A Assumptions of the Bell theorem

[martinbn]

Well, I'm not sure what do you mean by "locality" here. The locality used in the EPR argument is not signal locality, nor operators-commuting-at-spatial-separations locality, nor local-Hamiltonian locality. Technically it's also not Bell locality (because EPR did it much before Bell entered the scene), but it's vary akin to Bell locality.

Yes, I meant that it is not Bell's factorizability. It is Bell's locality in the sense that going ons here do not affect going ons there.

I would add this to the assumptions if there was at least one interpretation of QM which claims to avoid nonlocality by not dealing with individual objects. But I am not aware of any such interpretation.

The statistical interpretation!

 

[vanhees71]

Again, we are at a point that we have to define "locality", because this word has so many meanings that it's hard to discuss without giving a clear definition whenever it's used.

For me "locality" means that there is no faster-than-light signalling in any relativistic theory, and that's fulfilled by local (sic!) relativistic QFT, which implements it in its foundations by assuming the microcausality condition, i.e., that any local observables commute at space-like separated arguments. This particularly holds for the commutator between any local observable and the Hamilton density.

 

[Demystifier]

For me "locality" means that there is no faster-than-light signalling in any relativistic theory, and that's fulfilled by local (sic!) relativistic QFT, which implements it in its foundations by assuming the microcausality condition, i.e., that any local observables commute at space-like separated arguments. This particularly holds for the commutator between any local observable and the Hamilton density.

By this definition, even Bohmian mechanics is local.

 

[Demystifier]

The statistical interpretation!

Please provide a reference claiming that statistical interpretation avoids nonlocality by not dealing with individual objects. As far as I am aware, there is none.

 

[martinbn]

Please provide a reference claiming that statistical interpretation avoids nonlocality by not dealing with individual objects. As far as I am aware, there is none.

I am not claiming that. All I said was that I don't see how the argument goes. You stubbornly refuse to explain.

 

[Demystifier]

I am not claiming that. All I said was that I don't see how the argument goes. You stubbornly refuse to explain.

If I don't explain, that's because I don't see what kind of explanation would satisfy you. (It's not that I haven't try to explain it, but obviously you were not satisfied.) That's certainly not a reason to add the assumption to the list.

 

[Demystifier]

It is Bell's locality in the sense that going ons here do not affect going ons there.

Yes, that's correct.

 

[martinbn]

If I don't explain, that's because I don't see what kind of explanation would satisfy you. (It's not that I haven't try to explain it, but obviously you were not satisfied.) That's certainly not a reason to add the assumption to the list.

An explanaition that is phrased in the language of the statistical interpretation. You keep talking about the spin of the particles.

Let's start here. Answer my question from post #146. Alice receives particles, one at a time, and measures the spin along the z-axis. Half of the results are "up", half "down". What is the value of spin-z?

 

[Demystifier]

In standard QM the spin component in a given direction of a spin-1/2 particle is either determined or undetermined. If it is determined the particle is prepared in an eigenstate of this spin component's representing self-adjoint operator and the spin component then takes the corresponding eigenvalue. If the particle is not prepared in such an eigenstate the spin-component's value is indetermined, and Born's rule gives you the probabilities to get each of the possible eigenvalues when measuring this spin component.

I don't know, what EPR are thinking. The more often I try to understand this paper the less I succeed ;-).

You overlearned quantum theory, so you are no longer able to frame your thinking in terms of concepts more general than those of standard quantum theory. That's why EPR and various quantum interpretations don't make sense to you. If someone explained it to you when you were in your early 20's, I'm sure it would be very different.

 

[Demystifier]

Let's start here. Answer my question from post #146. Alice receives particles, one at a time, and measures the spin along the z-axis. Half of the results are "up", half "down". What is the value of spin-z?

Let's start at something even more elementary. Alice receives coins, one at a time, and watches their upper side. Half of the results are "heads", half "tails". What is the upper side?

 

[stevendaryl]

For me "locality" means that there is no faster-than-light signalling in any relativistic theory...

"Local" doesn't mean "no FTL". If someone asks you what's a good local restaurant, they're not asking about any restaurant that can be reached before dinner time by traveling at slower than the speed of light.

