Does the Bell theorem assume reality?

[DarMM]

If it's describable by math it probably needs to contain at least a universal wavefunction; that's what the Bell, PBR, FR and CR theorems suggest to me

To me they have a universal wavefunction as among a few of the possibilities not eliminated by them, but I don't think they suggest it more strongly than any others. The wavefunction being real has its own problems, so depending on taste you'll choose one of the others.

The problem is that if you assume multiple agents can use QM as a subjective tool it places pretty stringent constraints on what that reality can be

An example?

It's suggestive that QM is so closely related to rational agents and logical constraints, but that doesn't mean reality is something different. It could be that they share the same structure because it's a universal structure.

No it doesn't mean it, my intent wasn't to prove these interpretations are correct. It was to say here is a derivation of QM purely from agential concerns. It shows how it is possible to hold their view. Also to be frank, as somebody who isn't decided on interpretations, it's a pretty damn strong argument. How many other interpretations derive QM without postulating large chunks of it? Many seem more like reactions to the formalism.

Usually in probability theories the epistemic space doesn't have the same structure as the ontic space over which it is built and epistemic states tend to obey very different theorems.

Could you explain a bit more what you mean?

What kind of world do you have in mind where states of reasoning and belief updating function identically to the actual "stuff" down to obeying the same theorems.

That naively sounds further than QBism, that the stuff is agent belief.

Is it even a reasonable thing to suggest it's outside the realm of math?

Again this is all based on taste, but if you take Godel's theorem or other lines of reasoning to suggest mathematics is purely in our heads, then sure there might be layers of reality that don't map to any structure like mathematics that comes from human thought.

At a weaker level, there are mathematical structures for which there is no algorithm to compute them. So even in a mathematically describable world the world mightn't be algorithmic.

 

[DarMM]

How does the idea reality is relational/participatory give any guidance in helping to show what it could be, if not QM?

Is that really a problem with these interpretations? They seek only to explain QM, their explanation is that it is a generalisation of the Bayesian reasoning framework. Some of them then say that the underlying reality is relational or participatory or both. The guidance is then that you now know reality is like that and can use that fact to guide future developments.

What I mean is if they hypothetically succesfully showed reality is relational/participatory and QM is just a form of Bayesian reasoning, then that isn't invalidated by them not also suggesting the complete underlying theory.

 

[akvadrako]

The problem is that if you assume multiple agents can use QM as a subjective tool it places pretty stringent constraints on what that reality can be.

An example?

I just mean the usual restraints those theories produce, like making it hard to combine locality and single outcomes while reproducing QM. QBism claims reality can do all three.

Usually in probability theories the epistemic space doesn't have the same structure as the ontic space over which it is built and epistemic states tend to obey very different theorems.

Could you explain a bit more what you mean?

What kind of world do you have in mind where states of reasoning and belief updating fubction identically to the actual "stuff" down to obeying the same theorems.

That naively sounds further than QBism, that the stuff is agent belief.

I mean a quantum world of course . One where anything can happen except inconsistencies. I'm not saying it's made of agent belief, just that they happen to have the same structure. It seems QM can be mostly if not totally derived from constraints on consistent reasoning. That doesn't imply it can't also be derived from logical constraints on ontic models. Though it's hard to rule out that it's made of the union of all "agent" beliefs.

What I mean is if they hypothetically succesfully showed reality is relational/participatory and QM is just a form of Bayesian reasoning, then that isn't invalidated by them not also suggesting the complete underlying theory.

The problem isn't that their model is incomplete. I am willing to accept that QM is a form of Bayesian reasoning and reality is relational/participatory – those are at least reasonable claims. But they don't address the issue, which is that a reality which satisfies the constraints of QBism doesn't seem possible due to Bell's theorem and the others. And they don't suggest any way it might work.

 

[DarMM]

I just mean the usual restraints those theories produce, like making it hard to combine locality and single outcomes while reproducing QM. QBism claims reality can do all three.

Retrocausal and acausal theories also escape these theorems and have one world, locality and replicate QM. It's not impossible, although QBism doesn't take the retrocausal route.

But they don't address the issue, which is that a reality which satisfies the constraints of QBism doesn't seem possible due to Bell's theorem and the others. And they don't suggest any way it might work.

Following from the above. They reject the existence of $\lambda$, mathematical variables controlling the world.

This is what Cabello discusses in his paper, no laws.

