Scholarpedia article on Bell's Theorem

[malreux]

(1) The MWI people will insist, and they have a good point (!), that the wf itself is already perfectly "physical", so why should you need to add some extra stuff for consciousness to emerge from?

(2)The reason people (should) want to avoid nonlocality is because it conflicts with relativity's alleged prohibition on superluminal causation. That is, to be against non-locality is to be *for* the proposition that all the physical influences in the world propagate around at or slower than light, which in turn presupposes that there is a world out there with causal influences propagating around in it at some speed or other.

Hi ttn, have been enjoying this thread immensely! Sorry for wading in at the tail - my recurrent 'problem of tails' - just a couple of points:

(1) I agree that in practice most modern MWI folks, especially of the oxonian decoherence stamp, will gesture towards some idea of emergence and possibly functionalism in the philosophy of mind. I think this is along the right lines, but it is very underdeveloped, although Wallace's latest book has a brilliant stab at it. However, note that many MWI bods, including Wallace, are not wavefunction monists. That is, they don't believe that the world is made out of wavefunction in the same way that e.g. Kim believes classical measuring apparatus are made out of quantum particles (as mereological sums?). Wallace, for example, is more interested in a coherent description of the quantum state, or rather just paying attention to the math in ones interpretation.

(2) I understand the context in which you made this point, but still feel that you have been a bit 'cut n' dried' about this here. As you know, Maudlin questions whether we are talking about causal influence when gesturing towards superluminal signalling within an EPR/Bell type scenario. So the alleged 'prohibition' might not be prohibiting the relevant factors. More importantly, does 'non-locality' really have to conflict with relativity? I would suggest that the answer is, at least, not obvious and not trivial. Additionally, I think we muddy the waters when getting hung up on 'speed' - two things spring to mind: Barbour's famous correction for relativists neglecting duration as a concept in his end of time escapade, and the fact such debates as the present are usually within the context of non-relativistic QM. Transported to the arena of QFT, where we're looking for a Lorentz-covariant unitary quantum theory, in which the primary dynamical variables are ST local operators like field strengths and in which particles are approximate and emergent, interpretations leaving the formalism intact pretty much carry through. Unlike modificatory strategies, although recent attempts have been made (e.g. modern GRW treatments). I bring up these measurement problem considerations to briefly illustrate the extent to which relativity is already present in the formalism(s) of QFT, coupling this point with the thought that 'pure' interpretations of QM (e.g. MWI) ought to carry over from non-relativistic to relativistic quantum theory.

Incidentally, how do accounts which strive for locality manage concepts that I think are very related, such as non-seperability, holism, etc.? (I think Healey analyses these related concepts well in 'Gauging what's Real'?)

 

[malreux]

I dislike [MWI] because, even though it does provide a mechanism for effective wave-function collapse, it does not provide a simple explanation of why this effective collapse obeys the Born rule.

Well, there aren't any simple explanations going out on the current MWI market's output. There are many attempts however, including formal derivations and so forth (the Deutsch approach). Or Greaves' caring measure. There have even been modifcatory strategies (again, Deutsch).

Do you think MWI proponents have any resources to recover the Born rule?

 

[Demystifier]

Well, there aren't any simple explanations going out on the current MWI market's output. There are many attempts however, including formal derivations and so forth (the Deutsch approach). Or Greaves' caring measure. There have even been modifcatory strategies (again, Deutsch).

Do you think MWI proponents have any resources to recover the Born rule?

To recover the Born rule, I think MWI proponents necessarily must introduce some additional assumptions or axioms in the theory, which destroys the main virtue of MWI: minimality of assumptions. In fact (ttn will kill me for saying it), I like to think of Bohmian interpretation as a variant of MWI which just picks one such assumption, which, unlike other attempts of that sort in MWI, seems very natural to me.

 

[ttn]

That's correct! (Note that I erased the part of your text mentioning consciousness, because in that part of my paper I don't mention consciousness at all.)

I thought it did -- you explicitly talk about "the point of view from" a particular branch. To me that kind of language is "code" for consciousness, but maybe you meant something else.

Ah, that's great! Now I finally clearly understand the source of our disagreement. Even though we both like Bohmian mechanics, we like it for totally different reasons. You like it because it provides ontology in spacetime, while I like it because it gives a simple mechanism for effective wave-function collapse.

Yes, that's interesting and clarifying. For the record, I wouldn't say I like it *just* because it gives ontology in spacetime. It's bound up with the measurement problem. Copenhagen also has ontology in spacetime, but there it is just *posited* and then we have the usual awkwardness of two separately-posited realms (classical and quantum, or micro and macro, or however you want to describe them) and the associated awkwardness of different sets of laws on the two sides (both of which are by the way set aside in favor of some new thing when the two sides "interact"), etc. So put it this way: the virtue of dBB is that it gives you the same "classical macro world" that Copenhagen has to just postulate, and it gives you that in the context of a fully precise and consistent microscopic theory whose equations don't need to be set aside when they become embarrassing. And, you know, it's empirically adequate, etc.

I don't really understand your reasons for liking it, that it provides a simple mechanism for effective wave-function collapse. That to me seems way too bound up with ideas from orthodox QM. My attitude is that if you think of *any* interpretation fundamentally as an attempt to solve some technical problem with ordinary QM, you're sort of missing what the real issues are. We are trying to figure out what's the best theory here, and it should be clear to everybody that ordinary QM ain't it. So the best approach is to *forget* ordinary QM and take the fundamental question to be: which theory does the best job, by the normal standards of judging scientific theories, of accounting for all the facts (by which I mean to include both pre-scientific facts like that there are trees and stuff outside my window, and then also the detailed quantitative results of all the various sophisticated experiments like 2-slit, atomic spectra, Bell, etc. etc. etc.).

Related to this, we both dislike MWI, but again for totally different reasons. You dislike it because it does not provide ontology in spacetime. I dislike it because, even though it does provide a mechanism for effective wave-function collapse, it does not provide a simple explanation of why this effective collapse obeys the Born rule.

Yikes, here we'd have to get deep into a discussion of what you (and MWI) even mean by "effective". But again my attitude is the above. Forget about explaining effective wave-function collapse. The question is, which theory is best at explaining what needs to be explained?

 

[ttn]

(1) I agree that in practice most modern MWI folks, especially of the oxonian decoherence stamp, will gesture towards some idea of emergence and possibly functionalism in the philosophy of mind. I think this is along the right lines, but it is very underdeveloped, although Wallace's latest book has a brilliant stab at it. However, note that many MWI bods, including Wallace, are not wavefunction monists. That is, they don't believe that the world is made out of wavefunction in the same way that e.g. Kim believes classical measuring apparatus are made out of quantum particles (as mereological sums?). Wallace, for example, is more interested in a coherent description of the quantum state, or rather just paying attention to the math in ones interpretation.

So what (according to Wallace or whoever) is the ontology of MWI? That is, what, exactly, according to MWI, is physically real?

(2) I understand the context in which you made this point, but still feel that you have been a bit 'cut n' dried' about this here. As you know, Maudlin questions whether we are talking about causal influence when gesturing towards superluminal signalling within an EPR/Bell type scenario. So the alleged 'prohibition' might not be prohibiting the relevant factors. More importantly, does 'non-locality' really have to conflict with relativity? I would suggest that the answer is, at least, not obvious and not trivial.

I agree. The relation between "locality" and "relativity" is more subtle than most people took it to be, before they appreciated that we are going to have to learn to live with nonlocality! I usually try to be careful with the words here, e.g., talking about "relativity's alleged prohibition on superluminal causation" as opposed to just stating that "nonlocality contradicts relativity". I'm don't think it necessarily does, though it's clear that attempts to *reconcile* nonlocality with fundamental relativity run into serious and difficult problems, not least of which is figuring out what the heck "fundamental relativity" should even mean.

I bring up these measurement problem considerations to briefly illustrate the extent to which relativity is already present in the formalism(s) of QFT, coupling this point with the thought that 'pure' interpretations of QM (e.g. MWI) ought to carry over from non-relativistic to relativistic quantum theory.

Yes, sure, relativity is already present in the formalism of QFT... But there are also some relevant things sorely lacking in standard formulations of QFT, e.g., clarity about what the heck it's *about*. This matters hugely, especially for discussions of locality/nonlocality, where the very concept denotes some feature of stuff happening in physical space / spacetime. Is there any stuff happening in physical space /spacetime according to ordinary QFT? Beats me. And I find this at least rather worrisome from the point of view of saying that ordinary QFT "is relativistic".

Incidentally, how do accounts which strive for locality manage concepts that I think are very related, such as non-seperability, holism, etc.? (I think Healey analyses these related concepts well in 'Gauging what's Real'?)