Locality is the idea of splitting spacetime into small regions, such that what happens in one region is only affected by conditions neighboring regions. Of course, this raises the question of what it means to "affect" something...

But suppose that there were a pair of coins such that, no matter how far separated, if you flip both coins, they always produce the same result: Either both heads or both tails. (More specifically: the sequence of heads and tails produced by one coin matches the sequence produced by the other coin.) Each coin taken separately is completely random--there is no pattern to the sequence of heads and tails. I would consider that a nonlocal effect. It's an effect that is not bound by distance. A theory in which that effect is a "law of physics" is a nonlocal theory. You can't signal using it, but it's not expressible in terms of local evolution. Now, it could be that there is a "deeper" theory that explains the nonlocal behavior using local law. Maybe each coin contains a hidden mechanism that produces a deterministic sequence of heads and tails, and the mechanisms in the two coins are identical. That would explain the nonlocal correlations in terms of a local mechanism.

But the correlations themselves are nonlocal.

There is a distinction between "nonlocal effects" and "nonlocal influences". A nonlocal effect can be "implemented" or "explained" in terms of local interactions by proposing a mechanism for establishing a correlation. The connection with FTL is not at all that FTL means the same thing as locality. Rather, the implication is this:

If you can show that the nonlocal effect can be used for FTL signaling,​

then you know that there can be no local explanation for the effect.​

So it's a theory-independent conclusion, in the sense that no matter underlying "deeper theory" one proposes to explain the effect, if there is FTL signalling involved, then it can't have a local explanation.

Bell's proof is another, more general, to derive a theory-independent conclusion.

I think it's much more productive to separate the idea of a "nonlocal effect" from a "nonlocal influence".

 

[stevendaryl]

If you can show that the nonlocal effect can be used for FTL signaling,​

then you know that there can be no local explanation for the effect.​

Once people start talking about "superdeterminism", even this conclusion becomes suspect. I assume that superdeterminism could be used to "implement" FTL signaling.

 

[WernerQH]

I would add this to the assumptions if there was at least one interpretation of QM which claims to avoid nonlocality by not dealing with individual objects. But I am not aware of any such interpretation.

There's the rub: talk of "objects". There's no need for "objects" traveling from A to B, and quantum theory is absolutely silent on what happens "in between". It just gives you correlations betwen "state preparation" and "measurement" events. Objects like "electrons" and "photons" are just classical ideas that we have foisted on the microworld.

I'm aware that it is a really compelling idea to explain the correlations with "particles" carrying information with them. But I'd forgo such explanations in favour of a mere description of events, if it offers a chance of restoring common sense.

 

[Demystifier]

There's the rub: talk of "objects". There's no need for "objects" traveling from A to B, and quantum theory is absolutely silent on what happens "in between". It just gives you correlations betwen "state preparation" and "measurement" events. Objects like "electrons" and "photons" are just classical ideas that we have foisted on the microworld.

I'm aware that it is a really compelling idea to explain the correlations with "particles" carrying information with them. But I'd forgo such explanations in favour of a mere description of events, if it offers a chance of restoring common sense.

I'm not convinced that that's enough to restore common sense. Furthermore, even if we accept that there are only events and not objects existing between two events, there is still the question why are those events correlated.

 

[Fra]

After all the last pages of posts, I would say locality is not the issue or concept we should be talking about here. The "correlation" kind of non-locality, is not problematic in itself. And all seem to also agree that we do not have instant causation (FTL). So this is mostly due to communication issues.

The core issue seems to still be the lack of an qualified explanatory causation chain or physical interactions, that explains the "non-local correlations", but WITHOUT beeing stopped by Bells theorem.

We know any theory with Bells theorems ansatz of partitioning of causation chain is wrong.

We know QM makes the right predictions, but it lacks the qualified explanatory value, so in this SENSE, it is obvious that QM if not "incomplete", at least unsatisfactory to use a less confusing word.

But then QM really does not say much more about the nature of physical interactions than does classical physics, as hamiltoninans or action formulations are usually pulled from a hat. The lesson we can draw from this is that physical interactions most certainly does not work like mechanical chains or physical influence. If there is anything we can guess from QM, its that physical interaction likely involved "self-reflection", meaning that INFORMATION is an integral part of understanding actions - unlike a completelty "mechanical" paradigm: Which means, that when A and B interact, itäs not best understood in terms of them physically poking each each, but that the action A chooses towards B, depends not on B, but in A's "image" of B. Such a parardigm seem to have the potential to explain correlations, but without beeing stopped by Bells theorem, as the partitioning assumption can not be justified.

