Could Tim Maudlin's Views on Bell and QM Be Flawed?

[bhobba]

Hi All

I have never been particularly impressed with Tim Mauldin's general take on Bell and QM. I am reading an article of his at the moment. Here is an excerpt (lightly edited by Grammarly to have correct punctuation, etc).

Start Quote

But for expository purposes, the point is most clearly made by an example later developed by Daniel Greenberger, Michael Horne and Anton Zeilinger (as exposited by David Mermin). This later example uses a triple of entangled particles sent off to Alice, Bob, and Charlie in arbitrarily widely separated labs. The separation ensures that in a local theory, Alice’s, Bob’s, and Charlie’s decision about how to arrange their experimental apparatus cannot be communicated to—or have any influence on—the way the particles in other labs interact with their apparatuses or what the outcomes of those experiments are.

What we now know—due to Bell’s proof and the experimental tests—is that the physics of the actual world must somehow violate Einstein’s proscription on “spooky action-as-a-distance”.

Alice, Bob, and Charlie can choose between two experimental arrangements, which we will call “x-spin” and “z-spin”. Practically, that means orienting a certain magnet in either the x-direction or the orthogonal z-direction. Since there are three labs with two possible experimental arrangements each, there are 8 possible global experimental conditions on each experiment run (after a central source delivers one of the three entangled particles to each lab). By a convenient and obvious notation, we will refer to these eight possible global arrangements as XAXBXc, XAXBZc, XAZBXc, ZAXBXc, XAZBZc, ZAXBZc, ZAZBXc, and ZAZBZc. Whenever Alice, Bob, or Charlie experiment on their particle, they get one of two possible results. They pass the particle through the magnetic field, and it is either deflected towards the north pole of the magnet (called an “up” result) or away from it (a “down” result). Regarding the experimental situation, that’s all you need to know.

Now, for a particular prepared initial quantum state (which is referred to as an “entangled” state because it cannot be expressed as just the sum of independent separate states of the two particles), the quantum formalism makes some 100% sure-fire, absolute predictions. These predictions play the same role in this argument as the EPR correlations play in their argument. Of course, the theory makes predictions for all eight possible experimental arrangements, but only four concern us: XAXBXc, XAZBZc, ZAXBZc, and ZAZBXc. Here are the predictions:

1) If all three orient their magnets in the x-direction (XAXBXc), then there will be an odd number of “up” outcomes. There might be one or three, but it will certainly be odd.

2) If exactly one orients her or his magnet in the x-direction (XAZBZc, ZAXBZc, or ZAZBXc), then there will be an even number of “up” outcomes. There might be zero and two, but it will certainly be even.

That’s it. These are predictions of the quantum formalism, and (more importantly!) they are what actually occurs in the lab. We will now show that no local theory can make these predictions.

The first part of the argument recapitulates EPR. Note that in any of these four cases, the results of any two experiments allow one to infer with certainty the result of the third. If the total number of “up”s must be odd, for example, given any two outcomes, there is only one acceptable value for the last. From this perfect correlation, we arrive at the EPR conclusion: if the physics is local, it must also be deterministic. If something irreducibly chancy happens in (say) Alice’s lab, then the particles in Bob’s and/or Charlie’s must be somehow sensitive to how it came out to ensure the correct number of “up” outcomes. Just as in the EPR argument, this determinism is not assumed but inferred from the locality and the correlations.

End Quote.

'If something irreducibly chancy happens in (say) Alice’s lab, then the particles in Bob’s and/or Charlie’s must be somehow sensitive to how it came out to ensure the correct number of “up” outcomes.'

Come again. Certainly, something irreducibly chancy happens in, say, Alice's lab. QM is irreducibly chancy (in most interpretations anyway - certainly in mine). Fine. But what also happens is entanglement is broken, i.e. the Quantum state changes. That can be instantaneous - no problem - if the state is considered just a tool to help predict probabilities. I am not saying that is true, but it is a valid interpretation. Then his whole argument falls to pieces, or to state it more carefully, one must be careful what one means by locality. QM is non-local in the Bell sense of probability correlations - but in other definitions of locality, there is no mystery, i.e. if, as I do, you think of the state as just a calculation device implied by Gleason's Theorem.