My own personal view is that the whole idea of "non-separability" is just a confused way of saying that a theory involves what Bell called non-local beables. In a theory of exclusively local beables (a "TELB" as I dubbed this in a recent paper) you couldn't *possibly* have "non-separability". The thing that people call "non-separabiliity" really just comes down to some kind of state description which says there are definite relations between "things at separate places" even though neither thing has definite values for the relata. But without fail, the assertion that this is happening is based on taking the quantum state (a nonlocal beable if it is a beable at all) as the description. But notice that it's tacitly assumed that this quantum state is some kind of description of "things at separate places". My view is that people talking this way typically are not at all entitled to this assumption. If the only thing in the theory is some crazy wf on some crazy abstract configuration space, what in the world makes you think there are "two particles, at different locations" (or whatever) in the picture at all? So the whole thing arises from the following confusion: mistaking what should be taken as a non-local beable, for some kind of description of local beables. If the ontology is really just the wf (no local beables) then there is no "non-separability" -- the state is perfectly local and separable in its proper space, the configuration space. On the other hand, if there are local beables in the ontology we should be a lot clearer and more explicit about what those are: put them squarely on the table before we get lost in arguing about how "separable" the ontology is...

 

[malreux]

[1]To recover the Born rule, I think MWI proponents necessarily must introduce some additional assumptions or axioms in the theory
[2] [...] which destroys the main virtue of MWI: minimality of assumptions.

[3] I like to think of Bohmian interpretation as a variant of MWI which just picks one such assumption, which, unlike other attempts of that sort in MWI, seems very natural to me.

[1] Certainly this is a traditional criticism, and if it carries through then [2] follows inevitably. However, what if instead of additional assumptions or axioms we need some good philosophy rather than new physics? I'm going put the point very crudely - there is enough 'going on' to reconstruct classical 'worlds' in my view, although a lot else besides that is very far from classical worlds. The question is - can we so reconstruct in a principled manner? And, if so, is this to be understood as principle-style physics or a theory of emergence? To me the main question in such reconstruction projects is - can the Born rule really be derived from the formalism? Of course, no one is suggesting a bunch of uninterpreted mathematics tells us much in words. But the actual numbers we call probabilities and their relation to the modulus squared is a bit of mystery without further assumptions. Wavefunction realism at least has the virtue that one can talk about QM without reference to probabilities at some level. Perhaps the weakness of MWI in this regards hints at a proper understanding of fundamental physics?

[3] I agree with this, although I doubt ttn will! However, I think this is a bad way for proponents to argue for ddb, accepting as I do the thrust of Wallace&Brown's paper.

 

[malreux]

[1]So what (according to Wallace or whoever) is the ontology of MWI? That is, what, exactly, according to MWI, is physically real?

[2] [...]which is figuring out what the heck "fundamental relativity" should even mean.

[3]Yes, sure, relativity is already present in the formalism of QFT... But there are also some relevant things sorely lacking in standard formulations of QFT, e.g., clarity about what the heck it's *about*.

[4] Is there any stuff happening in physical space /spacetime according to ordinary QFT?

[5] My own personal view is that the whole idea of "non-separability" is just a confused way of saying that a theory involves what Bell called non-local beables. In a theory of exclusively local beables (a "TELB" as I dubbed this in a recent paper) you couldn't *possibly* have "non-separability". "[Non]-separabiliity" really just comes down to [a] state description which says there are definite relations between "things at separate places" even though neither thing has definite values for the relata. But without fail, the assertion that this is happening is based on taking the quantum state (a nonlocal beable if it is a beable at all) as the description. But notice that it's tacitly assumed that this quantum state is some kind of description of "things at separate places". My view is that people talking this way typically are not at all entitled to this assumption. If the only thing in the theory is some crazy wf on some crazy abstract configuration space, what in the world makes you think there are "two particles, at different locations" (or whatever) in the picture at all? [...]If the ontology is really just the wf (no local beables) then there is no "non-separability" -- the state is perfectly local and separable in its proper space, the configuration space.

[1] Well Wallace argues that the Everett interpretation is "really just quantum mechanics itself understood in a conventionally realist fashion." But what does this mean? The main insight here is that to suppose that the linearity of quantum mechanics commits us to macroscopic objects being in superpositions, in indefinite states, is false. How? He offers an analogy - In electromagnetism, a certain conguration of the field - say, F1(x; t) (here F is the electromagnetic 2-form) might represent a pulse of ultraviolet light zipping between Earth and the Moon. Another conguration, say F2(x; t), might represent a dierent pulse of ultraviolet light zipping between Venus and Mars. What then of the state of affairs represented by:

F(x; t) = 0:5F₁(x; t) + 0:5F₂(x; t)?

Must it not represent a pulse of ultraviolet light that is in a superposition of traveling between Earth and Moon, and of traveling between Mars and Venus?Of course, this is nonsense. There is a perfectly prosaic description of F: it does not describe a single ultraviolet pulse in a weird superposition, it just describes two pulses, in different places. And this, in a nutshell, is what the Everett interpretation claims about macroscopic quantum superpositions: they are just states of the world in which more than one macroscopically denite thing is happening at once. Macroscopic superpositions do not describe indeniteness, they describe multiplicity. I think this is the main insight, as to what is physically real - the answer is sought in decoherent tales of emergence...

[2] Good point, I often think about this in the context of QG.

[3] Yes, this is all interpretation-dependent.

[4] As you suggest, very difficult to say in 'standard' QFT (whatever that is). If you think quantum theory qua spacetime theory is a way to go, I like Baez' category-theoretic approach to cobordisms. I won't bore you with the details as this is way beyond the focus of our discussion.

[5] Very interesting, I'd love to download your paper and check it out, which depository? As to the bit I emboldened, I've hinted at my own view in my presentation of Wallace's (basically I agree with him, but am unsatisfied with the lacuna in the 'emergence' picture, and I think this does relate to incomplete physical theory, not solely nice philosophy).

Further thought: the ordinary separability you suggest might tacitly rest on the assumption that configuration space is e.g. an 3N space exactly analogous to 3 space, does this follow?

 

[malreux]

Ah yes, found it, guess its http://arxiv.org/abs/0909.4553

I'll read it this eve, thanks!

 

[ttn]

Ah yes, found it, guess its http://arxiv.org/abs/0909.4553

I'll read it this eve, thanks!

Yes, that's the paper with the "TELB" idea. But note: it has nothing to do with the "separability" stuff that led me to mention it!

 

[ttn]

[1] Well Wallace argues that the Everett interpretation is "really just quantum mechanics itself understood in a conventionally realist fashion."

That's either obviously false, or obvious propaganda. It's of course controversial what exactly "just quantum mechanics itself" should mean, but everybody knows the standard textbook formulations include axioms about measurement that MWI wants to get rid of. That's of course to its credit. The point is, one should really think of MWI as an attempt to get rid of the "measurement problem" that plagues "quantum mechanics itself".

But what does this mean? The main insight here is that to suppose that the linearity of quantum mechanics commits us to macroscopic objects being in superpositions, in indefinite states, is false. How? He offers an analogy - In electromagnetism, a certain conguration of the field - say, F1(x; t) (here F is the electromagnetic 2-form) might represent a pulse of ultraviolet light zipping between Earth and the Moon. Another conguration, say F2(x; t), might represent a dierent pulse of ultraviolet light zipping between Venus and Mars. What then of the state of affairs represented by:

F(x; t) = 0:5F₁(x; t) + 0:5F₂(x; t)?

Must it not represent a pulse of ultraviolet light that is in a superposition of traveling between Earth and Moon, and of traveling between Mars and Venus?Of course, this is nonsense. There is a perfectly prosaic description of F: it does not describe a single ultraviolet pulse in a weird superposition, it just describes two pulses, in different places. And this, in a nutshell, is what the Everett interpretation claims about macroscopic quantum superpositions: they are just states of the world in which more than one macroscopically denite thing is happening at once. Macroscopic superpositions do not describe indeniteness, they describe multiplicity. I think this is the main insight, as to what is physically real - the answer is sought in decoherent tales of emergence...

It's a nice argument. But unfortunately I get off board right at the beginning. (Here I am in total agreement with at least Maudlin and Goldstein.) In the example with the electromagnetic waves, the argument works great, because each of the superposed terms genuinely describes / corresponds to "a pulse of ultraviolet light". On the quantum/MWI side of the analogy though, I do not accept that the kind of thing that is ordinarily called "a single branch of the universal wf" -- I mean supposing that this "one branch" were the whole wave function, i.e., supposing the universal wf has just one branch -- corresponds in any obvious way to "a world". You see, the problem is that even a universal wf with "one branch" is still what... some field with support only in some small region of a huge configuration space. This looks nothing like a world full of galaxies and planets and people and trees and cats and whatnot. (Sure, the quantum state is some approximate eigenstate of various operators like "there's a galaxy over there", "there's a cat-shaped lump over here", etc... But that is *not the same thing at all*! Note that in ordinary QM, where most of us develop our intuitions about when quantum states possesses definite properties and what this means, the *meaning* is always cashed out in terms of some classical/macro apparatus that somehow registers the result of an experiment. So it is totally unwarranted to extend this intuition to MWI, whose whole point is to *deny* that there is a distinct non-quantum macro/classical posited world.)

So I don't buy this kind of argument at all. If it were true that each "branch" of the universal wave function somehow corresponded to some definite sensible bit of ontology in 3 space, then I would be with the argument all the way. But it doesn't. So the MWI people I think need to explain either how they get local beables out of the wf, or they need to posit some local beables distinct from the wf. Then maybe an argument like that could fly.