/Fredrik

 

[Demystifier]

And all seem to also agree that we do not have instant causation (FTL).

No! In Bohmian mechanics, for instance, there is instant FTL causation. But all interpretations agree that there is no instant FTL signaling. Do I have to explain the difference?

 

[WernerQH]

even if we accept that there are only events and not objects existing between two events, there is still the question why are those events correlated.

Some people may well find a QFT calculation sufficient as an explanation. I certainly do, and I don't abhor propagators reaching backwards in time.

 

[Fra]

No! In Bohmian mechanics, for instance, there is instant FTL causation. But all interpretations agree that there is no instant FTL signaling. Do I have to explain the difference?

Unless you by FTL-causation, means FTL-correlation, do you mean that causation is a one-way communication, and signaling is two-way communication?

With causation, I assume you mean that something here changes the physical situation at a remote location - not that the local INFORMATION about the remove location is changed? IS that correct?

Would your FTL causation allow us to set up an "instant" trigger for a one shot communication, where A can send a one-way "trigger signal" instantly to B? (And perhaps A and B, can pre-agree on the meaning of this trigger)

/Fredrik

 

[stevendaryl]

Unless you by FTL-causation, means FTL-correlation, do you mean that causation is a one-way communication, and signaling is two-way communication?

I'm not sure exactly what @Demystifier is meaning by the distinction, but to me, FTL causation is in terms of a proposed law of physics. If the state of one object at a future time depends on the state of distant objects in the recent past (too recently for light to propagate), then that implies FTL causation.

FTL signaling is a special case in which the conditions can be manipulated.

Here's a made-up law of physics that might illustrate the difference. Suppose that there is some weird object, a will-o-the-wisp, which just randomly appears at various locations, and then disappears, only to re-appear at some random spot. Suppose that there is a force $F_{wow}$ which acts instantaneously on electrons everywhere in the universe, and is constant in magnitude, and is directed toward the will-o-the-wisp.

This would imply FTL causation: the will-o-the-wisp affects electrons instantaneously. But it couldn't be used for FTL signaling, since there is no way to control where the will-o-the-wisp appears.

 

[vanhees71]

"Local" doesn't mean "no FTL". If someone asks you what's a good local restaurant, they're not asking about any restaurant that can be reached before dinner time by traveling at slower than the speed of light.

Locality is the idea of splitting spacetime into small regions, such that what happens in one region is only affected by conditions neighboring regions. Of course, this raises the question of what it means to "affect" something...

But suppose that there were a pair of coins such that, no matter how far separated, if you flip both coins, they always produce the same result: Either both heads or both tails. (More specifically: the sequence of heads and tails produced by one coin matches the sequence produced by the other coin.) Each coin taken separately is completely random--there is no pattern to the sequence of heads and tails. I would consider that a nonlocal effect. It's an effect that is not bound by distance. A theory in which that effect is a "law of physics" is a nonlocal theory. You can't signal using it, but it's not expressible in terms of local evolution. Now, it could be that there is a "deeper" theory that explains the nonlocal behavior using local law. Maybe each coin contains a hidden mechanism that produces a deterministic sequence of heads and tails, and the mechanisms in the two coins are identical. That would explain the nonlocal correlations in terms of a local mechanism.

But the correlations themselves are nonlocal.

There is a distinction between "nonlocal effects" and "nonlocal influences". A nonlocal effect can be "implemented" or "explained" in terms of local interactions by proposing a mechanism for establishing a correlation. The connection with FTL is not at all that FTL means the same thing as locality. Rather, the implication is this:

If you can show that the nonlocal effect can be used for FTL signaling,​

then you know that there can be no local explanation for the effect.​

So it's a theory-independent conclusion, in the sense that no matter underlying "deeper theory" one proposes to explain the effect, if there is FTL signalling involved, then it can't have a local explanation.

Bell's proof is another, more general, to derive a theory-independent conclusion.

