]

I chose A level since I believe that it would be fruitless to address the issue at a lower level. But I am definitely not personally at an A level in QM, which is why I haven't really participated.

My main interest was to clarify the foundational assumptions. In this context, as much nuance as possible is appreciated, meaning that even if a majority of those in the community have decided certain assumptions or nuances can be glossed over or abstracted, I would be interested to hear the basis for glossing over or abstracting these nuances or assumptions in as much objective depth as possible.

This could mean exploring not only the assumptions but also the definitions. Locality and realism have always been confusing for me in this regard, because it seems that either a lot that I don't know is being assumed (well almost certainly this is true), and/or these concepts are not fully agreed on or objectively defined.

So if something is expected to be known based on it being an A level thread, it would be nice if that thing was something objective and not legitimately contested, even if only by a minority.

In terms of locality and Hess's argument that Bell's theorem assumes the algebra of real numbers applies, I wonder how would you even define locality if your hidden variable theory doesn't follow the algebra of real numbers. It seems like an issue where you first need the hidden variable theory with its explicit mathematical abstractions known before you can meaningfully define locality?

Anyways, sorry for the interruption, carry on.

 

[PeterDonis]

I chose A level since I believe that it would be fruitless to address the issue at a lower level.

I think that's true; the issues involved require an "A" level background, if for no other reason that without it it is pretty much impossible to follow the literature, since papers in this area are almost always written for other experts.

 

[PeterDonis]

Hess's argument that Bell's theorem assumes the algebra of real numbers applies

I am unable to access that particular paper since it's behind a paywall. Just reading the abstract, the claim doesn't seem to me to be about the algebra of real numbers but about Boolean algebra: in other words, the algebra of variables that can only take the values $0$ or $1$. But no such assumption is made in Bell's theorem, or indeed in QM itself: Bell's theorem deals with probabilities, which can be any real number from $0$ to $1$, and QM deals with probability amplitudes, which are in general complex numbers. So I find it very hard to believe that that particular paper has identified a real issue; it seems far more probable to me that the authors are simply misapplying Boolean algebra.

 

[Jarvis323]

Here is the arxiv version. The discussion on Boole is not understood clearly by me, at least, because I lack the background knowledge.

This paragraph seems to be illustrative of the idea.

Progress related to Boole’s consistency tests with inequalities was made by Vorob’ev [13]. He showed, in a very general way, that non-trivial inequalities and conditions of the Boole type can be found by constructing topological-combinatorial “cyclicities” of functions on σ -algebras. For the purpose of our paper, it is sufficient to understand these general cyclicities just by the above example: the AiAj with i,j = a,b.c are functions on a probability space (random variables) and form a closed loop, meaning that the choices in the first two products of the inequality determine the third. An infinite number of such inequalities can, therefore, be composed by arranging algebraic expressions of functions that determine the value of other algebraic expressions of the same inequality. Any violation of such inequalities by the measured averages means that the mathematical abstractions describing the experiments are not functions on a σ -algebra.

https://arxiv.org/pdf/1108.3583

 

[Demystifier]

Does the entire universe share the same wave function in your interpretation?

Not necessarily, only those parts which are mutually entangled.

Why does the change in the wave function from Alice's measurement affect Bob?

Because it affects their common entangled wave function.

And why does it not effect some other pair of locally prepared entangled photons.

Because the other pair is not entangled with Alice and Bob.

And again, why is the wave function of Bob's future measuring apparatus affected or is is only affected once the light cone from Bob reaches it?

Again, there is no such thing as wave function of Bob or of his apparatus. There is only the total wave function of all mutually entangled particles. This total wave function is affected instantaneously. Note also that a total wave function depends on many spatial positions but only one time coordinate, so space and time are not treated on an equal footing, so the wave function is not a Lorentz invariant object.

 

[vanhees71]

Well, how to say this in friendly words: "quoted above" might be true, but you routinely leave the task to guess the parts you are actually quoting to the reader.