Further thought: the ordinary separability you suggest might tacitly rest on the assumption that configuration space is e.g. an 3N space exactly analogous to 3 space, does this follow?

I didn't understand what you meant here.

 

[Demystifier]

The question is, which theory is best at explaining what needs to be explained?

The only problem with this is to define what exactly it means to explain something "the best". Obviously, we don't have a function f:E -> R from the set of all explanations E to the set of real numbers R, where the real number can be interpreted as a measure of "quality" of an explanation. So, in the absence of such an objective measure, different physicists use different subjective vague measures of it, which results in different interpretation of QM without a possibility to reach a consensus about which one is "the best".

The only such function that comes to my mind is the inverse number of words used in the explanation. But by this definition, the best explanation would be the shut-up-and-calculate interpretation, and I am sure you wouldn't accept that this interpretation is "really" the best. (Although, for most practical physicists it probably is.)

Or if you can propose another concrete objective measure, I would be REALLY REALLY happy to see your proposal.

Anyway, even without such a measure, I think you and I agree which interpretation is "the best" - the Bohmian one. But perhaps the problem is that we don't agree which is "the second best" or "the third best".

 

[Demystifier]

I don't really understand your reasons for liking it, that it provides a simple mechanism for effective wave-function collapse. That to me seems way too bound up with ideas from orthodox QM.

For many purposes, orthodox QM is not so bad at all. Of course, I am not satisfied with it and I want more, but it doesn't necessarily mean that a better theory should not borrow some ideas from orthodox QM. In fact, being strictly against orthodox QM is an orthodoxy itself, so by not being strictly against orthodox QM I am perhaps less orthodox than you.

which theory does the best job, by the normal standards of judging scientific theories, of accounting for all the facts (by which I mean to include both pre-scientific facts like that there are trees and stuff outside my window, and then also the detailed quantitative results of all the various sophisticated experiments like 2-slit, atomic spectra, Bell, etc. etc. etc.).

There is one related joke I think you might like:
http://abstrusegoose.com/276

 

[Demystifier]

Yes, sure, relativity is already present in the formalism of QFT... But there are also some relevant things sorely lacking in standard formulations of QFT, e.g., clarity about what the heck it's *about*. This matters hugely, especially for discussions of locality/nonlocality, where the very concept denotes some feature of stuff happening in physical space / spacetime. Is there any stuff happening in physical space /spacetime according to ordinary QFT? Beats me. And I find this at least rather worrisome from the point of view of saying that ordinary QFT "is relativistic".

On that issue, I would like to note that, in my view, ordinary QFT is not "relativistic enough", so in
http://xxx.lanl.gov/abs/0904.2287
I attempt to make it "more relativistic" than it is in the usual formulation.

 

[ttn]

The only problem with this is to define what exactly it means to explain something "the best". Obviously, we don't have a function f:E -> R from the set of all explanations E to the set of real numbers R, where the real number can be interpreted as a measure of "quality" of an explanation. So, in the absence of such an objective measure, different physicists use different subjective vague measures of it, which results in different interpretation of QM without a possibility to reach a consensus about which one is "the best".

Yes, I agree, it's hard and controversial to measure. But I still think it's best to keep one's eyes on the real goal and not get too sidetracked by the goal of fixing what's wrong with the theory one learned in school. That last attitude tends to make one focus on the wrong things and head off in wrong directions.

Re: the cartoon you shared, that's great. I do like it very much! Indeed, it captures very well a big part of my objection to MWI and other such theories. It's really ridiculous for us to conclude -- after long thought based exclusively on evidence from the senses -- that actually everything the senses give us is some kind of delusion. It's like the ultimate circular argument. So one of my fundamental priorities in trying to understand QM is to avoid doing this. That's why the ability to recover something that genuinely looks like the ordinary world of ordinary perception is so important to me, and why I am very dismissive of "solipsist" type ideas.

 

[Demystifier]

Re: the cartoon you shared, that's great. I do like it very much! Indeed, it captures very well a big part of my objection to MWI and other such theories.

I'm glad to hear that.

It's really ridiculous for us to conclude -- after long thought based exclusively on evidence from the senses -- that actually everything the senses give us is some kind of delusion. It's like the ultimate circular argument. So one of my fundamental priorities in trying to understand QM is to avoid doing this. That's why the ability to recover something that genuinely looks like the ordinary world of ordinary perception is so important to me, and why I am very dismissive of "solipsist" type ideas.

Yes, I can understand it very well, because most of the time (spent on doing science) I think the same way. But still, I find it important, amusing and intellectually challenging to try the other ways of thinking as well. If some scientists may be religious part of their time, then also a Bohmian may be a slightly Bohrian part of the time.
It's better to be Bohred than to be bored.

 

[ttn]

By the way, I wonder if mattt is still reading? Mattt, I'm still really interested in hearing your thoughts on Bell's formulation of "local causality". It seemed like you were skeptical at first, then you read my paper and bought into it completely, but then went back to skepticism. I'm really anxious to hear what caused that last transition!

 

[malreux]

[1]That's either obviously false, or obvious propaganda.

[2] The point is, one should really think of MWI as an attempt to get rid of the "measurement problem" that plagues "quantum mechanics itself".

[3] On the quantum/MWI side of the analogy though, I do not accept that the kind of thing that is ordinarily called "a single branch of the universal wf" -- I mean supposing that this "one branch" were the whole wave function, i.e., supposing the universal wf has just one branch -- corresponds in any obvious way to "a world".

[4] Note that in ordinary QM [...] the *meaning* is always cashed out in terms of some classical/macro apparatus that somehow registers the result of an experiment.

[5] So I don't buy this kind of argument at all. If it were true that each "branch" of the universal wave function somehow corresponded to some definite sensible bit of ontology in 3 space, then I would be with the argument all the way.

[6] I didn't understand what you meant here.

[1] Lol! I'm sorry, I was being deliberately controversial here, and being unfair to you (in terms of the level of debate, i.e. me reducing it to a slanging match) and Wallace (he actually carefully presents his views, albeit this is a direct quote).

[2] Sure!

[3] I agree this isn't obvious, if what you want is either an exact MWI, or even an aprox decoherent MWI. This is where I depart from proponents like Wallace, I interpret Everett in a way closer to e.g. Barrett.

[4] Agreed. However this presentation could go wrong in a way similar to how the Verification Principle goes wrong, by referring to semantics when what we want to know is what the world is like. I know the previous sentence is vague, I just don't want to go down this route. I'll interpret your 'meaning' as 'referring' if you don't mind.

[5] By the principle of charity, I would choose to believe MWI proponents aren't arguing this as is, since most don't seem bothered by problems like branch count and so forth. Clearly their urging something aprox, emergent, decoherent, fill-in-blank.

[6] Something involved that's only going to take us further away from the topic of this thread.

Talking of which: I feel we could have a really interesting discussion about interpretations of QM, or 'QM's'. However, I feel like I've steadily drawn you further and further away from the topic of this thread. Sorry about that! I mean, obviously Bell's Theorem is enmeshed with such issues, but I feel like I want to debate the merits and other re Bohm v Everett and perhaps that's not actually conducive to the topic. So I'll cease fire, for now.

 

[ttn]

[3] I agree this isn't obvious, if what you want is either an exact MWI, or even an aprox decoherent MWI. This is where I depart from proponents like Wallace, I interpret Everett in a way closer to e.g. Barrett.

I'm not sure you understood the worry I have in mind. It really has nothing to do with how exactly you'd "carve" the big wf into "branches". There are undoubtedly difficult questions for MWI there, too, but that's not at all what I meant to be expressing worry about. Let's just imagine (i.e., take for granted) that there was some clear way of defining a "branch" and that we didn't have to worry about different branches overlapping/interfering or anything like that.

Let me try to express the worry this way. Suppose the universe just had a bajillion particles in it, and suppose those bajillion particles clumped together to make a ball. Let's ignore the bajillion-3 *relative* degrees of freedom (just assume those are always in a nice "making a ball" kind of eigenstate) and just focus on the 3 'center of mass' degrees of freedom. The usual worry about MWI goes something like this (I'm trying to relate this back to the example about the two/superposed light rays):

1. If the center-of-mass degrees of freedom are in an (approximate) position eigenstate corresponding to the ball being "here", then the ball is here, and there's no problem.

2. If the center-of-mass degrees of freedom are in an (approximate) position eigenstate corresponding to the ball being "there", then the ball is there, and there's no problem.

3. But in QM, and inevitably according to the unitary evolution, we're going to end up with the state being a non-trivial *superposition* of the state mentioned in 1 and the state mentioned in 2. And then that's really weird, because the ball isn't in either place, or it's in both, or maybe there are two balls in parallel/noninteracting worlds, or whatever.