I think it's much more productive to separate the idea of a "nonlocal effect" from a "nonlocal influence".

Well, you also didn't precisely tell us, what you mean by "locality". If we want to have chance to know what we are talking about, we'd need a precise mathematical definition. I was referring to the microcausality condition of relativistic QFTs, and that's what I think is what's "locality" with a really important meaning in the discussion about EPR.

I don't know, what you precisely mean by "splitting spacetime into small regions, such that what happens in one region is only affected by conditions neighboring regions."

That doesn't hold for any physical theory, and it doesn't hold by observation, because there are of course signals which can traveling a very far distance and are very extended. E.g., we receive light from galaxies being, the the best of our knowledge, billions of light years away, i.e., electromagnetic waves propagate from their "pretty local" sources over large distances and spread practically "all over space" given enough time.

I also agree with you that one has to distinguish clearly between "long-ranged correlations" (I try to avoid to say "non-local" here) and "long-ranged causal effects".

For me the point about the long-ranged correlations between observables of far-distant parts, fully and accurately describable by local, i.e., "microcausal", relativistic QFT, and their confirmation by various Bell tests, show that there is no contradiction between microcausal QFT, which simply by construction does not allow for faster-than-light propagating causal effects but at the same time describe the said observed long-ranged correlations. There is no spooky interaction at a distance but rather "local interactions" in the sense of microcausality. I'm not sure, whether at the time of the EPR paper microcausality was already so clearly pronounced as it is today. I guess not, because that was before the seminal work of Streater and Wightman et al, where the "axiomatic foundations" of QFT were more clearly worked out.

As I said, I have a hard time to understand what EPR really wanted to say. It's also clear that Einstein himself was not very happy with this paper. There's another paper of 1948, where Einstein himself wrote (in German, which is perhaps important, because Einstein was for sure way more fluent in German than in English) that the real point about quantum theory and entangledment that was bothering him is the "non-separability" rather than the faster-than-light spooky actions at a distance. I think "inseparability" is a much better phrase than calling it "non-local", because it precisely describes the far-distant correlations of parts of a quantum system which are stronger than any such correlations as described by what Bell called "local realistic theories". As we know today, thanks to this work by Bell, Nature rather behaves as predicted by quantum theory than as is describable by "local realistic" theories.

 

[gentzen]

Again, we are at a point that we have to define "locality", because this word has so many meanings that it's hard to discuss without giving a clear definition whenever it's used.

I understand that you have a real problem with the word "locality" independent of this current discussion on Bell's theorem. I was so happy that stevendaryl gave a clear explanation of nonlocal randomness, but somehow I already suspected that it would help you only a tiny little bit. And your response confirms that expectation. I am fully aware that I will be even less able to help you, but I will try nevertheless.

For me, the fact that QM is nonlocal is not identical to what is proved by Bell's theorem. Even worse, there is no longer a single Bell's theorem, but a variety of related theorems that all go under the heading of Bell's theorem. For each single one of those theorems, you could (and should) exactly write down the assumptions and what the specific theorem proves based on those assumptions. So you have to make precise in each case what exactly you mean by "locality". In most cases this boils down to the separability condition mentioned multiple times in this thread.

However, the word "locality" is not really unclear. It may mean slightly different things in different context, but it is still clear in the "you know it when you see it" sense. So for Bohmian mechanics, the way the trajectories influence each other is nonlocal. For Copenhagen, the way the Born rule updates the wavefunction is nonlocal. Not in the sense of a judgment, but in the sense that this is what we mean when we say that the interpretation is nonlocal. And in the sense of "conservation of difficulty", the expectation is that you will find similar elements of nonlocality in any complete and valid interpretation of quantum mechanics. As an example, consistent histories in its basic form (as a logical framework) does not contain elements of nonlocality. But if you complete it to a full interpretation, then nonlocal elements appear.

 

[Demystifier]

Unless you by FTL-causation, means FTL-correlation, do you mean that causation is a one-way communication, and signaling is two-way communication?

With causation, I assume you mean that something here changes the physical situation at a remote location - not that the local INFORMATION about the remove location is changed? IS that correct?