If you have no $\lambda$ Bell's theorem has no effect on you.

Now I don't like this either, but they do have reasons to think it. Just even reflect on the fact that all actual derivations of QM (Cabello's is my favourite, but there are others) make no ontic assumptions beyond measurements and agents existing.

They take this to mean there is no point in thinking of $\psi$ as real, since you can derive it from epistemic considerations. This is one reason why they'd dismiss Many Worlds and Bohmian Mechanics. There are other reasons as well if you want to know them.

Okay so $\psi$ is epistemic, about what?

The only options from the various ontological framework theorems are a retrocausal world, nonlocal world, superdeterministic world or a non-mathematical world.

First two are out from fine tuning arguments, links if you want. Third is out because it means everything is a massive conspiracy, maybe minerals just happened to concentrate in the shape of dinosaur bones.

That leaves only the fourth option.

QM is the Bayesian reasoning you must use for parts of the world admitting no fundamental mathematical description.

 

[zonde]

Following from the above. They reject the existence of $\lambda$, mathematical variables controlling the world.

This is what Cabello discusses in his paper, no laws.

If you have no $\lambda$ Bell's theorem has no effect on you.

Well, maybe we can imagine that Bell's $\lambda$ is not the only way how EPR determinism can be modeled or we can imagine that perfect correlations is false prediction of QM. But there is elegant Eberhard's derivation of inequalities without $\lambda$ and perfect correlations. You can look at Eberhard's derivation here: https://www.physicsforums.com/threa...y-on-probability-concept.944672/#post-5977632

 

[Demystifier]

The QBists are definitely saying there is an external reality.

But then they must accept the Bell theorem that reality obeys nonlocal laws. Yet they don't accept it.

 

[DarMM]

But then they must accept the Bell theorem that reality obeys nonlocal laws. Yet they don't accept it.

Reality doesn't have to be nonlocal from Bell's theorem, as I mentioned above retro or acausal theories also remain local (although this isn't what QBism supposes).

 

[Demystifier]

Reality doesn't have to be nonlocal from Bell's theorem, as I mentioned above retro or acausal theories also remain local (although this isn't what QBism supposes).

So how exactly is QBism local? Is it just signal locality or something more? If it is just signal locality, then Bohmian mechanics is local too.

 

[zonde]

Reality doesn't have to be nonlocal from Bell's theorem, as I mentioned above retro or acausal theories also remain local (although this isn't what QBism supposes).

It seems that in retro and acausal models even superluminal communication device can satisfy locality. So I'm not sure you can use theories like that as an argument.

 

[akvadrako]

This is what Cabello discusses in his paper, no laws.

No laws doesn't necessarily imply something indescribable happens. Another option is everything computable happens, within logical consistency requirements like those for agents. For example along the lines of Tegmark's mathematical universe.

They take this to mean there is no point in thinking of $\psi$ as real, since you can derive it from epistemic considerations.

I think you got my point, but what I'm saying is just because it's derivable this way doesn't mean it has to be only epistemic. It's suggestive, but it doesn't logically follow that the ontic space needs to be something different. Along the lines of the ontology theorems, one can even derive the ontic space from the epistemic considerations and a few extra assumptions.

QM is the Bayesian reasoning you must use for parts of the world admitting no fundamental mathematical description.

Thanks - that was more clear than any explanation of QBism I can remember. I can see how they've found reason to believe reality is non-mathematical. But it's hard to distinguish that conclusion from saying they've reached a contradiction. Since their assumptions are questionable it seems much more likely one of them should be dropped.

 

[akvadrako]

But then they must accept the Bell theorem that reality obeys nonlocal laws. Yet they don't accept it.

If you say something can't be described mathematically or as Fuch's said above, beyond anything grammatical or rule-bound expression can articulate, then I suppose theorems become powerless.

 

[Demystifier]

If you say something can't be described mathematically or as Fuch's said above, beyond anything grammatical or rule-bound expression can articulate, then I suppose theorems become powerless.

Yes, for me that's nothing but mysticism. Bohr, indeed, has often been classified as a mystic. Given that Fuchs said the above, can we conclude that QBism is just an euphemism for mysticism?

 

[Lord Jestocost]

Bohr, indeed, has often been classified as a mystic.