Now I think you were responding as if my worry was "in the superposition kind of situation mentioned in 3, how can you really say that there are two balls in parallel/noninteracting worlds when really the two superposed terms have tails and maybe they overlap a little bit ..." or something like that. But that isn't the worry at all. The worry is: I don't agree with 1 and I don't agree with 2. That is, if the wave function is the only thing in the game, then I don't see how the (rough) eigenstate mentioned in 1 has *anything to do with* there being a ball at some place. I think the burden is on the MWI people to explain, precisely, what the quantum state mentioned in 1 has to do with there being a ball here (i.e., some kind of lump of matter at a particular place in 3-space). I of course know of various ways you could do some mathematical thing to the wave function and arrive at something that could be interpreted as a mathematical representation of a ball here. But why in the world should I take that particular mathematical thing seriously, as yielding some "real ontological stuff", when there are many other mathematical things I could have done that (I assume??) I'm *not* supposed to interpret as giving me some "real ontological stuff".

I can never quite tell which of the following the MWI answer is supposed to be: (a) It's obvious, you project down from 3N space to 3 space in the obvious way, something like the way the "m" field is computed in GRWm or Sm, and that "m" is the local beables; or (b) no, you're missing the point, there are no local beables at all, instead what we think of as "matter in 3 space" is really just an illusion in the minds that emerge directly from the 3N-space wave function which is the only physical reality. Basically the question comes down to: what the heck are the local beables of MWI? Are there some? Or none? If some, I want to know exactly what they are, and maybe something along the lines of "why those??". Then we can have a fair comparison with other theories like dBB (without making it seem like one is "simpler" really only because half of it was left tacit!). Or if none, if (b), then we should acknowledge how weird and almost solipsist that is even though in some sense this is still a "realist" theory.

Talking of which: I feel we could have a really interesting discussion about interpretations of QM, or 'QM's'. However, I feel like I've steadily drawn you further and further away from the topic of this thread. Sorry about that! I mean, obviously Bell's Theorem is enmeshed with such issues, but I feel like I want to debate the merits and other re Bohm v Everett and perhaps that's not actually conducive to the topic. So I'll cease fire, for now.

Well, nobody's really discussing Bell here anymore, so I have no objection to chatting about other related stuff if you want to. Or email me or something.

 

[lugita15]

Well, nobody's really discussing Bell here anymore, so I have no objection to chatting about other related stuff if you want to. Or email me or something.

I'm still interested in discussing Bell. Although I haven't yet come up with a good counterargument to your "several axes" version of EPR, it still seems to me that counterfactual definiteness is important. Earlier this thread, when I brought it up you said that CFD is either metaphysical and unimportant, or insofar as it is important it is so essential for all scientific theories that it shouldn't be questioned. Yet I think that quantum mechanics does not possesses it; to wit, if you measure the polarization of a photon at 0 degrees, then in QM the question "What would have been the result if you had instead measured the polarization at 45 degrees" has no definite answer. This seems to me to be saying more than just that quantum mechanics is nondeterministic. You can have a nondeterministic theory in which given the present state of the world, you cannot determine the future state of the world, but you CAN determine what would have been the alternate present states of the world if different measurement decisions had been made. In contrast, in quantum mechanics the quantum state right now is not sufficient to tell you what the present quantum state would have been in alternate histories. I think that this is a significant fact, don't you?

 

[ttn]

I'm still interested in discussing Bell. Although I haven't yet come up with a good counterargument to your "several axes" version of EPR, it still seems to me that counterfactual definiteness is important. Earlier this thread, when I brought it up you said that CFD is either metaphysical and unimportant, or insofar as it is important it is so essential for all scientific theories that it shouldn't be questioned.

I don't think I said that latter about CFD. Or at least that's not exactly what I meant. What I think is more like this: you will realize that this whole issue of CFD simply melts away into nothingness (I mean, it becomes clear that there is no issue here at all) if you think of Bell's theorem as a constraint on *what theories say* -- as opposed to trying to think of every last character in the math as somehow referring directly to some real experimental outcome.

Yet I think that quantum mechanics does not possesses it; to wit, if you measure the polarization of a photon at 0 degrees, then in QM the question "What would have been the result if you had instead measured the polarization at 45 degrees" has no definite answer.

But this question does have a definite answer: "If you had instead measured at 45 degrees, what would the possible results have been, and what are their probabilities?" That is, the reason QM gives no definite answer to your question is only that QM is not deterministic. But that certainly doesn't matter. You can derive the Bell inequality just fine, from locality, without invoking determinism.

Of course, you might (as many people have) look at some derivation of the Bell inequality in some textbook and see that it seems to *start with* -- to *presume* -- pre-existing (deterministic) answers/outcomes to all these different possible questions/measurements. But that's just because many commentators and textbook authors confuse (what we call in the article) "Bell's inequality theorem" for the full "Bell's theorem". The full "Bell's theorem" starts just with the assumption of locality and *derives* the pre-existing (deterministic) answers/outcomes, using basically the EPR argument. So really the whole thing leading to this red herring about CFD is simply missing this, failing to realize that "Bell's inequality theorem" and "Bell's theorem" are not the same thing. Put it this way: it's true that QM is not the type of theory that is assumed in standard derivations of "Bell's inequality theorem". But this is of no real relevance whatsoever. Actually what is shows is just this: QM is not a local theory! (Because, if it were, it would have to explain the perfect correlations with pre-existing values, the way the EPR argument proves any local theory must.)

This seems to me to be saying more than just that quantum mechanics is nondeterministic.

I don't agree. It is no more than that. But the real issue is the EPR half of the argument.

You can have a nondeterministic theory in which given the present state of the world, you cannot determine the future state of the world, but you CAN determine what would have been the alternate present states of the world if different measurement decisions had been made.

I don't think so, but who cares. The real point is this: you cannot have a non-deterministic theory that explains the perfect correlations in a local way.

In contrast, in quantum mechanics the quantum state right now is not sufficient to tell you what the present quantum state would have been in alternate histories. I think that this is a significant fact, don't you?

Nope. Except, as I explained above, insofar as it's just an obscure way of confessing that QM is nonlocal. Which of course means that it is hardly some kind of counterexample to Bell's claim that nonlocality is required to generate the QM predictions.

 

[mattt]

Travis, I am having a terrible sinusitis case, but as soon as I recover, I'll try to explain my thoughts about the relation between "The Factorizability Condition (4) in the CHSH-Theorem", a "Fundamental Stochastic Theory that pretends to predict (correctly) the outcomes of that type of experiments", and "the Causal Structure of Special Relativity".

I say again that the CHSH-Theorem is a mathematical statement with a correct mathematical proof.

The only issue for me is that at first I thought that a hypothetical fundamental stochastic theory that does not satisfy "your factorizability condition (4)" would not be necessarily in conflict with the idea of "Causal Structure" of Special Relativity. Then (after reading a very good paper of yours) I changed my mind and agreed with you, but after a second reading of that same paper I kind of started to doubt again but then I got ill, so as soon as I recover the energy I'll try to explain my thoughts about that issue.

 

[ttn]

Travis, I am having a terrible sinusitis case, but as soon as I recover, I'll try to explain my thoughts about the relation between "The Factorizability Condition (4) in the CHSH-Theorem", a "Fundamental Stochastic Theory that pretends to predict (correctly) the outcomes of that type of experiments", and "the Causal Structure of Special Relativity".

I say again that the CHSH-Theorem is a mathematical statement with a correct mathematical proof.

The only issue for me is that at first I thought that a hypothetical fundamental stochastic theory that does not satisfy "your factorizability condition (4)" would not be necessarily in conflict with the idea of "Causal Structure" of Special Relativity. Then (after reading a very good paper of yours) I changed my mind and agreed with you, but after a second reading of that same paper I kind of started to doubt again but then I got ill, so as soon as I recover the energy I'll try to explain my thoughts about that issue.

Sounds good. There's no hurry. Hope you feel better soon, and I'll look forward to discussing it a little more when you do.

 

[billschnieder]

Earlier this thread, when I brought it up you said that CFD is either metaphysical and unimportant, or insofar as it is important it is so essential for all scientific theories that it shouldn't be questioned. Yet I think that quantum mechanics does not possesses it; to wit, if you measure the polarization of a photon at 0 degrees, then in QM the question "What would have been the result if you had instead measured the polarization at 45 degrees" has no definite answer.

I believe ttn is wrong, that there is no CFD involved but I think you are also misunderstanding how CFD comes in. Take for example the CHSH inequality from ttn's article. Forget for a moment about how it is derived and just focus for the moment only on the terms within the inequality and their meanings:

|C(a,b)−C(a,c)|+|C(a′,b)+C(a′,c)|≤ 2

Now, consider that you have measured along (a,b) and you now have C(a,b) as factual. The remaining terms are therefore necessarily counter-factual. This therefore begs the question, is it possible to test such an inequality experimentally when measuring one term necessarily makes measurement of the other terms impossible?

ttn tries to argue that you can still test it experimentally by assuming so-called "no-conspiracy", which is an affirmative defense which effectively says: "the remaining terms are indeed counterfactual but we can substitute factual measured correlations in their place because what is measured can only be different if there is conspiracy". Now this is a strange argument which can be rephrased as follows:

"if local causality is true, factual outcomes and counterfactual predictions can only differ if conspiracy is involved"

Assuming for the moment that this argument is true, it means if you start by using ONLY factual terms you should end up with the same inequality as if you start by assuming counterfactual terms. However, Starting with factual terms ONLY we end up with an inequality:

|C1(a,b)−C2(a,c)|+|C3(a′,b)+C4(a′,c)|≤ 4

Which is different from the one with counterfactual terms. Therefore the only argument which allows ttn to avoid the counterfactual problem, leads to a contradiction and we must reject his defense.