For you, "to quote" seems to mean more that you could come up with an actual quote if pressed. But for most others, to quote means to select a specific piece of text from a longer text to provide a focus point. Perhaps you did it in this specific case, and I would find it if I searched above (and had some special skill to guess right at which post to look). But more likely, your "quote above" was just a general recommendation to read that entire book.

I can't quote entire chapters of textbooks. It's not so difficult to just read the book, isn't it?

Yesterday by a simple Google research I also found out that the first part of Coleman's brillant QFT book (which emphasizes the importance of locality and microcausality from the very beginning!) is freely available through the arXiv:

https://arxiv.org/abs/1110.5013

 

[vanhees71]

I chose A level since I believe that it would be fruitless to address the issue at a lower level. But I am definitely not personally at an A level in QM, which is why I haven't really participated.

In fact the nice thing with these issues is that it is not that complicated math. You can do everything with quite basic notions of Hilbert-space theory, and it's sufficient to discuss a two-state system, particularly in the here discussed case of polarization entanglement of photon pairs. It's also of help when you can express it in terms of annihilation and creation operators of photons. Then it's simple algebra.

To follow the argument about microcausality you need the first few chapters of an introductory QFT book. It's a bit more advanced but also not that complicated. Again I can recommend to read the first few chapters of Coleman's QFT lectures, which are also available from the archive, i.e., NOT behind a paywall:

https://arxiv.org/abs/1110.5013

 

[vanhees71]

Not necessarily, only those parts which are mutually entangled.

Because it affects their common entangled wave function.

Because the other pair is not entangled with Alice and Bob.

Again, there is no such thing as wave function of Bob or of his apparatus. There is only the total wave function of all mutually entangled particles. This total wave function is affected instantaneously. Note also that a total wave function depends on many spatial positions but only one time coordinate, so space and time are not treated on an equal footing, so the wave function is not a Lorentz invariant object.

Wave functions are not a very good description of relativistic QFT anyway. One needs a Fock space since particle annihilation and creation processes are prevalent, particularly in the early universe, where the matter was in a QGP + perhaps unknown dark-matter particles + perhaps something completely unknown (dark energy).

The quantum state of the entire universe is anyways a fictitious concept, because it's not observable. We can only observe a small part of the universe, and also here locality is a blessing of Nature. We don't need to bother too much about far-distant processes when doing local observations.

 

[vanhees71]

But I'm allowed to use the standard terminology of my scientific community too! That's why I always add my definition of "locality", namely the assumption of the microcausality constraint for operators that represent local observables as used in standard relativistic QFT since 1926!

PS: BTW also in the quantum-optics community the use of the word "locality" is not completely orthogonal to the use of the term in the HEP community. At least Zeilinger et al define "locality" in this very way, as you can read from one of their groundbreaking papers particularly on this issue:

G. Weihs et al, Violation of Bell's Inequality under Strict Einstein Locality Conditions, Phys. Rev. Lett 81, 5039 (1998)
https://doi.org/10.1103/PhysRevLett.81.5039

The abstract reads [emphasis mine]

We observe strong violation of Bell's inequality in an Einstein-Podolsky-Rosen-type experiment with independent observers. Our experiment definitely implements the ideas behind the well-known work by Aspect et al. We for the first time fully enforce the condition of locality, a central assumption in the derivation of Bell's theorem. The necessary spacelike separation of the observations is achieved by sufficient physical distance between the measurement stations, by ultrafast and random setting of the analyzers, and by completely independent data registration.

 

[martinbn]

I can't quote entire chapters of textbooks. It's not so difficult to just read the book, isn't it?

I am with you on this one. This is an "A" level thread. Participants should have read a standard textbook on the topics involved if they want to comment on them. One cannot quote a paragraph from page 350 when most of those 350 pages are need to understand it.

 

[LittleSchwinger]

Nonlocality in many studies of entanglement means "violating Bell's inequalities".
In most other areas of physics it means "action at a distance".