Tim is a well known researcher in the field, so I am opening up the question to what others think.

Thanks
Bill

 

[PeterDonis]

I am reading an article of his at the moment.

Is it online? Can you give a link?

 

[bhobba]

Is it online? Can you give a link?

Yes:

https://iai.tv/articles/einstein-was-wrong-about-quantum-mechanics-tim-maudlin-auid-2700

But it is on the Institute of Arts and Ideas site, and I am a member. It may be behind a paywall unless you are a member. I logged out and it still let me view it but it may have some 'smarts' that knows I am a member.

Thanks
Bill

 

[Demystifier]

But what also happens is entanglement is broken, i.e. the Quantum state changes. That can be instantaneous - no problem - if the state is considered just a tool to help predict probabilities. I am not saying that is true, but it is a valid interpretation.

It seems to me that you are saying that, in this interpretation, the change is not an ontological change, but just an epistemic one. I know Tim very well, so I can say that he would not accept a purely epistemic interpretation as valid. Physics, for him, is a theory of the real world as such, not a theory of our knowledge about the world.

 

[bhobba]

I know Tim very well, so I can say that he would not accept a purely epistemic interpretation as valid. Physics, for him, is a theory of the real world as such, not a theory of our knowledge about the world.

Ahhh. Now I think we are getting to the heart of the matter.

I think though, in an article on QM, admittedly not written for those that have studied QM from a book like Ballentine, it might be wise to mention the caveats.

As mentioned, it is from the Institute of Arts and Ideas website, and there is a bug currently - you can't leave comments - which is a pity. BTW Tim is much better than others on that site about QM, but that is another story.

Just as an aside, they have tons of interviews/talks with Roger Penrose, who is always interesting.

Thanks
Bill

 

[gentzen]

'If something irreducibly chancy happens in (say) Alice’s lab, then the particles in Bob’s and/or Charlie’s must be somehow sensitive to how it came out to ensure the correct number of “up” outcomes.'

Come again. Certainly, something irreducibly chancy happens in, say, Alice's lab. QM is irreducibly chancy (in most interpretations anyway - certainly in mine). Fine.

Sounds just like the „normal“ non-local randomness to me. I have no problem with it. If your interpretation has no problem with it either, then Tim is just preaching to the choir, I guess.

 

[WernerQH]

Physics, for him, is a theory of the real world as such, not a theory of our knowledge about the world.

I'd agree to that! What's important is not what happens in our minds, but what happens in the real world. But our minds are befuddled with classical preconceptions. We think of the world around us as composed of objects, objects having properties and having a continuous existence in time. These objects are composed of myriads of smaller objects, which we call quantum objects. But these quantum objects are not like classical objects. The Bell and GHZ experiments seem to indicate that quantum objects cannot really have properties. Whatever is measured comes about through the interaction with measuring instruments. It is unclear if it's appropriate to speak of the "property" of an object if it is something that is attributed with the help of a measuring device.

On the other hand we feel an urge to explain the observed correlations. And how to explain them other than by objects continuously carrying information from the source to the detectors? If we insist on continuity, we are forced to assume some kind of superluminal conspiracy between quantum objects ("entanglement") or an extremely subtle pre-established pseudo-randomness (superdeterminism). My own take on this matter is to give up on the idea of "objects", and on "explaining" the correlations. We should be content to have a very successful theory (QFT) that merely describes the correlation of events in spacetime. For me a photon is nothing but a pair of "emission" and "absorption" events. Not only the interpretation of quantum theory should be scrutinized, but also the interpretation of the experiments! The ontology: what is it about?

 

[vanhees71]

It's the usual confusion with the notion of "local" and "non-local". One must distinguish clearly between "non-local correlations" described by entanglement and "local" in the sense of relativsitic QFT. Maybe, I'm thread-banned again, but I still want to make the statement of the mathematical fact. Quoting Maudlin from #1 (emphasis mine):

But for expository purposes, the point is most clearly made by an example later developed by Daniel Greenberger, Michael Horne and Anton Zeilinger (as exposited by David Mermin). This later example uses a triple of entangled particles sent off to Alice, Bob, and Charlie in arbitrarily widely separated labs. The separation ensures that in a local theory, Alice’s, Bob’s, and Charlie’s decision about how to arrange their experimental apparatus cannot be communicated to—or have any influence on—the way the particles in other labs interact with their apparatuses or what the outcomes of those experiments are.