Would your FTL causation allow us to set up an "instant" trigger for a one shot communication, where A can send a one-way "trigger signal" instantly to B? (And perhaps A and B, can pre-agree on the meaning of this trigger)

No. Causation is influence of one physical object (or phenomenon) on another. Signaling is deliberate influence of a subject (human or intelligent animal) on something else (another subject or a physical object or phenomenon). Signaling is a very anthropomorphic concept, causation is not so much. In deterministic interpretations of QM such as Bohmian mechanics, there is FTL causation (the position of one particle influences the velocity of another particle), but there is no FTL signalling (a human does not have a control over Bohmian particle positions, i.e. she cannot deliberately put the particle here rather than there).

 

[PeterDonis]

do Bertlmann socks violate the factorizability assumption?

No.

 

[PeterDonis]

I meant that it is not Bell's factorizability. It is Bell's locality

This makes no sense. Bell's locality is Bell's factorizability.

 

[PeterDonis]

The theorem in question is a bit more than the inequities and their violations.

If you mean Bell's theorem, no, the theorm is the inequalities. Proving that any theory that satisfies the assumptions must make predictions that satisfy the inequalities is the whole point of the theorem.

 

[PeterDonis]

we are at a point that we have to define "locality"

We shouldn't for this thread, since in the context of Bell's theorem, we already have a definition of locality: the factorizability assumption. That is "locality" as far as Bell's theorem is concerned. Discussions of other definitions of "locality" belong in another thread, not this one.

 

[PeterDonis]

there is no longer a single Bell's theorem, but a variety of related theorems that all go under the heading of Bell's theorem

Please give references for this "variety of related theorems". If we are going to discuss something, we should know what we are discussing.

 

[PeterDonis]

Please give references

And to follow my own advice, here is the original paper by Bell on his theorem:

https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf

What I am calling the factorizability assumption is equation (2) in that paper.

 

[Nullstein]

Discussions based on the EPR argument are pretty unproductive, because the argument is known to be flawed. Contrary to their postulate, the absence of interactions really does not imply pre-existing values. Bohmian mechanics for example serves as a counterexample. Since Bell, there is no more need to appeal to the EPR argument. All assumptions are pretty neatly exposed in the theory of probabilistic causality, i.e. the causal Markov condition (which generalizes such assumptions as Bell factorizability or the Reichenbach principle).

 

[vanhees71]

However, the word "locality" is not really unclear. It may mean slightly different things in different context, but it is still clear in the "you know it when you see it" sense. So for Bohmian mechanics, the way the trajectories influence each other is nonlocal. For Copenhagen, the way the Born rule updates the wavefunction is nonlocal. Not in the sense of a judgment, but in the sense that this is what we mean when we say that the interpretation is nonlocal. And in the sense of "conservation of difficulty", the expectation is that you will find similar elements of nonlocality in any complete and valid interpretation of quantum mechanics. As an example, consistent histories in its basic form (as a logical framework) does not contain elements of nonlocality. But if you complete it to a full interpretation, then nonlocal elements appear.

If it were so clear, you could give a clear definition. The only really clear language you can discuss about physics is math. So can you give a clear mathematical definition of what you mean by "local"? E.g., you say the "wave function" is "not local". I've no clue what you mean. Also you are then obviously discussing non-relativistic quantum theory. Then it's a function of time and arguments with the meaning of the eigenvalues of a complete set of compatible self-adjoint operators (e.g., $3N$ position-vector components and spins of a of an $N$-particle system). What specifies this function to be "local" or "non-local"? I've no idea what it means to say a quantum state is local or nonlocal.

Before the scientific side of the question, what we mean by "local" or "non-local" is clarified, it doesn't make sense to discuss interpretations or other philosophy concerning this question.

 

[vanhees71]

Discussions based on the EPR argument are pretty unproductive, because the argument is known to be flawed. Contrary to their postulate, the absence of interactions really does not imply pre-existing values. Bohmian mechanics for example serves as a counterexample. Since Bell, there is no more need to appeal to the EPR argument. All assumptions are pretty neatly exposed in the theory of probabilistic causality, i.e. the causal Markov condition (which generalizes such assumptions as Bell factorizability or the Reichenbach principle).

In this sense QT is not local, because the time evolution of quantum systems is non-Markovian. E.g., Markovian master equations in the theory of open quantum systems are for sure an approximation.