This obviously causes confusion as seen on this thread, which has lead to the quantum information community increasingly calling the violation of Bell's inequality "Non-classical correlations" as opposed to Non-locality. For example:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.220403

It's especially confusing in studies of quantum gravity where one has both violations of Bell's inequality and a form of action at a distance, e.g. String Theoretic treatments of Black Holes.

 

[gentzen]

One cannot quote a paragraph from page 350 when most of those 350 pages are need to understand it.

Of course you can. It is way better than "quoting" 350 pages without any indication of a specific piece that would support your argument.

 

[vanhees71]

To understand the basics of quantum field theory it is not sufficient to read snippets of text. If you are not interested enough in the subject to read some introductory chapters of a textbook, why are you then discussing about it?

 

[gentzen]

To understand the basics of quantum field theory it is not sufficient to read snippets of text. If you are not interested enough in the subject to read some introductory chapters of a textbook, why are you then discussing about it?

Are you saying that you are "quoting" QFT textbooks because you assume that I would not be familiar with some introductory chapters of such textbooks? Why would you assume that? Maybe I even read the introductory chapters of Coleman's lectures, and even compared the arXiv version of them with the published book. Not because I am not familiar with the introductory material, but because I was curious of how he presents the material, and curious of the differences between the arXiv version and the final version? Or maybe not, but is this really relevant for my remark that most of us interpret "quoting" as selecting "a specific piece of text from a longer text to provide a focus point"?

And you know perfectly well that this different attitude towards "quoting" doesn't just arise with respect to QFT textbooks, but already when you reply to somebody in a thread, and you routinely don't find it necessary to select a specific part of a post you reply to, or even indicate which post you are replying to.

 

[Fra]

Here is the arxiv version. The discussion on Boole is not understood clearly by me, at least, because I lack the background knowledge.

This paragraph seems to be illustrative of the idea.
https://arxiv.org/pdf/1108.3583

I might get time to read and get back later but skimming it, I spot that it reflects over things that relates to problems in the foundations of probability theory as applied to measurements that I also acknowledge and thinks needs a solution. I wonder if that its what you meana:

"Boole [2] discussed a mathematical-logical way to deal with statistics and probabilities. He dissected experiments into events that could only assume two values obeying a calculus that resembled the algebra of real numbers, but with the operations of multiplication, addition and subtraction replaced by the respective logical operations of conjunction, disjunction and negation. The experimental results were replaced by these mathematical abstractions, as soon as a valid one-to-one correspondence between the experiments and the abstractions was established."

If one steps back and asks, for how an agent can represent it's "own degree of belief" in the [0,1]range, the real numbers are the typical response. And of course the real numbers do the job and is a good general abstraction, but it has a problem, namely that it suggests that there are not noly infinitely many, but even uncountably many different "states of degree of belief". This is not a problem for mathematics, but if you for a split second mixes up the complexions of the model and the complexions of the actual real physica agent, we are lost in a soup and expected from this are plentiful problems of renormalization. And this not even physics, it's a the foundation of the mathematical model (normally standard probability theory) for representing degrees of belieif. The real numbers seems to me to make things easier so it is well motivate, but it has a con-side, but improve it seems to make it ALOT more complicate as the notion of subjectivity enters at the level of foundations of probability. This alone will reject many.

There are several papers around these issues, but almost none of the papers I've read so far address what disturbs me the most.

To set you off in the direction here is one

Quantifying Rational Belief​

"Some criticisms that have been raised against the Cox approach to probability theory are addressed. Should we use a single real number to measure a degree of rational belief? Can beliefs be compared? Are the Cox axioms obvious? Are there counterexamples to Cox? Rather than justifying Cox's choice of axioms we follow a different path and derive the sum and product rules of probability theory as the unique (up to regraduations) consistent representations of the Boolean AND and OR operations. "
-- https://arxiv.org/abs/0908.3212

/Fredrik

 

[Simple question]

The abstract reads [emphasis mine]

That's mind-boggling. You manage to quote a text that disprove your opinions as it was supporting them
If you believe that QFT is complete and describe everything that can be measured, specifically because space-like events cannot have correlation beyond those of microcausality (strict Einstein causality) following preparation
then
"The necessary spacelike separation of the observations" give you few logical options

1. Those observations are wrong, because your philosophy cannot explain them
2. Those observations are inconsequential because you cannot do FLT signaling with them, so who cares about inconsequential laboratory truth ?
3. Those observations reveal the incompleteness of your mathematical framework (Bell put it in math, to force you picking your axiomatic assumptions, to make them clear). This is more of an inconvenient truth.