 

[billschnieder]

Another criticism which has not been addressed is the one concerning the locality assumption. Note that "Locality" and "local causality" mean the same thing in the context of this discussion, because locality simply means there is no causal connection between two remote events A and B that can propagate faster than the velocity of light. Therefore the locality requirement is the same as a requirement for "no causality" between the two remote events and non-locality means there IS a causal connection between the two.

ttn says P(AB|X) = P(A|BX)P(B|X) = P(A|X)P(B|X) because according to him, the lack of a causal connection between A and B implies that P(A|BX) = P(A|X). Ttn's argument then is effectively:

~C(L) -> I and ~I -> C(~L). L=Locality, C=causality, I=Independence.

A single counter example of a case in which lack of causality (~C,L) does not imply independence (I), or lack of independence (~I) does not imply causality (C, ~L) is sufficient to demolish the argument. For that purpose, I will repeat the Bernouli's urn example:

X = Our urn contains N balls, M of them are red, the remaining (N-M) white. They are drawn out blindfolded without replacement."
Ri = Red on the i'th draw, i = 1, 2, ..."

P(R1|X) = M/N

Now if we know that red was found on the first draw, then that changes the contents of the urn for the second:

P(R2|R1, X) = (M - 1)/(N - 1) ≠ P(R2|X) = M/N

and this conditional probability expresses the causal influence of the first draw on the second. But suppose we are told only that red was drawn on the second draw; what is now our probability for red on the first draw? If ttn is being consistent he would say:

P(R1|R2, X) = P(R1|X) = M/N

because whatever happens on the second draw cannot exert any physical influence on the condition of the urn at the first draw (ie C -> ~I). But this result is wrong! The correct answer should be

P(R1,R2, X) = P(R2 |R1, X)

To see this consider the case in which we have only 1 red ball (M = 1); if we know that the one red ball was taken in the second draw, then it is certain that it could not have been taken in the first.

Therefore P(R1|X) = 1/N ≠ P(R1|R2,X) = 0.

So we have a case in which there is no causality (~C) and there is no independence (~I) and the proof fails. So far ttn's only response to this argument has been to ask us to provide a better way of representing local causality, which is a tacit admission that the locality causality condition is fatally flawed.

 

[ttn]

I believe ttn is wrong, that there is no CFD involved but I think you are also misunderstanding how CFD comes in. Take for example the CHSH inequality from ttn's article. Forget for a moment about how it is derived and just focus for the moment only on the terms within the inequality and their meanings:

|C(a,b)−C(a,c)|+|C(a′,b)+C(a′,c)|≤ 2

Now, consider that you have measured along (a,b) and you now have C(a,b) as factual.

C(a,b) is a correlation coefficient. It is the product of the outcomes *averaged over many runs*. So it already takes many many runs to measure even just this one individual term.

The remaining terms are therefore necessarily counter-factual.

Each term is an average (of outcome products) over many many runs. All the runs are "factual" in the sense that they all really happened.

This therefore begs the question, is it possible to test such an inequality experimentally when measuring one term necessarily makes measurement of the other terms impossible?

What's true is that each individual "run" (particle pair) contributes data to one and only one of the four terms. That is, you can only measure along one of (a,b), (a',b), etc., at a time. This hardly makes measurement of the other terms impossible. It just means you need to make lots and lots of runs and take averages. But you already have to do that even to measure just one of the terms!

ttn tries to argue that you can still test it experimentally by assuming so-called "no-conspiracy", which is an affirmative defense which effectively says: "the remaining terms are indeed counterfactual but we can substitute factual measured correlations in their place because what is measured can only be different if there is conspiracy". Now this is a strange argument which can be rephrased as follows:

"if local causality is true, factual outcomes and counterfactual predictions can only differ if conspiracy is involved"

Anybody who wants to understand the actual argument should see the scholarpedia article.

 

[ttn]

ttn says P(AB|X) = P(A|BX)P(B|X) = P(A|X)P(B|X) because according to him, the lack of a causal connection between A and B implies that P(A|BX) = P(A|X).

Here I get no credit at all. I'm just following Bell. And this explanation of the factorization condition is inadequate. It makes sense as a necessary condition of locality only if certain assumptions are made about X. Interested people should see my recent AmJPhys paper on "JS Bell's Concept of Local Causality" for a detailed presentation.

Ttn's argument then is effectively:

~C(L) -> I and ~I -> C(~L). L=Locality, C=causality, I=Independence.

A single counter example of a case in which lack of causality (~C,L) does not imply independence (I), or lack of independence (~I) does not imply causality (C, ~L) is sufficient to demolish the argument. For that purpose, I will repeat the Bernouli's urn example:

X = Our urn contains N balls, M of them are red, the remaining (N-M) white. They are drawn out blindfolded without replacement."
Ri = Red on the i'th draw, i = 1, 2, ..."

P(R1|X) = M/N

Now if we know that red was found on the first draw, then that changes the contents of the urn for the second:

P(R2|R1, X) = (M - 1)/(N - 1) ≠ P(R2|X) = M/N

and this conditional probability expresses the causal influence of the first draw on the second. But suppose we are told only that red was drawn on the second draw; what is now our probability for red on the first draw? If ttn is being consistent he would say:

P(R1|R2, X) = P(R1|X) = M/N

because whatever happens on the second draw cannot exert any physical influence on the condition of the urn at the first draw (ie C -> ~I). But this result is wrong! The correct answer should be

P(R1,R2, X) = P(R2 |R1, X)

To see this consider the case in which we have only 1 red ball (M = 1); if we know that the one red ball was taken in the second draw, then it is certain that it could not have been taken in the first.

Therefore P(R1|X) = 1/N ≠ P(R1|R2,X) = 0.

So we have a case in which there is no causality (~C) and there is no independence (~I) and the proof fails. So far ttn's only response to this argument has been to ask us to provide a better way of representing local causality, which is a tacit admission that the locality causality condition is fatally flawed.

No, Bill, my response to this argument is that you need to do some homework, because you simply have not understood Bell's formulation of locality. You *think* that Bell is saying "any time the probability for one thing depends on another thing, that means the other thing causally influences the one thing". And then you think you can refute Bell by this kind of example where there is a probabilistic/statistical dependence of this sort, but no causal dependence.

But the truth is that you are just *wrong* about what Bell says. Bell is light years ahead of you. Read what he writes about Lille and Lyon, about the cooking of the egg and the ringing of the alarm, and many other examples like this where he goes into great, explicit, careful detail about the need to *distinguish* causality from mere correlation. Read what he writes about how he actually formulates locality and try to appreciate how it is a response to this need, i.e., how the locality conditions is violated *only* when there is genuine nonlocal causation and *not* when there is "mere statistical dependence". Sound impossible? Sound too good to be true? Go and do your homework and find out for sure, and I'll be happy to discuss it after you make it clear somehow that you actually understand what Bell said. So far all of your objections are of the straw man variety.

 

[lugita15]

I don't think I said that latter about CFD. Or at least that's not exactly what I meant.

OK, you had said this earlier, but maybe I misinterpreted it:

"We just have to remember that we are talking about *theories* -- and a theory, by definition, is something that tells you what will happen *if you do such-and-such*. *All* of the predictions of a theory are in that sense hypothetical / counterfactual. Put it this way: the theory doesn't know and certainly doesn't care about what experiment you do in fact actually perform. It just tells you what will happen if you do such-and-such.

So back to your #2 above, of course it makes sense to ask what would have happened if you had turned the polarizers some other way. It makes just as much sense (after the fact, after you actually turned them one way) as it did before you did any experiment at all. How could the theory possibly care whether you've already done the experiment or not, and if so, which one you did? It doesn't care. It just tells you what happens in a given situation. QM works this way, and so does every other theory. So there really is no such thing as option #2."

I thought you meant that insofar as counterfactual definiteness is a necessary assumption for Bell's theorem, it is a trivial feature of all scientific theories.

What I think is more like this: you will realize that this whole issue of CFD simply melts away into nothingness (I mean, it becomes clear that there is no issue here at all) if you think of Bell's theorem as a constraint on *what theories say* -- as opposed to trying to think of every last character in the math as somehow referring directly to some real experimental outcome.

I'm not sure what you're talking about here. I certainly agree that there are some parts of most if not all theories that do not directly relate to experiments. Quantum mechanics contains plenty of that: Hilbert space theory and spectral theory and representation theory, oh my! But what does that have to do with counterfactual definiteness?

But this question does have a definite answer: "If you had instead measured at 45 degrees, what would the possible results have been, and what are their probabilities?" That is, the reason QM gives no definite answer to your question is only that QM is not deterministic.