 

[PeterDonis]

the word "locality" is not really unclear. It may mean slightly different things in different context, but it is still clear in the "you know it when you see it" sense.

Since this thread is about Bell's Theorem, the definition of "locality" for this thread should be the one Bell used in his theorem, which, as I have already pointed out, is the factorizability assumption.

can you give a clear mathematical definition of what you mean by "local"?

We already have one for this thread; see above.

 

[vanhees71]

We shouldn't for this thread, since in the context of Bell's theorem, we already have a definition of locality: the factorizability assumption. That is "locality" as far as Bell's theorem is concerned. Discussions of other definitions of "locality" belong in another thread, not this one.

Good, can you give a reference with that precise definition. Then at least we have finally one!

 

[PeterDonis]

can you give a reference with that precise definition.

I already did. See post #178.

 

[Nullstein]

In this sense QT is not local, because the time evolution of quantum systems is non-Markovian. E.g., Markovian master equations in the theory of open quantum systems are for sure an approximation.

Well, now you're confusing Markov with Markov . The "causal Markov condition" is actually completely unrealated to the "Markov condition" in stochastic processes. Unfortunately, we are stuck with this terminology.

 

[vanhees71]

Ok, thanks. Then I'm completely lost.

 

[vanhees71]

I already did. See post #178.

Sorry, I've overlooked this.

 

[Nullstein]

The causal Markov condition is just a more elaborate version of the screening off conditions that are used in the derivation of Bell's theorem. In the absence of superdeterminism and similarly fancy loopholes, e.g. under the assumption that there is just one common cause and no conspiracies, it reduces to the Reichenbach principle, which leads to the Bell factorization condition. The CMC is basically the state of the art in causality research. However, it still uses classical probability and might not apply to quantum systems, as has been acknowledged by Pearl.

 

[Demystifier]

Discussions based on the EPR argument are pretty unproductive, because the argument is known to be flawed.

No it isn't. The EPR conclusions follow from the EPR assumptions. The assumptions could be wrong, but it doesn't make the argument flawed.

the absence of interactions really does not imply pre-existing values.

Yes it does, given their other assumptions.

Bohmian mechanics for example serves as a counterexample.

It does not, because in Bohmian mechanics particles interact with each other. That's most explicitly seen when Bohmian mechanics is formulated in terms of the quantum potential.

Since Bell, there is no more need to appeal to the EPR argument.

But Bell himself used EPR argument as a part of his argument. First he used EPR to show that the assumption of locality implies preexisting values. Then he has shown that preexisting values lead to another contradiction. Therefore, he concluded, the initial assumption (locality) has been wrong.

 

[Nullstein]

No it isn't. The EPR conclusions follow from the EPR assumptions. The assumptions could be wrong, but it doesn't make the argument flawed.Yes it does, given their other assumptions.It does not, because in Bohmian mechanics particles interact with each other. That's most explicitly seen when Bohmian mechanics is formulated in terms of the quantum potential.But Bell himself used EPR argument as a part of his argument. First he used EPR to show that the assumption of locality implies preexisting values. Then he has shown that preexisting values lead to another contradiction. Therefore, he concluded, the initial assumption (locality) has been wrong.

The EPR argument is wrong, because it missed the possibility for contextuality or less desirable explanations like superdeterminism. Their conclusion just doesn't follow from their assumptions if one doesn't exclude these possibilities. EPR certainly didn't mention them at all. That's why a precise formulation such as Bell's is required. Bell's theorem is completely independent of the EPR argument. However, he also missed contextuality and superdeterminism in his first paper. He corrected himself later on. The derivations of his theorem given in his later papers basically resemble exactly what a derivation from the CMC would yield.

 

[PeterDonis]

First he used EPR to show that the assumption of locality implies preexisting values.

Note that Bell's $\lambda$ doesn't necessarily have to be "preexisting values", although Bell does say that that is the kind of thing Einstein was envisioning when he talked about a "more complete specification of the state".

 

[PeterDonis]

He corrected himself later on.

Can you give a reference to a later paper that shows this?

 

[Nullstein]

Can you give a reference to a later paper that shows this?