BTW 2) is not even inconsequential. Teleportation of state, or information (even if, at the end of the day, is "validated" a speed lower then C) is still a physical guarantee that the information is absolutely protected while "teleporting".

 

[vanhees71]

Are you saying that you are "quoting" QFT textbooks because you assume that I would not be familiar with some introductory chapters of such textbooks? Why would you assume that? Maybe I even read the introductory chapters of Coleman's lectures, and even compared the arXiv version of them with the published book. Not because I am not familiar with the introductory material, but because I was curious of how he presents the material, and curious of the differences between the arXiv version and the final version? Or maybe not, but is this really relevant for my remark that most of us interpret "quoting" as selecting "a specific piece of text from a longer text to provide a focus point"?

And you know perfectly well that this different attitude towards "quoting" doesn't just arise with respect to QFT textbooks, but already when you reply to somebody in a thread, and you routinely don't find it necessary to select a specific part of a post you reply to, or even indicate which post you are replying to.

If I don't quote the posting I'm replying to I'm answering to the posting just before my posting. Otherwise I quote the posting. Since I do this for several years now and nobody has complained before I thought that's self-evident.

Also I haven't had specifically you in mind when quoting these textbooks, but obviously many people here are not familiar with the microcausality condition and its meaning. So I quoted textbooks, where the concept is well explained. What's wrong with that?

I hope we can now come back to discuss physics rather than fighting about formalities of conversations in a forum.

 

[vanhees71]

That's mind-boggling. You manage to quote a text that disprove your opinions as it was supporting them
If you believe that QFT is complete and describe everything that can be measured, specifically because space-like

Of course it supports precisely that locality means that space-like separated events are not causally connected, and this is true in standard relativistic QFT imposing the microcausality constraint on local obsesrvable operators.

events cannot have correlation beyond those of microcausality (strict Einstein causality) following preparation
then
"The necessary spacelike separation of the observations" give you few logical options

1. Those observations are wrong, because your philosophy cannot explain them

I have no philsophy, I have a physical theory called QFT (or specificially in the here discussed experiments with photons) QED, and indeed this theory explains all the observations, including the violation of Bell's inequalities. Why should the observations be wrong? If anything could be wrong is, of course, the theory, assuming that there's no mistake in the experiments, but here obviously both the experiments and the theory agree. So either both are correct or both are wrong.

1. Those observations are inconsequential because you cannot do FLT signaling with them, so who cares about inconsequential laboratory truth ?

Of course you cannot do FLT (I guess you mean FTL) signalling, because space-like separated events are not causally connected within QED. The experiment itself doesn't prove that there's no FTL signalling possible, but the authors of the quoted paper take the fact that the measurement events are space-like separated that there cannot be any causal influence of one measurement on the other and thus that the locality assumption is realized in this experiment, and this is the central point of this very paper.

1. Those observations reveal the incompleteness of your mathematical framework (Bell put it in math, to force you picking your axiomatic assumptions, to make them clear). This is more of an inconvenient truth.

There's no incompleteness of "my mathematical framework" (as if I'd have invented QED ;-)) but to the contrary the experimental results are precisely described by this framework.

BTW 2) is not even inconsequential. Teleportation of state, or information (even if, at the end of the day, is "validated" a speed lower then C) is still a physical guarantee that the information is absolutely protected while "teleporting".

I don't mean what you mean by "the information is absolutely protected".

 

[Demystifier]

Wave functions are not a very good description of relativistic QFT anyway.

I use a common jargon in which "wave function" means a state in the Hilbert space, which may be represented in many ways, e.g. wave functional in the field space, wave function in the momentum space (for fixed number of particles), or a Fourier transform of the latter in the position space.