This is a property standard "local" (sic, that how it's named in the relativistic-QFT/HEP community, I can't help it!): Indeed within relativistic QFT there cannot be any causal influence among the measurements if the results are fixed at mutually space-like separated events. It's not only a property of "local realistic theories" a la Bell but also a property of local QFT, which of course is not "realistic", i.e., as in any QT not all observables of a quantum system take determined values. Particularly in the GHZ state the polarizations of each of the three photons are indetermined (unpolarized)

https://en.wikipedia.org/wiki/Greenberger–Horne–Zeilinger_state

 

[WernerQH]

Particularly in the GHZ state the polarizations of each of the three photons are indetermined (unpolarized)

Talk of the "state of polarization" of a photon betrays deep-rooted metaphysical assumptions.

 

[Fra]

It's the usual confusion with the notion of "local" and "non-local". One must distinguish clearly between "non-local correlations" described by entanglement and "local" in the sense of relativsitic QFT.

I agree. Even if most of us by know are aware of the various definitions, I do not get the point of the article. I think it adds no clarity, it merely addes fuel to the historical "state confusion"... than it does help bring clarity to anything.

/Fredrik

 

[vanhees71]

Have you ever gotten a point of an article by Maudlin?

 

[Frabjous]

I have never been particularly impressed with Tim Mauldin's general take on Bell and QM. I am reading an article of his at the moment.

Given the the sentiment of the first sentence, the action of the second sentence seems counter productive.

 

[vanhees71]

Well, sometimes authors can surprise you in the positive way. Recently I read the old article by CFvW about the "Heisenberg microscope", and I was surprised how well he could write about physics as in the literal sense of a natural science ;-)).

 

[WernerQH]

Have you ever gotten a point of an article by Maudlin?

Well, I must say that I find Maudlin more intelligible than your view that causality rules because the correlations are due to the preparation of the initial state. The initial state does not fully determine the detected polarizations of the photons.

in any QT not all observables of a quantum system take determined values

So only at the moment of their "death" do the GHZ photons acquire a definite polarization?

 

[vanhees71]

In QT no state determines the values of all observables. That's the generic feature of QT that it is not "realistic" and that there thus is generic randomness in Nature. Nevertheless the correlations are due to the preparation of the initial state. In QT these correlations between the outcomes of measurments of the single-photon polarizations are there despite the fact that these single-photon polarizations are maximally undetermined when the photons are prepared in the said entangled state (in the here discussed example a GHZ three-photon state).

The photons don't acquire a definite polarization since they are absorbed in the process of observing them. All there is are the outcomes of these measurements and their statistics, which is predicted by QED in accordance with all experiments done with them.

 

[WernerQH]

the outcomes of measurments of the single-photon polarizations

Why do you adopt this peculiar language, if the photons do "not really" have a polarization? How does "measurement" produce information about something that does not exist? Don't you notice a contradiction here?

 

[vanhees71]

The polarization observable of course exists, i.e., you can measure it on a photon, no matter whether the measured polarization is determined by the state of this photon or not. If the polarization is not determined due to the preparation, then the outcome of the measurement is random with probabilities given by Born's rule. There is no contradiction but very basic properties of QT!

 

[Morbert]

So only at the moment of their "death" do the GHZ photons acquire a definite polarization?

An instrumentalist would not interpret a measurement, destructive or nondestructive, as a microscopic system acquiring a property. They interpret it as a macroscopic datum to be collated with others, so that statistical predictions of the theory can be tested.

 

[WernerQH]

The polarization observable of course exists, i.e., you can measure it on a photon, no matter whether the measured polarization is determined by the state of this photon or not.

You may dignify it with the word observable, but you still don't offer a precise physical picture of what it is that is being measured, or what constitutes a measurement.

If the polarization is not determined due to the preparation, then the outcome of the measurement is random with probabilities given by Born's rule. There is no contradiction but very basic properties of QT!