In “Quantum Reality: Beyond the New Physics”, Nick Herbert remarks on Bohr:

“Einstein and other prominent physicists felt that Bohr went too far in his call for ruthless renunciation of deep reality. Surely all Bohr meant to say was that we must all be good pragmatists and not extend our speculations beyond the range of our experiments. From the results of experiments carried out in the twenties, how could Bohr conclude that no future technology would ever reveal a deeper truth? Certainly Bohr never intended actually to deny deep reality but merely counseled a cautious skepticism toward speculative hidden realities.”

 

[DarMM]

No laws doesn't necessarily imply something indescribable happens. Another option is everything computable happens, within logical consistency requirements like those for agents. For example along the lines of Tegmark's mathematical universe.

First, why the exclusion of non-computable mathematical objects?

Secondly, in Cabello's paper he has no restrictions on the behaviours, any consistent probability assignment occurs, that's what QM is in his derivation. How would this restrict the ontic space to "everything computable"? In fact I don't see the link with computability.

Also assuming a restriction down to something like "computable actions" is a step Cabello doesn't take, you'd have to show that that restriction doesn't affect his proof.

However that would be hard to imagine as he gets out the QM structure exactly, a restriction would have to reduce the assignments in some way and thus close off some parts of QM.

I think you got my point, but what I'm saying is just because it's derivable this way doesn't mean it has to be only epistemic. It's suggestive, but it doesn't logically follow that the ontic space needs to be something different. Along the lines of the ontology theorems, one can even derive the ontic space from the epistemic considerations and a few extra assumptions.

Regarding the first part, certainly, I'm not saying QBism or similar views are logically forced on us otherwise I'd be a committed QBist, I'm simply explaining them. However regarding the second part, I cannot think of an example in physics where the space of ontic objects is equivalent to the space epistemic estimates of them. Typically if the former is $Q$ let's say, the later is something like $\mathcal{L}^{1}(Q)$. Do you have an example or perhaps a sketch of what you mean?

But it's hard to distinguish that conclusion from saying they've reached a contradiction.

What contradiction do you mean?

 

[DarMM]

So how exactly is QBism local? Is it just signal locality or something more? If it is just signal locality, then Bohmian mechanics is local too.

Well you're not going to like it, but they say the world is local because there are no mathematical variables describing it, i.e. no $\lambda$, so no implications from Bell's theorem. Same as Copenhagen as viewed by Bohr and Heisenberg.

Yes, for me that's nothing but mysticism. Bohr, indeed, has often been classified as a mystic. Given that Fuchs said the above, can we conclude that QBism is just an euphemism for mysticism?

I suppose it depends on what you take mysticism to be, but QBism is what I said above, it sees QM as a Bayesian toolkit for managing expectations of a fundamentally lawless world. (This is not to say that the whole of the world is lawless, e.g. GR would still be correct, just that there are lawless components)

I don't think it's completely mad, as Cabello for example has a good derivation of QM assuming some observations obey no laws.

 

[DarMM]

It seems that in retro and acausal models even superluminal communication device can satisfy locality. So I'm not sure you can use theories like that as an argument.

No, there are retro and acausal models that have locality, but forbid superluminal signals. Propagating signals into the past light cone is fundamentally different to propagating them in spacelike directions.

Acausal theories would be even more different, no propagation at all just 4D consistency conditions.

 

[N88]

Does the Bell theorem assume reality? According to me: No!

Well, for me at least: not any meaningful version of physical reality when you are writing in the context of EPRB.

Here's my reason. From high-school algebra, without any refence to EPRB, Bell, etc, we irrefutably obtain:

$|E(a, b) - E(a,c)| \leq 1 - E(a,b)E(a,c). \qquad (1)$

Compare this with Bell's famous 1964 inequality:

$|E(a, b) - E(a,c)| \leq 1 + E(b,c). [sic] \qquad (2)$

Given [as I read him. p.195] that Bell's aim was to provide "a more complete specification of EPRB by means of parameter $\lambda$": I suggest that his supporters should pay more attention to his 1990 suggestion that maybe there was some silliness somewhere.

For example, let's rewrite (2). We find:

$|E(a, b) - E(a,c)| - E(b,c) \leq1. [sic] \qquad(3)$

But, under EPRB, that upper bound is $\tfrac{3}{2}.$

Thus, in that Bell uses inequality (2 ) as proof of his theorem: I believe that Bell's writings need to be challenged --- without any reference to nonlocality, QBism, BWIT, AAD, MW, etc [which, in my view, are also silly].

PS: While I am against Bell [who, in a dilemma in 1990, was against locality], I am for Einstein [and for Einstein-locality].