I agree that in the case of quantum mechanics, counterfactual definiteness is closely related to "future definiteness" AKA determinism. But I think that these two notions should still be logically distinguished from each other.

But that certainly doesn't matter. You can derive the Bell inequality just fine, from locality, without invoking determinism.

I agree that there are local probabilistic theories for which you can derive a Bell inequality. But it is not so clear to me that you can derive a Bell inequality from a local theory, deterministic or not, which does not have counterfactual definiteness.

Of course, you might (as many people have) look at some derivation of the Bell inequality in some textbook and see that it seems to *start with* -- to *presume* -- pre-existing (deterministic) answers/outcomes to all these different possible questions/measurements. But that's just because many commentators and textbook authors confuse (what we call in the article) "Bell's inequality theorem" for the full "Bell's theorem". The full "Bell's theorem" starts just with the assumption of locality and *derives* the pre-existing (deterministic) answers/outcomes, using basically the EPR argument. So really the whole thing leading to this red herring about CFD is simply missing this, failing to realize that "Bell's inequality theorem" and "Bell's theorem" are not the same thing.

I think I do recognize two-step nature of Bell's proof:

1. EPR, in which hidden variables is a conclusion, not an assumption of the argument
2. "Bell's inequality theorem" in which the hidden variables conclusion of EPR is used as an assumption in order to derive the Bell inequality

I think that the basic structure of the argument is valid (although I am curious about Demystifier's contention that the hidden variables conclusion of EPR cannot be quite the same as the hidden variables assumption of the inequality theorem). The only place where I think we differ on this is that you don't think counterfactual definiteness needs to be an assumption of EPR.

Put it this way: it's true that QM is not the type of theory that is assumed in standard derivations of "Bell's inequality theorem". But this is of no real relevance whatsoever. Actually what is shows is just this: QM is not a local theory! (Because, if it were, it would have to explain the perfect correlations with pre-existing values, the way the EPR argument proves any local theory must.)

I pretty much agree with you the QM is nonlocal, only because of wavefunction collapse (although I think DrChinese has some arguments to the effect that QM has "quantum nonlocality" but not "regular" nonlocality). And I also think that it would be pretty hard to come up with an explanation of perfect correlations that did not invoke either nonlocality or conspiracy. But I think it may not quite be logically impossible.

Your "several axes" version of EPR seems to avoid counterfactual definiteness, but I'm not completely convinced that there isn't a leap of logic somewhere, even though I haven't come up with a definitive counterargument yet. You're basically saying that anyone who denies the following statement (and rejects nonlocality) must be a superdeterminist: "If you WOULD have been able to predict with certainty the result of the 0-degree polarization measurement of the distant photon if you HAD performed a 0-degree polarization measurement of your photon, then there IS a pre-existing element of reality corresponding to the 0-degree polarization, even if you do not actually carry out a 0-degree polarization measurement." I think that someone could reject this statement and also reject superdeterminism, but I'm still trying to show how this could be possible.

 

[billschnieder]

C(a,b) is a correlation coefficient. It is the product of the outcomes *averaged over many runs*. So it already takes many many runs to measure even just this one individual term.

You mean averaged over many photon pairs. In my vocabulary, angle pair(a,b) is one run, in which many photon pairs are measured, I understand that in your vocabulary one "run" corresponds to one photon pair. This is a non-issue as far as my point is concerned.

All the runs are "factual" in the sense that they all really happened.

They are factual in the experiment but not in the inequalities. Nothing in the inequality happened. The series of particles you measure to be able to average and obtain C(a,b) can not be restored to measure C(b,c) therefore C(b,c) is counterfactual as soon as C(a,b) is measured. Your argument is that it doesn't matter because a different series of particles can be used to measure C(b,c). This is what I debunked in post #125. With a different series of particles, you have many more degrees of freedom (64 vs the original 16) and the resulting inequality is different.

What's true is that each individual "run" (particle pair) contributes data to one and only one of the four terms. That is, you can only measure along one of (a,b), (a',b), etc., at a time. This hardly makes measurement of the other terms impossible. It just means you need to make lots and lots of runs and take averages. But you already have to do that even to measure just one of the terms!

Obviously you have a different meaning what a "run" is which leads you to misunderstand my point.

 

[billschnieder]

Here I get no credit at all. I'm just following Bell. And this explanation of the factorization condition is inadequate. It makes sense as a necessary condition of locality only if certain assumptions are made about X. Interested people should see my recent AmJPhys paper on "JS Bell's Concept of Local Causality" for a detailed presentation. No, Bill, my response to this argument is that you need to do some homework, because you simply have not understood Bell's formulation of locality. You *think* that Bell is saying "any time the probability for one thing depends on another thing, that means the other thing causally influences the one thing". And then you think you can refute Bell by this kind of example where there is a probabilistic/statistical dependence of this sort, but no causal dependence.

But the truth is that you are just *wrong* about what Bell says. Bell is light years ahead of you. Read what he writes about Lille and Lyon, about the cooking of the egg and the ringing of the alarm, and many other examples like this where he goes into great, explicit, careful detail about the need to *distinguish* causality from mere correlation. Read what he writes about how he actually formulates locality and try to appreciate how it is a response to this need, i.e., how the locality conditions is violated *only* when there is genuine nonlocal causation and *not* when there is "mere statistical dependence". Sound impossible? Sound too good to be true? Go and do your homework and find out for sure, and I'll be happy to discuss it after you make it clear somehow that you actually understand what Bell said. So far all of your objections are of the straw man variety.

I'm responding to your argument in your article which is flawed. You keep repeating that I'm wrong and yet you do not refute the argument in any way.

 

[lugita15]

I'm responding to your argument in your article which is flawed. You keep repeating that I'm wrong and yet you do not refute the argument in any way.

I think he does claim to have refuted it, in his paper "JS Bell's Concept of Local Causality".

 

[billschnieder]

I think he does claim to have refuted it, in his paper "JS Bell's Concept of Local Causality".

For example let us look at his equation (1) in the article "J.S. Bell's Concept of Local Causality" which according to him lays out mathematically what Bell's means by "local causality"

P(b_1 |B_3 , b_2 ) = P (b_1 |B_3 )

What then does

P(b_1 |B_3 , b_2 ) \neq P (b_1 |B_3 )

imply? Non-local causality?

 

[billschnieder]

Oh and another misunderstanding: "stochastic" and "complete specification" are incompatible despite ttn's claims. He admits on page 10 that:

Of course, if one insists that any stochastic theory is ipso facto a stand-in for some (perhaps unknown) under-lying deterministic theory (with the probabilities in the stochastic theory thus resulting not from indeterminism in nature, but from our ignorance), Bell’s locality concept would cease to work.

Even if we were to accept that it is possible to have a complete specification and still only have a stochastic theory, he would be admitting that Bell's locality concept is invalid for deterministic hidden variable theories.

 

[billschnieder]

Another falsehood in the "JS Bell's Concept of Local Causality" paper.

ttn says:

Bell is not asking us to accept that any particular theory (stochastic or otherwise) is true; he’s just asking us to accept his definition of what it would mean for a stochastic theory to respect relativity’s prohibition on superluminal causation. And this requires us to accept, at least in principle, that there could be such a thing as a genuinely,irreducibly stochastic theory, and that the way “causality” appears in such a theory is that certain beables do,and others do not, influence the probabilities for specific events.

This is clearly a misrepresentation of Bell

Since we can predict in advance the result of measuring any chosen component of σ2, by previously measuring the same component of σ1, it follows that the result of any such measurement must actually be predetermined. Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state.

Let this more complete specification be effected by means of parameters λ.

...

So in this simple case there is no difficulty in the view that the result of every measurement is determined by the value of an extra variable and the statistical features of quantum mechanics arise because the value of this variable is unknown in individual instances.

Remember that this is directly relevant to EPR because they were discussing "completeness" and "prediction with certainty". It is impossible to predict with certainty the outcome of a measurement in a stochastic theory. Bell clearly understands that "incomplete" and "statistical"/stochastic/probabilistic are synonymous. Einstein understood that too.

 

[ttn]

I thought you meant that insofar as counterfactual definiteness is a necessary assumption for Bell's theorem, it is a trivial feature of all scientific theories.

The point is that it's not a necessary assumption at all. The "assumption" that you actually need is instead completely trivial: a theory predicts what will happen in some situation.

I agree that there are local probabilistic theories for which you can derive a Bell inequality. But it is not so clear to me that you can derive a Bell inequality from a local theory, deterministic or not, which does not have counterfactual definiteness.

I don't even think it makes sense to talk about being able to derive a Bell inequality for/from some particular theory. Bell's theorem is the derivation of the inequality from certain (mathematically formulated) physical principles (e.g. "locality" and "no conspiracies"). And the point here is that "counterfactual definiteness" is not among the principles needed to derive the inequality.

I think I do recognize two-step nature of Bell's proof:

1. EPR, in which hidden variables is a conclusion, not an assumption of the argument
2. "Bell's inequality theorem" in which the hidden variables conclusion of EPR is used as an assumption in order to derive the Bell inequality

I think that the basic structure of the argument is valid (although I am curious about Demystifier's contention that the hidden variables conclusion of EPR cannot be quite the same as the hidden variables assumption of the inequality theorem). The only place where I think we differ on this is that you don't think counterfactual definiteness needs to be an assumption of EPR.