I do not see contradictions in quantum theory, but in the obsolete metaphysical framework that is still shrouding the theory. You are probably so accustomed to it that you are unable to see it.

 

[DrChinese]

From Maudlin's article:

Mermin provides a beautiful graphical proof [of GHZ]. We need to pre-arrange outcomes for each of the three particles for each of two possible experimental arrangements in their lab. Hence there are a total of six decisions to make. We will represent each decision by a circle to be filled in with either a “U” or a “D” depending on whether the result should be up or down. We arrange these six circles as follows:

Pretty nice graphical presentation of GHZ from the article. I could not locate Mermin's version of it, as it did not appear in Maudlin's reference: https://2012.anzsup.org/notes/Margaret_Reid-Mermin's_article.pdf

The diagram features 1 dotted line and 3 straight lines. The puzzle is to place either a "U" or a "D" in each circle. The number of U's in the dotted line is to be odd, the other lines need to have an even number of U's. PS it can't be done, but local realism says it should be possible.

 

[DrChinese]

From Maudlin's article:

"The 2022 Noble Prize in Physics was awarded to John Clauser, Alan Aspect and Anton Zeilinger for experiments proving that Bell’s Inequality is, in fact, violated for similar experiments done in labs further and further apart and with more and more efficient detectors. Those experiments have ruled out locality in physics: whatever the correct physical theory is, it must somehow violate the locality condition that Bell assumed and Einstein demanded. What we now know—due to Bell’s proof and the experimental tests—is that the physics of the actual world must somehow violate Einstein’s proscription on “spooky action-as-a-distance”. It is a result as worthy as any in history of the Nobel Prize. It is a pity that Bell himself did not live long enough to receive it."

I couldn't agree more. Sounds suspiciously similar to what I have been posting in this subforum ever since Zeilinger et al received their Nobel in 2022 (along with the dozens of supporting experimental references). Namely: nonlocality is generally accepted science. And in fact the words "spooky action at a distance" are not words to be looked down upon; it's time to embrace them.

 

[DrChinese]

@vanhees71 (and hopefully everyone else reading this): In order not to restart our usual circular debate, perhaps we can agree as follows.

a) There are no FTL signals allowed in orthodox QM, QFT, or in any generally presented alternative theories or interpretations. No need to specify this point over and over as we are all in agreement on this point.

b) While QM (and therefore QFT as well) is nonlocal, the only experimentally confirmed such element is: ONLY random outcomes can be detected between remote (in spacetime) laboratory setups. Hopefully you can accept this point based on the hundreds of experiments showing exactly this result. An experimenter here can choose to entangle distant particles, but only random transmitted outcomes (what you call correlations) result.

c) Those outcomes cannot be said to causal in the QFT sense, because there is no clear causal direction since ordering makes no apparent difference to the outcome. We are in agreement on this point.

d) When you make a statement such as "QFT is locally causal", I will simply assume you mean the conjunction of the above.

 

[Fra]

I know Tim very well, so I can say that he would not accept a purely epistemic interpretation as valid. Physics, for him, is a theory of the real world as such, not a theory of our knowledge about the world.

I'd agree to that! What's important is not what happens in our minds, but what happens in the real world.

I don't see that there has to be a contradiction between ontology and epistemology, on the contrary do they back each other up.

For me two things are undeniable.

1) Our(or the "observers/agents") inferred theories by construction represent our knowledge about the world - what else?

2) But our(the agents) knowledge is constrained by what can be encoded and processed by means of real world resources.

QM and QFT does not quite respect this, as the observer there is essentially a unlimited environment. This is the problem that also is at the root of the probabilistic foundations of QM, fictive ensembles etc.

/Fredrik

 

[Fra]

I couldn't agree more. Sounds suspiciously similar to what I have been posting in this subforum ever since Zeilinger et al received their Nobel in 2022

Exactly what I was thinking when reading it as well: it sounds like somethingh DrChinese might as well have written! But I kept that thought to myself

/Fredrik

 

[bhobba]

Well, I must say that I find Maudlin more intelligible

Don't get me wrong - Mauldin is understandable. It's just at certain points, he makes comments I would challenge. On IAI, such can't be said of everyone who opines on QM. They have people like Gerard 't Hooft who are very careful about what they say, but others, how to put it, are very handwavey and would benefit from studying a book like Ballentine. A number are philosophers, so it is understandable.