 

[Simple question]

Of course it supports precisely that locality means that space-like separated events are not causally connected,

But they are connected (and this is indeed non-causal)

and this is true in standard relativistic QFT imposing the microcausality constraint on local obsesrvable operators.

Those "observable" are non-local, remember ? you cannot do FTL signaling with them !

I have no philosophy, I have a physical theory called QFT (or specificially in the here discussed experiments with photons) QED, and indeed this theory explains all the observations, including the violation of Bell's inequalities.

You have a philosophy full of contradiction like: QED predict non-local phenomenon by no being able to compute them. Or hand-waving about "projection" of state between space-like region while your own theory explicitly forbid that.

Why should the observations be wrong?

They are not, you are. So stop saying they are non-local in some other way that breaking "Einstein causality". There is no need to use other language to fit your philosophical need. Breaking Einstein causality do NOT mean FTL signaling.

If anything could be wrong is, of course, the theory, assuming that there's no mistake in the experiments, but here obviously both the experiments and the theory agree. So either both are correct or both are wrong.

Wrong. A theory may be incomplete, but still be useful. Like QM whose "fantastic" precision is to predict 1/2 chance of being spin up. Nature do way better than this, including spooky correlation at a distance.

...that there cannot be any causal influence of one measurement on the other and thus that the locality assumption is realized in this experiment, and this is the central point of this very paper

That you didn't quite grasp, because it means your "projection" could not happened, because it would be non-causal, and you keep denying that a-causal phenomenon are observed, and cannot even be present (in principle, because of micro causality) in your theory solution. And cherry on top you believe that theory to be complete and describing everything.

There's no incompleteness of "my mathematical framework" (as if I'd have invented QED ;-)) but to the contrary the experimental results are precisely described by this framework.

You cannot have your quantum cake and eat it.

I don't mean what you mean by "the information is absolutely protected".

Picture a quantum snail, it can teleport from A to B, even at a snail pace. "While" it is gone from "space-time", while its world line is suspended, no bird will be able to eat it. Absolute protection.

 

[vanhees71]

But they are connected (and this is indeed non-causal)

The two photons are "connected", because they are prepared in an entangled state, but this does not imply that a measurement on one photon has an instantaneous or faster-than-light influence influence on the other photon. The entangled state describes correlations observed for the outcome of such measurements. Einstein called it "inseparability".

Those "observable" are non-local, remember ? you cannot do FTL signaling with them !

I don't understand what you mean by "non-local". The experimentalists measure one photon at one place and the other at another far distant one, i.e., the detectors used to register the photons have a well-defined position and are well separated from each other, i.e., you perform local measurements, and the setup is such that the measurement events ("clicks") are space-like separated. In this sense the observables measured on the photon are "local" in the usual sense of QFT.

You have a philosophy full of contradiction like: QED predict non-local phenomenon by no being able to compute them. Or hand-waving about "projection" of state between space-like region while your own theory explicitly forbid that.

QED cannot predict non-local phenomena, because it's a local QFT by construction. The contradiction is on your side! What's described by an entangled state are correlations of observables referring to parts of the entangled system which are measured at far distant places.

They are not, you are. So stop saying they are non-local in some other way that breaking "Einstein causality". There is no need to use other language to fit your philosophical need. Breaking Einstein causality do NOT mean FTL signaling.

Einstein causality simply means that space-like separated events are not causally connected, and by construction QED cannot violate Einstein causality by construction, i.e., because the micorcausality constraint is fulfilled for local observables.

Wrong. A theory may be incomplete, but still be useful. Like QM whose "fantastic" precision is to predict 1/2 chance of being spin up. Nature do way better than this, including spooky correlation at a distance.

That doesn't make sense. Nature behaves precisely as predicted by QM, including stronger-than-classical correlations between far-distant observables, which however are not spooky in any sense.

That you didn't quite grasp, because it means your "projection" could not happened, because it would be non-causal, and you keep denying that a-causal phenomenon are observed, and cannot even be present (in principle, because of micro causality) in your theory solution. And cherry on top you believe that theory to be complete and describing everything.