Thus, in that "Einstein argued that the EPR correlations could be made intelligible only by completing the quantum mechanical account in a classical way," Bell (2004:86): that's what I work on.

It being my hope that QFT would not reject my ideas.

 

[akvadrako]

First, why the exclusion of non-computable mathematical objects?

Secondly, in Cabello's paper he has no restrictions on the behaviours, any consistent probability assignment occurs, that's what QM is in his derivation. How would this restrict the ontic space to "everything computable"? In fact I don't see the link with computability.

It's just an example of how "no rules" can be satisfied with mathematically describable objects. If you haven't seen Markus P. Mueller's Law without Law, it's probably the paper I think back to most over the past year. It doesn't fully reproduce QM but some aspects of it, based on computational complexity. It's also subjective but I think with an extra assumption of multiple observers it could still work.

However regarding the second part, I cannot think of an example in physics where the space of ontic objects is equivalent to the space epistemic estimates of them. Typically if the former is $Q$ let's say, the later is something like $\mathcal{L}^{1}(Q)$. Do you have an example or perhaps a sketch of what you mean?

Well QM is special, so the existence of other examples doesn't matter much; it could be the only theory that works this way. Anyway, my current guess is subjective QM is basically Copenhagen but the combination of all subjects is MWI. So not exactly the same, but of the same structure.

What contradiction do you mean?

I mean saying something can't be described by math is equivalent to saying it's contradictory. If no formal rules apply, even roughly, then it seems like anything goes, even inconsistencies. At least I don't understand the difference.

 

[DarMM]

Well QM is special, so the existence of other examples doesn't matter much; it could be the only theory that works this way. Anyway, my current guess is subjective QM is basically Copenhagen but the combination of all subjects is MWI. So not exactly the same, but of the same structure.

Okay I see what you mean from the last bit. The epistemic objects and the ontic objects are the same type of thing, i.e. you can use a wavefunction epistemically as in standard QM for "local" events, but the actual ontic global wavefunction is the same type of object.

I have doubts about this though, for typical $\psi$-epistemic reasons. The most basic being that classical uncertainty about $\psi$ doesn't manifest as something like $\mathcal{L}^{1}(\mathcal{H})$, which you'd expect if $\psi$ was a real object you were ignorant of (because this is purely classical ignorance). Rather $\mathcal{H}$ is a subset of the observable algebra's dual (its boundary) and some of that dual has terms that mix classical and quantum probability in odd ways. So you can have a mixture $\rho$ which could be considered a mix of two states $\psi_1$ and $\psi_2$ or a mix of $\psi_3$ and $\psi_4$ and it's the exact same mixture. Hard to understand if $\psi$ is ontic (though not a killing argument of course), it makes pure states like $\psi$ just seem like a limiting type of probability assignment, not ontic.

I mean saying something can't be described by math is equivalent to saying it's contradictory. If no formal rules apply, even roughly, then it seems like anything goes, even inconsistencies. At least I don't understand the difference.

I don't think so. Inconsistency means that two contradictory mathematical properties would be assigned. Not relevant if the thing isn't mathematically describable.

It's just an example of how "no rules" can be satisfied with mathematically describable objects. If you haven't seen Markus P. Mueller's Law without Law, it's probably the paper I think back to most over the past year. It doesn't fully reproduce QM but some aspects of it, based on computational complexity. It's also subjective but I think with an extra assumption of multiple observers it could still work.

That's a cool looking paper, thanks!

Just to help orient a reading of it, what does he think the world is like underneath the reasoning of agents? I see our typical "laws" are seen to come about as a limiting behaviour in subjective probability assignments, but does he make any conjecture about the underlying world?

You are right, "no rules" doesn't logically mean "mathematically indescribable", again otherwise I'd be a QBist. However the QBist view is just as valid, that QM exposes a deep indeterminism, a not fully mathematically comprehensible nature. When I originally said it, it was in the context of Cabello's paper which does show that this way of thinking does work out, he derives QM from a world without laws, in the sense of no underlying mathematical variables describing things. The phrase "no laws" in abstract doesn't imply no mathematical variables controlling it, but when Cabello is saying it that's what he means. Just to be clear if I was vague:

Following from the above. They reject the existence of $\lambda$, mathematical variables controlling the world.

This is what Cabello discusses in his paper, no laws.

If you have no $\lambda$ Bell's theorem has no effect on you.