Demystifier explained clearly what was going on, and my issue was resolved. I want the comment function on the site to be fixed - that's all.

I have another question about Quantum Field Theory and the state being epistemic, but that is for another thread.

Thanks
Bill

 

[bhobba]

And in fact the words "spooky action at a distance" are not words to be looked down upon; it's time to embrace them.

Under Bell's definition of locality, you, of course, are correct. My issue is that is not the only one.

Thanks
Bill

 

[Morbert]

I'll offer a consistent histories approach to the GHZ paradox. The article written by Maudlin is unclear and has broken citations, so I will instead consider the paper by Mermin in the references (but not actually cited).

Mermin considers a 3-particle system $I$ in the state$$|\psi;I\rangle = \frac{1}{\sqrt{2}}\left[|1_z1_z1_z;I\rangle - |0_z0_z0_z;I\rangle\right]$$ and four observables: $\sigma_x\sigma_x\sigma_x$, $\sigma_x\sigma_y\sigma_y$, $\sigma_y\sigma_x\sigma_y$, $\sigma_y\sigma_y\sigma_x$. $\psi$ is an eigenvector of each observable, with respective eigenvalues -1, 1, 1, 1. We can construct a separate boolean lattice for each measurement scenario from the appropriate sample spaces. E.g. For $\sigma_x\sigma_x\sigma_x$ we have the support $\{\Pi_{1_x1_x0_x}, \Pi_{1_x0_x1_x},\Pi_{1_x1_x0_x},\Pi_{0_x0_x0_x}\}$. For $\sigma_x\sigma_y\sigma_y$ we have the support $\{\Pi_{1_x0_y0_y}, \Pi_{0_x1_y0_y},\Pi_{0_x0_y1_y},\Pi_{1_x1_y1_y}\}$ etc. Alternatively, we could construct a single support with a branching set of histories. We modify the state to include system $II$ and model the choice of measurements with a random integer between 1-4. $$\rho=\frac{1}{4}|\psi;I\rangle\langle\psi;I|\otimes\sum_{i=1}^4|i;II\rangle\langle i;II|$$and 16 branches of history. Each projector $|i;II\rangle\langle i;II|$ demarcates one of four measurement choices, and hence a branch that further divides into 4 other branches. The support is $$\begin{eqnarray*}\Pi_1\otimes\Pi_{0_x1_x1_x}&,&\Pi_1\otimes\Pi_{1_x0_x1_x}&,&\Pi_{1}\otimes\Pi_{1_x1_x0_x}&,&\Pi_{1}\otimes\Pi_{0_x0_x0_x}\\\Pi_{2}\otimes\Pi_{1_x0_y0_y}&,&\Pi_{2}\otimes\Pi_{0_x1_y0_y}&,&\Pi_{2}\otimes\Pi_{0_x0_y1_y}&,&\Pi_{2}\otimes\Pi_{1_x1_y1_y}\\\Pi_{3}\otimes\Pi_{1_y0_x0_y}&,&\Pi_{3}\otimes\Pi_{0_y1_x0_y}&,&\Pi_{3}\otimes\Pi_{0_y0_x1_y}&,&\Pi_{3}\otimes\Pi_{1_y1_x1_y}\\\Pi_{4}\otimes\Pi_{1_y0_y0_x}&,&\Pi_{4}\otimes\Pi_{0_y1_y0_x}&,&\Pi_{4}\otimes\Pi_{0_y0_y1_x}&,&\Pi_{4}\otimes\Pi_{1_y1_y1_x}\end{eqnarray*}$$With any of these lattices, Bell's local causality condition is satisfied.

[edit] - Fixed spin values

 

[vanhees71]

@vanhees71 (and hopefully everyone else reading this): In order not to restart our usual circular debate, perhaps we can agree as follows.

a) There are no FTL signals allowed in orthodox QM, QFT, or in any generally presented alternative theories or interpretations. No need to specify this point over and over as we are all in agreement on this point.