In his original paper, which you cited above, he assumed pre-existing values for all observables, because he assumed that functions like $A(\alpha,\lambda)$ exist and they indeed give values for every choice of $\alpha$ and $\lambda$ (i.e. given $\lambda$, there is simultaneously a value $A$ for each choice of $\alpha$). He was led to this assumption by the EPR argument.

In his paper "The theory of local beables," he relaxed this assumption and gave a derivation only based on probabilities, which opens up the possibility for contextuality. (If you want to express this in terms of observables, you would have to introduce two observables $A(\lambda)$ and $\alpha(\lambda)$, which depend only on $\lambda$ and not on each other. In order to still derive the inequality after this relaxation, you must additionally postulate certain probabilistic independence relations as he did in that paper.)

Then there was a paper called "La nouvelle cuisine," where he gave the same derivation again without tacitly excluding the possibility of superdeterminism.

You can find all of these papers in a nice little book called "Speakable and unspeakable in quantum mechanics." (And just to emphasize it: No trace of the EPR argument is left in his latter derivations. Instead, they show that the EPR argument was flawed and exlcuded certain possibilities. They arrive at their conclusion only due to tacit assumptions they weren't aware of.)

 

[PeterDonis]

In his paper "The theory of local beables,"

This one (at least in draft form) is also on the CERN website:

https://cds.cern.ch/record/980036/files/197508125.pdf

a paper called "La nouvelle cuisine,"

This one I have not been able to find online, although it is in the book you mention (which I have but don't have my copy handy right now).

 

[gentzen]

there is no longer a single Bell's theorem, but a variety of related theorems that all go under the heading of Bell's theorem

Please give references for this "variety of related theorems". If we are going to discuss something, we should know what we are discussing.

The article on Bell's theorem in the Stanford Encyclopedia of Philosophy starts as follows:

Bell’s Theorem is the collective name for a family of results, all of which involve the derivation, from a condition on probability distributions inspired by considerations of local causality, together with auxiliary assumptions usually thought of as mild side-assumptions, of probabilistic predictions about the results of spatially separated experiments that conflict, for appropriate choices of quantum states and experiments, with quantum mechanical predictions.

But that SEP article is just a proof that I am not the only one who believes that Bell's theorem has become a heading for a variety of theorems. What I had in mind personally were reformulations in terms of games, or presentations like Mermin's that try to make the counter intuitiveness of the quantum behavior even more concrete for a general audience. And in terms of different assumptions (instead of separability), I was thinking of papers like Asher Peres' Unperformed experiments have no results which goes with "Let us assume that the outcome of an experiment performed on one of the systems is independent of the choice of the experiment performed on the other."

 

[Nullstein]

The failure of the EPR argument can be demonstrated quite easily:
1. We know that the QM predictions can in principle be reproduced by a local, superdeterministic, contextual theory, i.e. such a theory can violate Bell's inequality.
2. However, EPR claim that the assumption of locality alone implies non-contextuality (pre-existing values). But non-contextuality (+ locality) implies that Bell's inequality holds, as shown in Bell's first paper.
Thus, we arrive at a contradiction.

Basically, EPR were asking the right questions but giving the wrong answers. They just missed the possibility of contextual theories and other undesirable loopholes like superdeterminism. Thus, all discussions based on the EPR argument are bound to fall into the same trap. Today, there is no need to appeal to it, because we have crystal clear quantitative conditions such as the CMC. Arguments based on EPR always tacitly assume all the postulates that are encompassed in the CMC. (And in my experience, more often than not, they do so in bad faith, e.g. Maudlin.)

 

[Fra]

I'm not sure exactly what @Demystifier is meaning by the distinction, but to me, FTL causation is in terms of a proposed law of physics. If the state of one object at a future time depends on the state of distant objects in the recent past (too recently for light to propagate), then that implies FTL causation.

FTL signaling is a special case in which the conditions can be manipulated.

Here's a made-up law of physics that might illustrate the difference. Suppose that there is some weird object, a will-o-the-wisp, which just randomly appears at various locations, and then disappears, only to re-appear at some random spot. Suppose that there is a force $F_{wow}$ which acts instantaneously on electrons everywhere in the universe, and is constant in magnitude, and is directed toward the will-o-the-wisp.