The projection is perfectly causal. It's achieved by registering photons 2 and 3 at different detectors and thus ensuring that they are found to be in the polarization-singlet Bell state. There's nothing acausal here. How to you come to this idea?

You cannot have your quantum cake and eat it.Picture a quantum snail, it can teleport from A to B, even at a snail pace. "While" it is gone from "space-time", while its world line is suspended, no bird will be able to eat it. Absolute protection.

I've no idea, what you want to say with ths.

 

[DrChinese]

I can't quote entire chapters of textbooks. It's not so difficult to just read the book, isn't it?

Yesterday by a simple Google research I also found out that the first part of Coleman's brillant QFT book (which emphasizes the importance of locality and microcausality from the very beginning!) is freely available through the arXiv:

https://arxiv.org/abs/1110.5013

Again, where to start? Again we have your gross failure to provide an actual quote that supports a single point you have made to date. Asking someone to read 335 pages and guess which part goes with what point? An insult to our intelligence. Just quote something that sounds like what you claim, then readers can read what leads up to it for themselves.

But that is not the most ridiculous part of the reference. If anyone were to actually READ the material, they would discover these gross deficiencies:

• References to the word "Bell" = 0
• References to the word "Entanglement" = 0
• References to "Monogamy" of Entanglement = 0
• References to Entanglement "Swapping" = 0

Explanation for the above: because all of the material was written pre-1988. The precise issues being discussed in this thread were not even discussed - because most of these ideas were developed post 1988. What a red herring and a waste of our time! Basically, you are just saying the same ol' stuff: QFT is local and microcausal. We get that you think so, and we also get that beyond those words you have yet to add any quotes to this discussion that are on point. Entanglement Swapping experiments are an experimental disproof of ideas of locality and Einsteinian causality. Support your disagreement with a suitable quote.

So I ask once again - since you have evaded the central argument (supported by the Monogamy of Entanglement, which is not disputed by you) I have demonstrated objective action at a distance via the BSM contribution to a distant entanglement swap:

Subensemble Before (Initial Preparation): $$\hat{\rho}=\hat{\rho}_{12} \otimes \hat{\rho}_{34}.$$
Subensemble After (Final Observation): $$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$
Objective Change: $$\hat{\rho}_{12} \otimes \hat{\rho}_{34} ≠ \hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$
If it isn't the BSM "quantum causing" the "quantum nonlocal" swap as I say: What exactly do you think did cause the objective state change that can be called "local and microcausal" in this experiment?

 

[vanhees71]

The objective state change is due to the selection of a subensemble by projecting photons (2&3) to a Bell state (in the discussed paper by Pan et al to the polarization-singlet state).

All you should read is the meaning of the microcausality condition as ruling out causal connections of space-like separated events within relativistic QFT (and that's why it's called a local relativistic QFT at least in the HEP community). For that it's sufficient to read the chapter labelled with "September 30" (pp. 21-28). These are 7, not 355 pages.

https://arxiv.org/abs/1110.5013

I didn't know that it is necessary to explain people who want discuss about entanglement in relativistic QFT, how to use a textbook/manuscript. SCNR.

 

[LittleSchwinger]

Very briefly you can "correlation swap" in classical probability, just like you can use correlations to "state teleport" in classical probability. Entanglement swapping and quantum teleporting are just quantum generalisations of these simple protocols.

 

[WernerQH]

The thread is supposed to be about whether there are hidden assumptions in Bell's theorem which leave the possibility open for a local hidden variable theory.

I've been following this thread since its beginning, and I thought that @Demystifier (post #4) and @DrChinese (post #5) had already summarized what I'd wanted to say about the topic. (Not that the coffin for local hidden variable theories needed any more last nails!) Questioning the appropriateness of the "algebra of real numbers" seems hardly relevant to a physicist like myself, but the "Event-by-event simulation of Einstein-Podolsky-Rosen-Bohm experiments" by Zhao et al. piqued my interest. Also a computer (properly programmed!) cannot violate Bell's theorem.