What I meant was Cabello deals with this view (non-mathematical world), not so much a comment on what the phrase "no laws" must mean in general.

 

[N88]

Does the Bell theorem assume reality? According to me: No!

Well, for me at least: not any meaningful version of physical reality when you are writing in the context of EPRB.

However, to be clearer: IF we accept Bell's 1964 move from the eqn after eqn (14) -- call it (14a) -- to the next equation, call it (14b): THEN it seems to me that Bell could be theorizing about these realities:

1. A set of objects (subject to non-perturbative testing) that are available for re-testing. Maybe a set of paired-billiard balls with their color tested under various lights?
2. A duplicate set of objects tested pertubatively. Say: pairs of linearly polarized photons that can be reproduced on demand.
3. I'd be pleased to learn of other possibilities; including quantum ones.

In these cases, (1, 2), Bell's inequality would be valid. But I find it hard to accept that Bell expected that a return to such classicality would provide a more complete specification of EPRB. In my view, the classicality that Einstein sought -- and that Bell acknowledged -- is more subtle, and available. But this gets us into interpreting EPR's "elements of physical reality" and their use of "corresponding" in this context. By my interpretation, EPR's "elements of physical reality" are such as we meet in 1 and 2 above. But they are also more than those in quantum settings: as in EPRB.

 

[akvadrako]

I have doubts about this though, for typical $\psi$-epistemic reasons. The most basic being that classical uncertainty about $\psi$ doesn't manifest as something like $\mathcal{L}^{1}(\mathcal{H})$, which you'd expect if $\psi$ was a real object you were ignorant of (because this is purely classical ignorance). Rather $\mathcal{H}$ is a subset of the observable algebra's dual (its boundary) and some of that dual has terms that mix classical and quantum probability in odd ways. So you can have a mixture $\rho$ which could be considered a mix of two states $\psi_1$ and $\psi_2$ or a mix of $\psi_3$ and $\psi_4$ and it's the exact same mixture. Hard to understand if $\psi$ is ontic (though not a killing argument of course), it makes pure states like $\psi$ just seem like a limiting type of probability assignment, not ontic.

If it's not ontic at least it's objective — something all observers have compatible beliefs about. Perhaps the missing piece is that observers are not only classically uncertain about $\psi$, but also simultaneously occupy multiple positions in it. I mean the concept of self-locating uncertainty that helped Carroll derive the Born rule. If an observer is characterized by a mixed state exactly equal to both $\psi_{1,2}$ and $\psi_{3,4}$, assuming they exist somewhere, then you can't say this copy is in one or the other, but that two copies of him occupy those two mixtures.

Just to help orient a reading of it, what does he think the world is like underneath the reasoning of agents? I see our typical "laws" are seen to come about as a limiting behaviour in subjective probability assignments, but does he make any conjecture about the underlying world?

It assumes bit-string physics. The observer is in some finite (or countable) strings of bits on a Turing machine. One interesting result of his analysis is that computation is free - only the complexity of the algorithm matters. Of course these bit-strings could even exist in classical computers, so no underlying world can really be picked out.

 

[DarMM]

Very interesting posts!

If it's not ontic at least it's objective — something all observers have compatible beliefs about. Perhaps the missing piece is that observers are not only classically uncertain about $\psi$, but also simultaneously occupy multiple positions in it. I mean the concept of self-locating uncertainty that helped Carroll derive the Born rule. If an observer is characterized by a mixed state exactly equal to both $\psi_{1,2}$ and $\psi_{3,4}$, assuming they exist somewhere, then you can't say this copy is in one or the other, but that two copies of him occupy those two mixtures.

I see your point.

First I would just say, I don't think Carroll derives the Born, I agree with the criticisms of his proof by Kent and Vaidman. Vaidman's attempt at a self-locating uncertainty derivation is much better I think. However it's still circular as it requires decoherence to have occured, which itself requires the Born rule. However if you accept that decoherence can be explained by some other mechanism, it seems to be a pretty good proof.

The only attempt at getting decoherence without the Born rule is the Quantum Darwinism program of Zurek, but it hasn't quite achieved this due circular issues related to the environment (incredibly strong assumptions about the form of the environment that essentially put in by hand a good amount of decoherence).

So as of yet, I don't think there is a solid derivation of the Born rule.