This would imply FTL causation: the will-o-the-wisp affects electrons instantaneously. But it couldn't be used for FTL signaling, since there is no way to control where the will-o-the-wisp appears.

No. Causation is influence of one physical object (or phenomenon) on another. Signaling is deliberate influence of a subject (human or intelligent animal) on something else (another subject or a physical object or phenomenon). Signaling is a very anthropomorphic concept, causation is not so much. In deterministic interpretations of QM such as Bohmian mechanics, there is FTL causation (the position of one particle influences the velocity of another particle), but there is no FTL signalling (a human does not have a control over Bohmian particle positions, i.e. she cannot deliberately put the particle here rather than there).

Thanks for the explanation. I have a similar association of causation and law, as Stevendaryl suggests. But due to the way I think about the nature and emergence of physical laws (my problem of course) in an observer/agent perspective, I tend to classify mentioned "FTL-causations" instead as FTL-correlation - for this reason:

On short time scale:

I think of causation as simply manifesting how the action of an agent/observer is chosen (This reflects the "physical law").

I see no fundamental meaning for an agent to rationally speak about "causation" in an observational record, this is just correlations. (This does not reflect law, it just is what it is, as there are no "choices" to be made)

(The contrast is on evolutionary time scales: I envision a more speculative connection between observed correlations and future causation, and thus formation of law.)

It seems to me what you describe as uncontrollable happenings are merely correlated. Although you imply a "hidden law" that imples the correlation - thus it's a causation (I get and appreciate this). I guess what I fail to see, is how such "hidden law" can be intrinsic to the observer in my own understanding. I agree this is not a hard argument at this point, I just reflects by strange bias.

But this is indeed deeply a question for the nature of causation and law, which was my point, that this seems to be that main troublesome point in the EPR discussion.

It's hard for me to to understand the presumed explanatory logic of the notion of laws, if they are hidden to those who are supposed to follow them? ie. to the inside observers? It seems as strange as to suggest that you need extrinsic curvatures to infer intrinsic geometry.

/Fredrik

 

[atyy]

The failure of the EPR argument can be demonstrated quite easily:
1. We know that the QM predictions can in principle be reproduced by a local, superdeterministic, contextual theory, i.e. such a theory can violate Bell's inequality.
2. However, EPR claim that the assumption of locality alone implies non-contextuality (pre-existing values). But non-contextuality (+ locality) implies that Bell's inequality holds, as shown in Bell's first paper.
Thus, we arrive at a contradiction.

Basically, EPR were asking the right questions but giving the wrong answers. They just missed the possibility of contextual theories and other undesirable loopholes like superdeterminism. Thus, all discussions based on the EPR argument are bound to fall into the same trap. Today, there is no need to appeal to it, because we have crystal clear quantitative conditions such as the CMC. Arguments based on EPR always tacitly assume all the postulates that are encompassed in the CMC. (And in my experience, more often than not, they do so in bad faith, e.g. Maudlin.)

Is the causal markov condition the same argument as given in Woods and Spekkens (Fig. 19)?
https://arxiv.org/abs/1208.4119

Why do you say Maudlin tacitly assumes postulates equivalent to CMC in bad faith?

 

[Demystifier]

And to follow my own advice, here is the original paper by Bell on his theorem:

https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf

What I am calling the factorizability assumption is equation (2) in that paper.

Bell does not call it "factorizability assumption". Indeed, it can be misleading to call it so because it involves a $\lambda$-integral over products, which is not a product itself. (In fact, I was misled myself when I asked you whether Bertlmann socks violate it.) Is it your own invention to call it "factorizability assumption", or is there another reference where it is called so?

 

[stevendaryl]

Bell does not call it "factorizability assumption". Indeed, it can be misleading to call it so because it involves a $\lambda$-integral over products, which is not a product itself.

I don’t know the answer to the question of who has called it “the factorizability assumption”, but I would argue that it’s appropriate, if you formulate it like this:

For any joint probability distribution $P(A \wedge B)$ describing distant measurement results, there is some collection of facts $\Lambda$ about conditions in the intersection of their backwards lightcones such that

$P(A \wedge B | \Lambda) = P(A|\Lambda) P(B|\Lambda)$

In other words, the assumption is that the conditional probabilities factor, if you condition on their mutual influences.