OK.

I pretty much agree with you the QM is nonlocal, only because of wavefunction collapse (although I think DrChinese has some arguments to the effect that QM has "quantum nonlocality" but not "regular" nonlocality).

...where "quantum nonlocality" is defined as "the kind of nonlocality that QM has and which we don't have to worry about because we decided in advance that we weren't going to worry about QM"?

And I also think that it would be pretty hard to come up with an explanation of perfect correlations that did not invoke either nonlocality or conspiracy. But I think it may not quite be logically impossible.

OK, I mean, that's the whole thing right there then. There's a derivation of it, so tell me where you think it's wrong if you think it's wrong. Or maybe it can be an official challenge. I'll gladly give $20 and a kiss on the cheek to anybody who can come up with a way to explain perfect correlations that is both local and non-conspiratorial and which doesn't involve "pre-existing values" or the equivalent.

Your "several axes" version of EPR seems to avoid counterfactual definiteness, but I'm not completely convinced that there isn't a leap of logic somewhere, even though I haven't come up with a definitive counterargument yet. You're basically saying that anyone who denies the following statement (and rejects nonlocality) must be a superdeterminist: "If you WOULD have been able to predict with certainty the result of the 0-degree polarization measurement of the distant photon if you HAD performed a 0-degree polarization measurement of your photon, then there IS a pre-existing element of reality corresponding to the 0-degree polarization, even if you do not actually carry out a 0-degree polarization measurement." I think that someone could reject this statement and also reject superdeterminism, but I'm still trying to show how this could be possible.

What can I say? I will not refuse to listen if/when you show how it's possible. But basically here it sounds like you are conceding that, after scrutinizing the argument, you can't see any flaw and thus think the argument is good... but your feelings haven't quite caught up with your conscious judgment yet. OK, that's cool, sometimes it takes some time to get yourself fully lined up behind a new and surprising conclusion that you realize the evidence compels you to embrace.

 

[ttn]

I think he does claim to have refuted it, in his paper "JS Bell's Concept of Local Causality".

Well, sure, but there's a (shorter) version of this in the scholarpedia article too. But people who have followed this whole (admittedly long) thread know that I've gone far above and beyond in giving Bill the benefit of the doubt, responding to his criticisms and questions, patiently refuting his arguments (over and over again one might say), etc. So forgive me if I don't get into it with him yet again here.

 

[ttn]

For example let us look at his equation (1) in the article "J.S. Bell's Concept of Local Causality" which according to him lays out mathematically what Bell's means by "local causality"

P(b_1 |B_3 , b_2 ) = P (b_1 |B_3 )

What then does

P(b_1 |B_3 , b_2 ) \neq P (b_1 |B_3 )

imply? Non-local causality?

Try reading the nearby words that say clearly what the various symbols *mean*.

 

[ttn]

Bell clearly understands that "incomplete" and "statistical"/stochastic/probabilistic are synonymous. Einstein understood that too.

Hogwash. Bell went out of his way to *avoid* any assumption of determinism, i.e, to formulate everything (in particular the concept of "locality") from the very beginning in a way that embraced the idea of irreducibly stochastic theories (deterministic theories being, in his words, just a special case where the probabilities are delta functions). He did this precisely because early commentators on his theorem already -- erroneously in his view -- said it only applies to deterministic theories. (One still hears, in textbooks and such, statements like "Bell refuted the idea of local determinism.") I explain all of this in my papers (quoting extensively from Bell). Or you could just read Bell. But Bill, contra Bell, simply doesn't know what he's talking about and seems unable to understand what he reads. But I am happy to see he's doing his homework!

 

[billschnieder]

Try reading the nearby words that say clearly what the various symbols *mean*.

This is a very simple question. Why don't you answer what P(b_1 |B_3 , b_2 ) \neq P (b_1 |B_3 ) implies. I'm not asking you to define the symbols. What does it mean for the LHS to be different from the RHS in the above "definition" of local causality.

You say local causality implies P(b_1 |B_3 , b_2 ) = P (b_1 |B_3 ). So I'm simply asking you what P(b_1 |B_3 , b_2 ) \neq P (b_1 |B_3 ) imples? Very simple question.

 

[Gordon Watson]

... I explain all of this in my papers (quoting extensively from Bell). Or you could just read Bell. But Bill, contra Bell, simply doesn't know what he's talking about and seems unable to understand what he reads. But I am happy to see he's doing his homework!

ttn, about a week ago I PMed for a copy of an AmJPhys article (of yours) that you cited. No reply so far received. Any chance? Also, can you link to papers of yours that you cite?

PS: I annotated the Scholarpedia article and will happily do the same on others.

Regards, GW.

 

[billschnieder]

Hogwash. Bell went out of his way to *avoid* any assumption of determinism, i.e, to formulate everything (in particular the concept of "locality") from the very beginning in a way that embraced the idea of irreducibly stochastic theories (deterministic theories being, in his words, just a special case where the probabilities are delta functions). He did this precisely because early commentators on his theorem already -- erroneously in his view -- said it only applies to deterministic theories. (One still hears, in textbooks and such, statements like "Bell refuted the idea of local determinism.") I explain all of this in my papers (quoting extensively from Bell). Or you could just read Bell. But Bill, contra Bell, simply doesn't know what he's talking about and seems unable to understand what he reads. But I am happy to see he's doing his homework!

I just quoted to you Bell's own words which refute what you claim here. Besides in your article you state clearly that Bell's definition of local causality does not work in a local deterministic theory.

 

[ttn]

ttn, about a week ago I PMed for a copy of an AmJPhys article (of yours) that you cited. No reply so far received. Any chance? Also, can you link to papers of yours that you cite?

I never got any PM from you. Maybe you forgot to put a stamp on it? A pre-print of the paper is online here:

http://arxiv.org/abs/0707.0401

 

[ttn]

I just quoted to you Bell's own words which refute what you claim here.

No, they don't. I don't think you understood either what I wrote, or what Bell wrote.

Besides in your article you state clearly that Bell's definition of local causality does not work in a local deterministic theory.

No, I don't say that at all. (See what I meant just above...) I say that if somebody refuses to accept the possibility of an irreducibly stochastic theory -- i.e., if they assume that determinism is true, such that stochasticity already implies incompleteness of the descriptions -- then they will think (erroneously) there is some kind of problem with the formulation. But that's their problem (indeed, your problem, since this seems to be your view!) not Bell's.

As to your other question, about what it means for two probabilities to be different... what kind of answer are you looking for?

 

[ttn]

This is a very simple question. Why don't you answer what P(b_1 |B_3 , b_2 ) \neq P (b_1 |B_3 ) implies. I'm not asking you to define the symbols. What does it mean for the LHS to be different from the RHS in the above "definition" of local causality.

You say local causality implies P(b_1 |B_3 , b_2 ) = P (b_1 |B_3 ). So I'm simply asking you what P(b_1 |B_3 , b_2 ) \neq P (b_1 |B_3 ) imples? Very simple question.

Oh, now I get the question. I thought you were asking what it *meant*, but your just trying to get me to say that P(b_1 |B_3 , b_2 ) \neq P (b_1 |B_3 ) implies non-locality.

Yes, it does. P(b_1 |B_3 , b_2 ) \neq P (b_1 |B_3 ) implies nonlocality.

But you have to read and understand and remember the words -- in particular that B_3 denotes a complete description of the physical state of a certain spacetime region, that b_2 has to live in a certain spacetime region (and can't be just any old extra thing you want to throw in), and that the P's are the fundamental dynamical probabilities assigned by some physical theory (as opposed to the kinds of probabilities that are based on ignorance of various things, etc.). If you actually hold all this in mind, it's trivial to see why all your examples, with the balls in the urns and whatnot, don't show what you think they show. Seriously, you have to actually slow down and read and process Bell's formulation. Let it marinade. (Sorry, I'm watching American Idol in the background.) Understand and appreciate what he's doing. Bell is not a dummy and he didn't formulate "locality" in a way that would diagnose, as nonlocal, trivial cases of correlation-without-causation like the ones you bring up. If you think it's so easy to refute -- if you think Bell is a dummy -- it only shows that you haven't taken the time to understand and appreciate what he accomplished.

Here, I'll put it as a challenge. State clearly, for your balls and urns or whatever example you want, what b_1, b_2, and B_3 are. Convince yourself and me that these satisfy all the conditions Bell laid down. (So, for example, oh, i dunno, B_3 better not turn out to be something like "what somebody who doesn't know the color of the first ball pulled knows about the state of the urn", and b_2 better not turn out to be in the past of b_1 rather than at spacelike separation and also outside the future light cone of region 3.) Then see if you still think there is some counter-example to Bell's formulation here.

 

[billschnieder]

No, they don't. I don't think you understood either what I wrote, or what Bell wrote.