Secondly, I'd still have issues with $\psi$ being ontic given the above. Consider a state in quantum field theory for an inertial and accelerating observer. The same state can be a pure state for the inertial observer and a mixed state for an accelerating observer (Unruh effect), even though neither have performed measurements that would put copies of themselves in different branches of the state. This means a single ontic $\psi$ for an inertial observer is a mixed state of multiple ontic $\psi$ for an accelerating observer, even though there is no cause for self-locating uncertainty here.

This relates to another problem I have. Algebraic Field Theory, especially QFT in curved spacetime, shows that the Hilbert space structure is derivative not primary to quantum theory. Primary is the observable algebra $\mathcal{A}$ and its dual the space of algebraic states $\mathcal{A}^{*}$. A Hilbert space comes about when given a specific $\rho \in \mathcal{A}^{*}$ the GNS theorem shows that you can construct a Hilbert space $\mathcal{H}$ in which $\rho$ is represented as a vector $\psi$ and $\rho(A)$ is represented by $\langle\psi,A\psi\rangle$. However different observers will construct the different Hilbert spaces and the theory has several possible non-Unitarily equivalent Hilbert spaces. I find it hard to think $\psi \in \mathcal{H}$ is ontic.

 

[stevendaryl]

Well, for me at least: not any meaningful version of physical reality when you are writing in the context of EPRB.

Here's my reason. From high-school algebra, without any refence to EPRB, Bell, etc, we irrefutably obtain:

$|E(a, b) - E(a,c)| \leq 1 - E(a,b)E(a,c). \qquad (1)$

Compare this with Bell's famous 1964 inequality:

$|E(a, b) - E(a,c)| \leq 1 + E(b,c). [sic] \qquad (2)$

Given [as I read him. p.195] that Bell's aim was to provide "a more complete specification of EPRB by means of parameter $\lambda$": I suggest that his supporters should pay more attention to his 1990 suggestion that maybe there was some silliness somewhere.

For example, let's rewrite (2). We find:

$|E(a, b) - E(a,c)| - E(b,c) \leq1. [sic] \qquad(3)$

But, under EPRB, that upper bound is $\tfrac{3}{2}.$

Thus, in that Bell uses inequality (2 ) as proof of his theorem: I believe that Bell's writings need to be challenged --- without any reference to nonlocality, QBism, BWIT, AAD, MW, etc [which, in my view, are also silly].

I am not at all sure what point you are making. Yes, Bell's inequality is just a mathematical fact, given certain assumptions. The question is how to interpret the fact that experimentally the inequality is violated. That's where nonlocality (or some other weird possibility) comes in.

When you say "Bell's writings need to be challenged", I'm not sure what specific claims by Bell you are objecting to.

 

[microsansfil]

But then they must accept the Bell theorem that reality obeys nonlocal laws. Yet they don't accept it.

It seem that for qbism, quantum physics does not require non-locality. Non-locality is not a fact, but the result of an interpretation.of physical theory. An Introduction to QBism with an Application to the Locality of Quantum Mechanics. /Patrick

 

[N88]

I am not at all sure what point you are making. Yes, Bell's inequality is just a mathematical fact, given certain assumptions. The question is how to interpret the fact that experimentally the inequality is violated. That's where nonlocality (or some other weird possibility) comes in.

When you say "Bell's writings need to be challenged", I'm not sure what specific claims by Bell you are objecting to.

The point I seek to make is that Bell's inequality is a mathematical fact of limited validity.

1. It is algebraically false.

2. It is false under EPRB (yet Bell was seeking a more complete specification of EPRB).

3. So IF we can pinpoint where Bell's formulation departs from #1 and #2, which I regard as relevant boundary conditions, THEN we will understand the reality that Bell is working with.

4. Now IF we number Bell's 1964 math from the bottom of p.197: (14), (14a), (14b), (14c), (15): THEN Bell's realism enters between (14a) and (14b) via his use of his (1).

So the challenge for me is to understand the reality that he introduces via the relation ...

$B(b,\boldsymbol{\lambda})B(b,\boldsymbol{\lambda}) = 1. \qquad(1)$

... since this is what is used --- from Bell's (1) --- to go from (14a) to (14b).

And that challenge arises because it seems to me that Bell breaches his "same instance" boundary condition; see that last line on p.195. That is, from LHS (14a), I see two sets of same-instances: the set over $(a,b)$ and the set over $(a,c)$. So, whatever Bell's realism [which is the question], it allows him to introduce a third set of same-instances, that over $(b,c)$.