The tricky part seems to be the artificial time delays they introduce in their simulations, which depend on the detector settings:

There are not many reasonable options to choose the functional dependence of T.

We found that T(x) = T0|sin 2x|^d yields the desired results [15].

It's not clear to me why these time delays should be introduced in such a simulation at all. The dependence on the polarizer orientations introduces an additional (anti-)correlation that together with the assumed strict orthogonality of the photon states $\xi_n$ helps beat the Bell inequality. For the particular (peculiar!) case $d=4$ the integrals (eq. 26) are dominated by small values of $\theta$.

The reason why people still search for loopholes in Bell's theorem must be psychological. Some of them seem to think of locality and determinism as the essence of physics. The Hess et al. paper is similar in spirit to Superdeterminism, but is different in how it deals with Probability Theory. While Superdeterminism seems to reject Probability Theory altogether, Hess et al insist that it is applied incorrectly. But as to the question of why the correlations are stronger than what local models can account for, Hess et al. are just as vague:

Possible time dependences within the light cone are numerous. We just list here a smorgasbord of those that matter for sets of particles with spin. The earth rotates around itself and this rotation introduces a time dependence on [...]

(In other words: anything might happen.)

How plausible are alternative abstractions which don't, or which don't and support locality.

The mathematical abstractions must of course match the physical concepts of the theories. And, at least in my view, among the "hidden assumptions" there is an elephant in the room: the existence of photons. It is compelling to explain the observed correlations in the experiments of last year's Nobel prize winners in terms of photons. How else could you explain them, if not through photons having polarization? But this explanation raises more questions than it answers. What are the properties of those photons? They seem to be "undefined" or uncertain most of the time, and properties of the detectors as much as the properties of those photons. Photons have paradoxical properties (especially when they are "entangled"). It reminds me of the paradoxical properties of the ether, which was an equally compelling idea for Maxwell and Michelson. (How else can a light wave propagate? What could an electric field be if not the stress in an elastic medium?) Today we interpret the Michelson-Morley experiment as evidence against the existence of the ether. But this was not Michelson's view! I like to believe that when quantum theory is finally understood, the Aspect et al. experiments will be seen as evidence against the existence of photons.

 

[DrChinese]

1. My main interest was to clarify the foundational assumptions. In this context, as much nuance as possible is appreciated, meaning that even if a majority of those in the community have decided certain assumptions or nuances can be glossed over or abstracted, I would be interested to hear the basis for glossing over or abstracting these nuances or assumptions in as much objective depth as possible.

This could mean exploring not only the assumptions but also the definitions. Locality and realism have always been confusing for me in this regard, because it seems that either a lot that I don't know is being assumed (well almost certainly this is true), and/or these concepts are not fully agreed on or objectively defined.

In terms of locality and Hess's argument that Bell's theorem assumes the algebra of real numbers applies, I wonder how would you even define locality if your hidden variable theory doesn't follow the algebra of real numbers. It seems like an issue where you first need the hidden variable theory with its explicit mathematical abstractions known before you can meaningfully define locality?

2. Anyways, sorry for the interruption, carry on.

@Jarvis323

1. a. I believe the correct foundational assumptions go back to the 1935 EPR paper. They defined Realism ("Elements of Reality") and assumed Locality (simply that an action here cannot affect an outcome there). They also explicitly assumed that all possible elements of reality should be considered as simultaneously real. I.e. they conclude that outcomes of all possible measurements must therefore be predetermined, and since QM does not predict those outcomes, it must be incomplete.

b. Bell successfully attacked that conclusion, and note that discussion of "algebra of real numbers" is not a component of either EPR or Bell. The De Raedt team is trying to attack Bell with their simulations, trying to demonstrate that there is a local realistic solution that reproduces the QM statistics. In a way, they are able to show that... but their simulation in turn exploits a variety of experimental type assumptions: detection loophole, varying angle settings and issues around that, etc. But subsequent experiments where there is detection of all events renders their simulation moot.

c. My point has been that the advent of experiments featuring entanglement swapping from independent distant sources, there just isn't a mechanism to base ANY "local" simulation on. In the context of their simulations, what happens with the BSM on [2 & 3] is not relevant as long as it is distant from the Bell test. It is then only the [1 & 4] photons - which originate distant from each other but are now entangled (and still distant) - that are of interest. Clearly, such photons should not be entangled if they have never even existed in a common light cone AND you assert strict locality. You don't really need to go any further.2. It is we who are interrupting you! Apologies, I am ready and willing to discuss the De Raedt papers further if you like.

