Scholarpedia article on Bell's Theorem

ThomasT

Well, that's the language associated with the mathematics. But (and my question was a rhetorical one) what any theory is actually about is the prediction of instrumental behavior. Isn't it?

Instrumental behaviors are the fundaments of physical science. Aren't they? Any theory can purport to be about anything that we have no way of ascertaining or verifying sensorily. Isn't direct objective sensory apprehension the basic criterion of empirical science?

Do we have any way of knowing how or if any of the mathematical constructions involved in models of quantum phenomena correspond to an underlying reality that's outside the purview of our senses?

I think you might well be right. The problem is that we have no way of knowing.

I agree. It's a constraint on all possible Bell-LR models of quantum entanglement. And the question remains: what might this have to do with an underlying reality? I'm not saying we can't infer something about a presumed underlying reality from the conceptual content of theories that correctly predict instrumental behavior. But what you're saying is that we can infer something about a presumed underlying reality from the literal content of a theory that doesn't correctly predict instrumental behavior.

Ok, no problem. Nature is either exclusively local or it isn't. A theory assumes exclusive locality, and encodes that assumption in a certain way. The theory is proven wrong.

One conclusion might be that, ergo, there's some nonlocality in nature. Another conclusion might be that, ergo, the theory incorrectly models the experimental situation in a way that has nothing to do with whether or not nature is exclusively local.

The latter is my working hypothesis. But I'll keep an open mind while rereading and attempting to understand your article.

And thanks for the replies. Everything helps.

harrylin

MWI etc. are interpretations or models of physical theories, just like the Lorentz ether. But yes indeed, Bell's theorem is an extremely far-reaching claim, not just about existing theories but about possible theories including those that haven't even been conceived yet.

harrylin

That may be true, but if that is true then Bell's theorem is wrong - for his theorem is an assertion about the incompatibility of any possible local model of nature with QM.

ThomasT

No. His assertion has to do with the form specified in equation 2 of his 1964 paper. Which form, he proved, cannot reproduce the QM predictions for the singlet state wrt the Stern-Gerlach experiment. This has been subsequently extended to apply to any quantum entanglement setup, and has been verified mostly wrt optical entanglement setups.

Of course, you can maintain that there is no other possible way to explicitly encode locality other than the way Bell did it. I can't think of one.

harrylin

Sorry but I think we should let Bell speak for himself - and that is not what he asserted. Let's first check if ttn's article explains this well:

"Bell's theorem states that the predictions of quantum theory (for measurements of spin on particles prepared in the singlet state) cannot be accounted for by any local theory"

Yes, that is exactly what Bell's theorem states. But regretfully the article doesn't contain a link to Bell's statement... Here are two citations of Bell's assertion (his "theorem"):

"In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measurement device can influence [instantaneously] the reading of another instrument, however remote"
- Bell 1964
"Could we device a model that which reproduces the quantum formulae completely? No it cannot be done, so long as action at a distance is excluded. [...] the quantum correlatations are locally inexplicable"
- Bell 1980

ttn

Forgive me for answering a rhetorical question, but ... NO.

No. I mean, they're important, especially in the sense that our evidence for/against the truth of various candidate theories comes largely from "instrumental behaviors". But why in the world should that mean that "instrumental behaviors" is all theories can say anything about? That's insane. Is paleontology required to be only about the location of bone scraps in the dirt, never about dinosaurs themselves? Do we not know something about (say) the temperature in the core of the sun? How species evolved? It is completely and totally commonplace, normal, and proper for theories to say all kinds of things going far far beyond "instrumental behaviors".

harrylin

On a side note, I saw that the special relativity in Scholarpedia to which your article refers contains at least one misrepresentation (faulty description of second postulate, a misunderstanding that was discussed in the AJP). As this forum isn't the place to discuss that topic (and thus I won't), you could suggest those authors to bring their article up for discussion in the relativity forum.

martinbn

But why should there be any influence?

martinbn

The proof of what? There is no QM involved in Bell's inequalities.

Well, I clearly said 'for example', nothing about _only_ messages.

But what causal influences are we talking about here?


So I have to go to the library.

malreux

Quite, and what a miracle it would be if, knowing nothing about the world in itself, our theories being merely useful tools, yet our tools work so often and so well? QM is so successful it would be a miracle if it did not approximate the truth, even slightly. I don't believe in miracles. Besides, the real question here is 'why is QM so successful?' -part of the answer, presumably, is that human theory has managed to latch onto a bit of reality, or at least approximates it.

ttn

Uh, the proof of Bell's theorem. I agree that "there is no QM involved", if I understand correctly what you mean. The point is just that, in deriving the inequality from the assumption of locality, one doesn't have to assume that the state of the particle pair can be broken up as "the state of the first particle" and then, separately, "the state of the second particle". It is perfectly compatible with the derivation for the state to be somehow "holistic" (i.e., not "separable") as is basically the case in ordinary QM.

harrylin

Bell's conclusion - which according to ttn has been perfectly proven - is that the predicted correlations cannot be explained without such an influence (a "spooky action at a distance", as Einstein called it).

martinbn

I thought that the conclusion is that if you want to explain it with and influence it cannot be local. But why should there be an influence?

martinbn

Yes, of course. So?

ttn

So, that answers the question you asked in 298.

harrylin

No, nothing like that! Again, what is meant with "an influence" or "spooky action at a distance": Bell concluded that the measurement at one place - however remote - instantly affects what is measured at another place; according to him the predicted correlations cannot be explained without such an influence.

See also my citations in post #294.
martinbn, perhaps ttn's summary statement in his article is not clear enough and he should retain more of Bell's words? You are as an apparently "fresh" reader of this topic the best positioned to answer that question.

lugita15

ttn, would it be possible for you (or anyone else) to scan "La Nouvelle Cuisine" for those of us who don't have Bell's book handy?