It therefore seems to me that Bell is using a very limited classical realism: almost as if he had a set of classical objects that he can non-destructively test repeatedly, or he can replicate identical sets of objects three times; though I am open to -- and would welcome -- other views.

Thus, from my point of view: neither nonlocality nor any weirdness gets its foot in the door: for [it seems to me], it all depends on how we interpret (1).

PS: I do not personally see that Bell's use of (1) arises from "EPR elements of physical reality." But I wonder if that is how Bell's use of his (1) is interpreted?

For me: "EPR elements of physical reality" correspond [tricky word] to beables [hidden variables] which I suspect Bell may have been seeking in his quest for a more complete specification of EPRB. However, toward answering the OP's question, how do we best interpret the reality that Bell introduces in (1) above?

Or, perhaps more clearly: the reality that Bell assumes it to be found in Bell's move from (14a) to (14b). HTH.

 

[stevendaryl]

I'm still not sure I understand what you're saying. To me, the key move in Bell's proof is to assume that probabilities "factor" when all relevant causal information is taken into account: He assumed that

$P(A, B | a, b) = \sum_\lambda P(\lambda) P(A | a, \lambda) P(B | b, \lambda)$

Basically, the assumption is that all correlations between two events can be explained by a common causal influence on both of them.

 

[DrChinese]

ITo me, the key move in Bell's proof is to assume that probabilities "factor" when all relevant causal information is taken into account: He assumed that

$P(A, B | a, b) = \sum_\lambda P(\lambda) P(A | a, \lambda) P(B | b, \lambda)$

Basically, the assumption is that all correlations between two events can be explained by a common causal influence on both of them.

This is Bell's condition that the setting at A does not affect the outcome at B, and vice versa. You could call that the Locality condition. The other one is the counterfactual condition, or Realism. Obviously, the standard and accepted interpretation of Bell is that no Local Realistic theory can produce the QM results. So both of these - Locality and Realism - must be present explicitly as assumptions.

 

[DrChinese]

... almost as if he had a set of classical objects that he can non-destructively test repeatedly, or he can replicate identical sets of objects three times...

If you believe in classical realism, you don't need to talk about "non-destructive" testing. Because they pre-exist as specific values. If they pre-exist, well... what are the values? There are none that reproduce the QM expectation values.

So you have to commit. Do they exist (independent of measurement)? Or don't they? As I read it, you are taking both sides.

 

[ShayanJ]

Rovelli's Relational QM

After taking a look at his 1996 paper, I should say I have finally found my favorite interpretation. I hope there has been some progress since then. Does anyone know about any recent papers on this?

 

[akvadrako]

Secondly, I'd still have issues with $\psi$ being ontic given the above. Consider a state in quantum field theory for an inertial and accelerating observer. The same state can be a pure state for the inertial observer and a mixed state for an accelerating observer (Unruh effect), even though neither have performed measurements that would put copies of themselves in different branches of the state. This means a single ontic $\psi$ for an inertial observer is a mixed state of multiple ontic $\psi$ for an accelerating observer, even though there is no cause for self-locating uncertainty here.

I don't have much to say about the other points, so I'll just comment on this one. How could a mixed state not imply multiple copies of an observer, given unitary evolution? It would seem to require that the observer is both entangled with a qubit representing a future measurement and not entangled with it. In more general terms, I would say SLU always applies to all observers, because there is a lot about their environment they are uncertain about.

 

[Demystifier]

It seem that for qbism, quantum physics does not require non-locality. Non-locality is not a fact, but the result of an interpretation.of physical theory. An Introduction to QBism with an Application to the Locality of Quantum Mechanics.

A quote from the paper you link:
"QBist quantum mechanics is local because its entire purpose is to enable any single agent to organize her own degrees of belief about the contents of her own personal experience."

My translation of this is the following: Sure, there is objective reality, but it's just not described by (QBist) QM. The things which are described by QM do not involve objective reality. Objective reality, since it exists, is non-local as proved by Bell, but QM as a theory with a limited scope is a local theory.

 

[N88]

I'm still not sure I understand what you're saying. To me, the key move in Bell's proof is to assume that probabilities "factor" when all relevant causal information is taken into account: He assumed that

$P(A, B | a, b) = \sum_\lambda P(\lambda) P(A | a, \lambda) P(B | b, \lambda)$

Basically, the assumption is that all correlations between two events can be explained by a common causal influence on both of them.