In QM, which is non-relativistic, of course there are FTL signals allowed. Action at a distance is the paradigmatic way how interactions are described in non-relativistic physics (both classical and quantum). There's also no notion of "locality" in the sense of the word used in relativistic physics in non-relativistic physics.

In QFT by construction, no FTL signal propagation occurs. I think we finally agree on this.

b) While QM (and therefore QFT as well) is nonlocal, the only experimentally confirmed such element is: ONLY random outcomes can be detected between remote (in spacetime) laboratory setups. Hopefully you can accept this point based on the hundreds of experiments showing exactly this result. An experimenter here can choose to entangle distant particles, but only random transmitted outcomes (what you call correlations) result.

The problem is that again it is not clear, what you mean by "nonlocal" here. You have to clearly define it, because obviously it cannot have the meaning of "local" in the QFT language, which describes mathematically well-defined properties of relativistic QFTs:

(a) There are bosonic or fermionic field operators that transform "locally" under Poincare transformations, i.e., under space-time translations
$$\hat{U}_T(a) \psi(x) \hat{U}_T^{\dagger}(a)=\psi(x-a)$$
and under proper orthochronous Lorentz transformations
$$\hat{U}_L(\Lambda) \psi(x) \hat{U}_T^{\dagger}(\Lambda)=S(\Lambda) \psi(\Lambda^{-1} x),$$
where $S(\Lambda)$ is a matrix depending on the type of field (e.g., it's simply 1 if $\psi$ is a scalar field, or $\Lambda$ if $\psi$ is a vector field etc.).

(b) Microcausality: if $\hat{A}(x)$ and $\hat{B}(x)$ are self-adjoint operators that describe local observables, then $[\hat{A}(x),\hat{B}(y)]=0$ for $(x-y)^2<0$ (with the (+---) signature of the metric, i.e., if $x$ and $y$ are space-like separated events). Since the Hamilton density is an observable, this microcausality condition definitely excludes faster-than-light signals.

Taken together you can prove the spin-statistics theorem, the CPT theorem, and the cluster-decomposition principle as well as the unitarity and Poincare covariance of S-matrix elements.

You seem to mean by "nonlocal" is the fact that there can be long-ranged correlations between outcomes of measurements on far-distant parts of a system prepared in and entangled state. This notion of "locality" has nothing to do with the notion of "locality" in the meaning of the HEP community. It's not what, e.g., Haag means in the title of his book "Local quantum physics". There is no contradiction in standard QFT being "local" in the HEP sense and being "nonlocal" in the sense that there are long-ranged strong correlations between the outcomes of measurements on far-distant parts of an entangled quantum system (like two photons from parametric downconversion). Due to this confusing use of the words "local" and "nonlocal" it's very important to clearly define what you mean by them in each discussion.

c) Those outcomes cannot be said to causal in the QFT sense, because there is no clear causal direction since ordering makes no apparent difference to the outcome. We are in agreement on this point.

What is very clear from the mathematical properties of "local" QFT is that the correlations are not by causal influences of the local measurements at far distant places, if the measurement results are fixed in space-like separated events. That's why in the entanglement-swapping experiment it's irrelevant in which temporal order you do the measurements on photons 1 and 4 and the projection of photons 2 and 3 to one of the four Bell states. These can even be space-like separated so that there is no definite temporal order at all. I think we also agree on this.

d) When you make a statement such as "QFT is locally causal", I will simply assume you mean the conjunction of the above.

I don't know, what you mean here. I've never heard the phrase "QFT is locally causal", and I've no clue what you mean by that. QFT is "local" in the above described mathematical sense, and these assumptions on this mathematical structure is a sufficient condition for a causal description for a relativistic QT. Whether there are causal "non-local" formulations of relativistic QT, I don't know. At least I'm not aware of any such theory.

QFT is "nonlocal" in the sense that there are entangled state (in fact it's very difficult if not impossible to perpare non-entangled states in QFT) and that there are strong long-ranged correlations between the outcome of local measurements on far-distant parts of an entangled quantum system, leading to the violation of all kinds of Bell inequalities, ruling out local realistic descriptions.

The important point is that in addition to locality (i.e., the impossibility of causal connections between space-like separated events) also realism (i.e., that all observables always take predetermined values) must be assumed in order to prove Bell's inequality (or similar properties in contradiction with QT).