3. It's not clear to me why these time delays should be introduced in such a simulation at all.

3. I completely agree. They have a number of little tricks like this that appear to make the simulation work. What they have done is essentially fine tune their model away from a straight simulation and towards a series of detection and measurement loopholes. All ones that they dream up.

The problem with that is that there are literally hundreds/thousands of different Bell-type tests, and their models are only "correct" for one/few at a time. Any individual local realistic computer program they invent can be falsified by some other Bell test.

 

[DrChinese]

1. The objective state change is due to the selection of a subensemble by projecting photons (2&3) to a Bell state (in the discussed paper by Pan et al to the polarization-singlet state).

2. All you should read is the meaning of the microcausality condition as ruling out causal connections of space-like separated events within relativistic QFT (and that's why it's called a local relativistic QFT at least in the HEP community). For that it's sufficient to read the chapter labelled with "September 30" (pp. 21-28). These are 7, not 355 pages.

https://arxiv.org/abs/1110.5013

1. We agree. The projection causes the state change.

2. I read those pages previously, and it definitely does NOT say anything that applies to an entanglement swap. Long distance Entanglement Swaps are experimental reality, which trumps words in an outdated and irrelevant college lecture.

3. Very briefly you can "correlation swap" in classical probability, just like you can use correlations to "state teleport" in classical probability. Entanglement swapping and quantum teleporting are just quantum generalisations of these simple protocols.

3. Assuming I understood your comment: Obviously false. There can be no classical analog of swapping that generates perfect correlations and violates Bell inequalities. Not when the individual components have never existed in a common light cone. That's the whole point of this thread. That is what the De Raedt simultations (OP) attempted to demonstrate. So you will need to give up some backup here. There are dozens of papers that say exactly the opposite. Here for example:

https://arxiv.org/abs/1211.3560
Entangled states cannot be classically simulated in generalized Bell experiments with quantum inputs
"A natural way to compare quantum resources against classical ones is via the simulation [6] of quantum measurement scenarios [2]. There, one tries to simulate the correlations obtained by measuring a given quantum state in a Bell scenario [7, 8], allowing the parties to use in the simulation shared randomness and possibly classical communication [9]. If no communication is allowed, the set of simulable correlations is bounded by Bell inequalities [10], whereas an infinite amount of communication allows the simulation of any correlations."

No communication is possible in the swapping regime we've discussed, as the each of the observations are recorded before any classical communication can arrive.

 

[LittleSchwinger]

Assuming I understood your comment: Obviously false. There can be no classical analog of swapping that generates perfect correlations and violates Bell inequalities

That's not what I mean. Classical probability theory of course doesn't violate Boolean inequalities. It's that you can correlation swap and teleport states in classical probability theory as well. The quantum part is generating correlations beyond the classical bounds, not so much the swapping or teleporting. So entanglement swapping is:

Correlation swapping [Has a classic analogue]
+
Boolean inequalities violations [Has no classical analogue]

When you study Probability theories in general Entanglement swapping and teleporting are lifts/generalisations of classical protocols. That's what I meant by entanglement swapping is a generalisation of classical protocols.

 

[Fra]

1. We agree. The projection causes the state change.

I still have the impression that again the disagreement is to a large extent focused around the terms "caused by" vs "explained by". There seems to be agreement as to what actually happens (objectively), but not howto "understand it", to bring in yet another word.

It's like causation is a sacred word for physicists, who has the right to use it?

/Fredrik