In offering an answer to the OP, I was expressing my view that Bell assumes reality in his move from (14a) to (14b). It seems to me that it was the result of his (15) that Bell regarded as the source and the proof of his theorem.

In my view, Bell's expression that "probabilities factor ..." came later as he refined his definition of locality.

So I think it would help the OP and myself if we could learn how you, Dr Chinese, etc., interpret the reality that Bell is defining in his move from (14a) to (14b).

It is widely used in text-books. But, in the ones I've seen, it is used mathematically without explanation of the reality that Bell is trying to capture.

PS: I don't see that he successfully captures EPR's "elements of physical reality". He says (p.195) that he was seeking a more complete specification of EPRB via λ (as I read him).

 

[Demystifier]

Well you're not going to like it, but they say the world is local because there are no mathematical variables describing it, i.e. no $\lambda$, so no implications from Bell's theorem.

Regarding this, I think there are two types of QBists. One type says that there is no $\lambda$ in Nature. Those deny the existence of objective reality. Another type says that there is objective reality, so there is $\lambda$ in Nature, but there is no $\lambda$ in a specific theory of Nature that we call QBist QM.

 

[Lord Jestocost]

So I think it would help the OP and myself if we could learn how you, Dr Chinese, etc., interpret the reality that Bell is defining in his move from (14a) to (14b).
It is widely used in text-books. But, in the ones I've seen, it is used mathematically without explanation of the reality that Bell is trying to capture.

"From a classical standpoint we would imagine that each particle emerges from the singlet state with, in effect, a set of pre-programmed instructions for what spin to exhibit at each possible angle of measurement, or at least what the probability of each result should be…….

From this assumption it follows that the instructions to one particle are just an inverted copy of the instructions to the coupled particle……..

Hence we can fully specify the instructions to both particles by simply specifying the instructions to one of the particles for measurement angles ranging from 0 to π………."

see: https://www.mathpages.com/home/kmath521/kmath521.htm

 

[stevendaryl]

In offering an answer to the OP, I was expressing my view that Bell assumes reality in his move from (14a) to (14b). It seems to me that it was the result of his (15) that Bell regarded as the source and the proof of his theorem.

Well, I don't have Bell's paper in front of me, so that doesn't help. However, Wikipedia has derivations of the Bell inequality and the related CHSH inequality.

I don't know what 14a and 14b refer to. I see this paper of Bell's, posted by Dr. Chinese: http://www.drchinese.com/David/Bell_Compact.pdf
but it doesn't have a 14a and 14b.

PS: I don't see that he successfully captures EPR's "elements of physical reality". He says (p.195) that he was seeking a more complete specification of EPRB via λ (as I read him).

Well, I think that Einstein et al were reasoning along the lines of: If it is possible, by measuring a property of one particle to find out the value of a corresponding property of another, far distant particle, then the latter property must have already had a value. Specifically, Alice by measuring her particle's spin along the z-axis immediately tells her what Bob will measure for the spin of his particle along the z-axis. (EPR originally were about momenta, rather than spins, but the principle is the same). So to EPR, this either means that (1) Alice's measurement affects Bob's measurement (somehow, Bob's particle is forced to be spin-down along the z-axis by Alice's measurement of her particle, or (2) Bob's particle already had the property of being spin-down along the z-axis, before Alice even performed her measurement.

So EPR's "elements of reality" when applied to the measurement of anti-correlated spin-1/2 particles would imply (under the assumption that Alice and Bob are going to measure spins along the z-axis) that every particle already has a definite value for "the spin in the z-direction". If you furthermore assume that Alice and Bob are free to choose any axis they like to measure spins relative to (I don't know if the original EPR considered this issue), then it means that for every possible direction, the particle already has a value for the observable "the spin in that direction".

Bell captured this intuition by assuming that every spin-1/2 particle produced in a twin-pair experiment has an associated parameter $\lambda$ which captures the information of the result of a spin measurement in an arbitrary direction. The functions $A(\overrightarrow{a}, \lambda)$ and $B(\overrightarrow{b}, \lambda)$ are assumed to give the values for Alice's measurement along axis $\overrightarrow{a}$ and Bob's measurement along axis $\overrightarrow{b}$, given $\lambda$.

So it seems to me that $\lambda$ directly captures EPR's notion of "elements of reality". $\lambda$ is just the pre-existing value of the spin along an arbitrary direction.