For me "local" relativistic QFT is a description, which is clearly "local" in this sense but of course not "realistic", because as in any quantum theory there's no state, where all observables take determined values, but that seems indeed to be an interpretation-dependent statement, and my statement seems to be consistent only with the minimal statistical interpretation, which is why for me that's the only plausible interpretation at all.

In this interpretation there is no causal explanation, why a specific measurement outcome when an observable is measured that's not determined due to the state preparation occurs, but it's assumed to be "objectively random" with probabilities given by Born's rule. E.g., if you have a polarization-entangled photon pair and you measure the polarization of one of these photons (which is exactly unpolarized in this case) by e.g., using a polarization filter there's no causal explanation whether a specific photon goes through the filter or not. All you can say is that with probability 1/2 it goes through, with probability 1/2 it doesn't. There's no cause for the one or the other outcome for any specific photon prepared in such a state.

 

[martinbn]

From Maudlin's article:

Mermin provides a beautiful graphical proof [of GHZ]. We need to pre-arrange outcomes for each of the three particles for each of two possible experimental arrangements in their lab. Hence there are a total of six decisions to make. We will represent each decision by a circle to be filled in with either a “U” or a “D” depending on whether the result should be up or down. We arrange these six circles as follows:

View attachment 337905
Pretty nice graphical presentation of GHZ from the article. I could not locate Mermin's version of it, as it did not appear in Maudlin's reference: https://2012.anzsup.org/notes/Margaret_Reid-Mermin's_article.pdf

The diagram features 1 dotted line and 3 straight lines. The puzzle is to place either a "U" or a "D" in each circle. The number of U's in the dotted line is to be odd, the other lines need to have an even number of U's. PS it can't be done, but local realism says it should be possible.

How does non-local realism work here?

 

[Morbert]

How does non-local realism work here?

Think of the Us and Ds as pre-existing properties, revealed by different measurements on individual particles. Local realism says it should be possible to write down an arrangement of Us and Ds that fully specify the outcomes of all possible measurement choices. So e.g. the dotted line represents a choice of the observable $\sigma^A_x\sigma^B_x\sigma^C_z$ and should yield an eigenvalue +1 (the product of the individual measurement results: e.g. UUU = 1*1*1 = 1, UDD = 1*-1*-1 = 1 etc). Other such observables can be constructed by following the appropriate solid lines.

It is not actually possible to write down an arrangement that satisfies all measurement choices.

 

[martinbn]

Think of the Us and Ds as pre-existing properties, revealed by different measurements on individual particles. Local realism says it should be possible to write down an arrangement of Us and Ds that fully specify the outcomes of all possible measurement choices. So e.g. the dotted line represents a choice of the observable $\sigma^A_x\sigma^B_x\sigma^C_z$ and should yield an eigenvalue +1 (the product of the individual measurement results: e.g. UUU = 1*1*1 = 1, UDD = 1*-1*-1 = 1 etc). Other such observables can be constructed by following the appropriate solid lines.

It is not actually possible to write down an arrangement that satisfies all measurement choices. So we cannot write down

Yes, but my question is about non-local realism.

 

[Morbert]

Yes, but my question is about non-local realism.

Oh oops misread your original post.

 

[Morbert]

With non-local realism, there is no need to specify an arrangement of Us and Ds everywhere because a choice of measurement at one site can immediately influence values at other sites. If it were possible to write down all Us and Ds that satisfy quantum predictions, there would be no need to suppose this immediate influencing.

 

[martinbn]

With non-local realism, there is no need to specify an arrangement of Us and Ds everywhere because a choice of measurement at one site can immediately influence values at other sites. If it were possible to write down all Us and Ds that satisfy quantum predictions, there would be no need to suppose this immediate influencing.

So they have some U or D value along some direction and when a measurement is made the values change to what they should be?

 

[Morbert]

So they have some U or D value along some direction and when a measurement is made the values change to what they should be?

I'm not sure how useful the diagram is for representing the non-local case. Its primary purpose is in representing the failure of the local case. I would imaging a nonlocal realist interpretation would have these values changing to what they should be, but maybe not directly. You would have to ask one of the Bohmian representatives here.