Bell's words are clear as to what he meant, I'm not even interpreting his words, I quote them to you verbatim. You haven't provided any quote to support your claim just a pronouncement without evidence that I'm wrong.

No, I don't say that at all. (See what I meant just above...) I say that if somebody refuses to accept the possibility of an irreducibly stochastic theory -- i.e., if they assume that determinism is true, such that stochasticity already implies incompleteness of the descriptions -- then they will think (erroneously) there is some kind of problem with the formulation. But that's their problem (indeed, your problem, since this seems to be your view!) not Bell's.

Now these are your words which you are now trying to undo:

Of course, if one insists that any stochastic theory is ipso facto a stand-in for some (perhaps unknown) underlying deterministic theory (with the probabilities in the stochastic theory thus resulting not from indeterminism in nature, but from our ignorance), Bell’s locality concept would cease to work.

(1) A *deterministic local hidden variable theory* which attempts to complete QM, is in fact making the *assumption* that the stochastic properties of QM simply arise due to incompleteness of QM, and such incompleteness can be completed by a "more complete specification". Now read Bell's original paper, excepts of which I posted above which clearly state this.
(2) It makes no sense for a *deterministic local hidden variable theory* to allow for the possibility of an irreducable stochastic theory, which is completely contrary to the concept of a *deterministic local hidden variable theory*.

THEREFORE, if you *assume a deterministic local hidden variable theory*, your statement implies that Bell's locality concept would cease to work in the narrow confines of your assumption. Maybe you misspoke in the article but this is clearly the meaning conveyed by the text.

 

[billschnieder]

Yes, it does. P(b_1 |B_3 , b_2 ) \neq P (b_1 |B_3 ) implies nonlocality.

To be more precise then you are saying the above implies non-local causality. What is causing what in the above? Is it your claim that b_1 and b_2 are simultaneous? My next question would be for you to define what you understand by "cause".

But you have to read and understand and remember the words -- in particular that B_3 denotes a complete description of the physical state of a certain spacetime region, that b_2 has to live in a certain spacetime region (and can't be just any old extra thing you want to throw in), and that the P's are the fundamental dynamical probabilities assigned by some physical theory (as opposed to the kinds of probabilities that are based on ignorance of various things, etc.).

Please define what you mean by fundamental dynamical probabilities.

If you actually hold all this in mind, it's trivial to see why all your examples, with the balls in the urns and whatnot, don't show what you think they show.

I do not believe that anyone who understands probability theory can hold all of those things in their mind while being intellectually honest as will soon be evident.

Seriously, you have to actually slow down and read and process Bell's formulation.

I hope you will be patient enough to go through the process with me and we'll see in the end who is right and who has no clue what they are saying. This is my challenge, answer the questions I have given above.

Here, I'll put it as a challenge. ... better not turn out to be something like "what somebody who doesn't know the color of the first ball pulled knows about the state of the urn".

I'm happy you are posting this challenge because now it turns out the issue is about the meaning of probability. So let us start there. I will provide defintion of what probability means, and you will provide yours. then I will provide my definition of "cause" and you will provide yours and then we can discuss who is being consistent and who is not. I'm also happy that you like the urn example because we can use it to illustrate our meanings of probability. Feel free to do so.

So here is my definition of "probability":

a probability is a theoretical construct, which is assigned to represent a state of knowledge, or calculated from other probabilities according to the rules of probability theory. A frequency is a property of the real world, which is measured or estimated.​

And my definition of "cause":

To say "C" (a cause) causes "E" (an effect) means that whenever C occurs, then E follows. Therefore we can not say "C" causes "E" if the two events are simultaneous. Similarly if "E" occurs before "C", then "C" can not be the cause of "E"​

I'll wait for your definitions.

 

[billschnieder]

While waiting for your definitions I thought I should also point out the following mathematical contradictions. NOTE, the following is simply a mathematics exercise, no physics whatever, but it clearly shows the problem Bell proponents are still unable to see:

Consider the CHSH inequality:

|E(a)E(b) - E(a)E(c)| + |E(d)E(b) + E(d)E(c)| ≤ 2, where E(a), E(b), E(c), E(d) ∈ [−1,1]

This inequality is violated IFF

(1) |E(a)E(b) - E(a)E(c)| + |E(d)E(b) + E(d)E(c)| > 2

We are interested to understand the mathematical properties of the 4 terms E(a), E(b), E(c), E(d) when this violation happens

From (1) we have via factorization

(2) |E(a)||E(b) - E(c)| + |E(d)||E(b) + E(c)| > 2

However, since E(a), E(b), E(c), E(d) ∈ [−1,1], it follows that
|E(b) - E(c)| ≤ 2 and |E(b) + E(c)| ≤ 2

Let us consider the different possible extremes of the values for E(b) and E(c).

If E(b) = E(c) then |E(a)||E(b) - E(c)| = 0 and |E(d)||E(b) + E(c)| must be greater than 2 for equation (1) to hold. But we know that |E(b) + E(c)| ≤ 2 which means |E(d)| must be greater than 2 which is impossible given that E(d) ∈ [−1,1].

If E(b) = -E(c) then |E(a)||E(b) + E(c)| = 0 and |E(a)||E(b) - E(c)| must be greater than 2 for equation (1) to hold. But we know that |E(b) - E(c)| ≤ 2 which means |E(a)| must be greater than 2 which is impossible given that E(a) ∈ [−1,1].

Therefore (1) is mathematically impossible. It is not possible mathematically to violate the CHSH inequality even before we start talking about any physics and what the terms might mean in any physical situation. This is the simple fact that Bell proponents are blind to. I challenge anyone to find values for E(a), E(b), E(c), E(d) ∈ [−1,1] that violate the above inequality from any source whatsover using any means whatsoever. You can even assume that E(a) are averages over many runs or whatever you like.

 

[ttn]

To be more precise then you are saying the above implies non-local causality. What is causing what in the above?

I say explicitly in my papers that you can't say, merely from the failure of this condition, what is causing what. You just know that there is some nonlocality somewhere.

Is it your claim that b_1 and b_2 are simultaneous?

No.

My next question would be for you to define what you understand by "cause".

It's increasingly clear with every question that you haven't read or processed what Bell wrote, or what I've written about what he wrote. I'm not going to play your games if you won't do your homework first.

Please define what you mean by fundamental dynamical probabilities.

That's explained in my papers. It is really simple (though I'm sure this won't satisfy you): it means the probabilities that some candidate fundamental theory attributes to an event.

I do not believe that anyone who understands probability theory can hold all of those things in their mind while being intellectually honest as will soon be evident.


I hope you will be patient enough to go through the process with me and we'll see in the end who is right and who has no clue what they are saying. This is my challenge, answer the questions I have given above.

Right, so accuse me of being intellectually dishonest, and then literally in the next sentence ask me to please be patient enough to answer all your questions (the ones you have because you won't read or can't understand things that you've been referred to). No thanks.

(Your def'n of "probability" is inapppropriate in this context, as I've explained. And your definition of "cause" smuggles in the presupposition of determinism, which is a problem for the reasons I've explained.)

Now I give up.

 

[billschnieder]

That's explained in my papers. It is really simple (though I'm sure this won't satisfy you): it means the probabilities that some candidate fundamental theory attributes to an event.

That is an incomplete definition. What does probability mean in that phrase, that was my question. Define probability.

Right, so accuse me of being intellectually dishonest,

No I'm saying *I* will have to be intellectually dishonest to believe all the things you want me to believe at the same time, in other words, that you do not understand probability theory. Prove me wrong by defining the terms I asked.

(Your def'n of "probability" is inapppropriate in this context, as I've explained. And your definition of "cause" smuggles in the presupposition of determinism, which is a problem for the reasons I've explained.)

You don't have to agree with my definitions but I've clearly explained to you what *I* mean when *I* say "cause", and "probability". You haven't provided any alternate definitions of your own which you think are more appropriate.

After your article "Against Realism" in explained that many people arguing about Bell do not know what "realism" means, I would have thought you would understand the importance of clear definitions of terms. Once, you provide your definitions it would become evident that you do not know what you are talking about. All your claims about having explained things clearly in your articles, when you don't even have consistent definitions of terms will become evident.

I'm still waiting for your definitions for "probabilities" and "cause".

 

[ttn]

I'm still waiting for your definitions for "probabilities" and "cause".

Sorry, I'm really done. You'll have to get the answers you seek from my papers, or better, Bell's. ("La Nouvelle Cuisine" is particularly strongly recommended.) It's just frankly no fun talking with you.

 

[billschnieder]

Sorry, I'm really done. You'll have to get the answers you seek from my papers, or better, Bell's. ("La Nouvelle Cuisine" is particularly strongly recommended.) It's just frankly no fun talking with you.

So you are unable to define here what you mean by "probability" and "cause". Now hopefully you can point exactly to somewhere else where they are defined the way you like. Please provide a reference to a book, or article and specify a page number and paragraph where those terms are defined in a way you approve. This is a simple request. Simply saying, "read all my papers" or "read La Nouvelle Cuisine" would not cut it. Provide a specific location where the definition can be found.

Getting to the truth is not always fun if you are on the wrong side. This is not an entertainment exercise.