Login Register

Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Bell's theorem - for or against Hidden Variables?
Thomas Ray: "Why non-locality?" NOT! It goes against everything we have learned about Nature.

That's as good an answer as any, but of course it's not decisive. Everywhere else in Nature influence is limited by speed of light, as far as we know. But apparently in QM the "collapse of the wave function" happens faster, for "entangled" particles, as shown in Bell type experiment. It's a new, different phenomenon, although it doesn't "go against" - i.e., doesn't contradict - any other facts. Often, in science and elsewhere, we run into NEW phenomena. This is one of those cases.

Thomas Ray: Let A = nonlocality  Let B = local realism

No. That explains why you didn't get my "logic lesson". In fact,

A = local realism
B = Bell's inequality

Thomas Ray: Local realism (Einstein causality) is constructed explicitly in the measure space of special relativity, and implicitly in general relativity, assuming spacetime is real. ("All physics is local".)  If we were comparing apples to apples, context would be supplied by measure space.  What is the measure space of Bell-Aspect?

There are (at least) two measure spaces involved. First, as you say, we assume Minkowski space (no need for curved GR space), but we're not really treating it as a measure space. Then there's the space of outcomes for Alice and Bob, which is simply tensor product of two copies of the pair of outcomes {-1, 1} with the obvious atomic PDF.

But the key one you're referring to is, no doubt, the space in which the premised "hidden variable", usually called lambda, lives. Its existence is only an hypothesis, which turns out to be wrong: evidently lambda doesn't exist. That means we can't say definitively what space it's an RV in. This point can cause confusion. Bell's theorem is supposed to be valid no matter what (reasonable) space you hypothesize for this RV! The normal choice would be SO(3), the 3-sphere (which, BTW, in mathematical topology we call the 2-sphere). The PDF would be assumed uniform, although other choices are possible. It doesn't matter whether you suppose this is the space of unit quaternions with zero real part (square roots of -1) or the more standard definition, vectors of norm 1. You could also use O(3) if you want. Even SO(2) could be used with appropriate assumptions. Bell's theorem works regardless. It also makes no difference if you justify the geometric algebra approach by invoking FLRW.

I hope that answers your question. Let me emphasize again the key source of confusion. Since it turns out lambda doesn't exist - the point of Bell's proof by contradiction - there isn't one definitive measure space for this RV. We should be able to assume any reasonable space for lambda. I can't imagine any that would invalidate Bell.

Finally note that what really counts here is the QM correlation function. Other aspects of Bell-Aspect experiment can be modelled differently, in various ways, not this one.
Reply
(07-23-2016, 04:56 PM)secur Wrote: Thomas Ray: "Why non-locality?" NOT! It goes against everything we have learned about Nature.

That's as good an answer as any, but of course it's not decisive. Everywhere else in Nature influence is limited by speed of light, as far as we know. But apparently in QM the "collapse of the wave function" happens faster, for "entangled" particles, as shown in Bell type experiment. It's a new, different phenomenon, although it doesn't "go against" - i.e., doesn't contradict - any other facts. Often, in science and elsewhere, we run into NEW phenomena. This is one of those cases.

That quote was me, not Tom. There is no "collapse of the wave function" problem in EPR. That is a very common misconception. And certainly the quantum experiments don't show that. All the experiments do is validate that the QM predictions for the EPR scenario are most likely correct. We know what the explanation is for the "new" phenomena; space has unique spinor properties.

(07-22-2016, 07:37 PM)Schmelzer Wrote: Ok, it may be your contention.  

You confuse here two things:  A mistake in Bell's derivation.  Given that Bell gives precise definitions, and the mathematics is fine, this is, to put it mildly, not very probable.  

If space has spinor properties, you cannot put that into Bell's derivation. So his mistake is that he did not make his argument general enough. I have not confused anything.
Reply
(07-24-2016, 05:52 AM)FrediFizzx Wrote: If space has spinor properties, you cannot put that into Bell's derivation.

Given that the derivation does not make any assumptions about the properties of space, nothing changes even if space would have such properties.
Reply
(07-24-2016, 06:51 AM)Schmelzer Wrote:
(07-24-2016, 05:52 AM)FrediFizzx Wrote: If space has spinor properties, you cannot put that into Bell's derivation.

Given that the derivation does not make any assumptions about the properties of space, nothing changes even if space would have such properties.

Well, there you go.  That is his mistake.  He didn't make any assumptions about the effects the properties of space could have when he should have.
Reply
"I hope that answers your question".

Not even close.

"Let me emphasize again the key source of confusion. Since it turns out lambda doesn't exist - the point of Bell's proof by contradiction - there isn't one definitive measure space for this RV."

That's what we've been saying. The theorem assumes nonlocality, and goes about "proving" it in a way that proves what is assumed in the first place.

"We should be able to assume any reasonable space for lambda. I can't imagine any that would invalidate Bell."

You can't imagine it, because you don't accept Einstein local realism. Granted, if spacetime isn't real, randomness rules. That spacetime is real is validated by LIGO, among other experiments.
Reply
Here's what Karl Hess (*Einstein was Right!*) had to say about the claim that lambda can be "anything":

"I was now convinced that I had detected a falsehood in Tony's (Leggett) statement that lambda could be 'anything' and in addition be statistically independent of the polarizer settings. Lambda could not be identified with a time variable, because the measurement time was different for each term of the inequality, while Bell had the same lambda in each term. The measurement times obey an ordering, while Bell's lambdas exhibit randomness". (p. 48)

This is the difference between a complete time indexed theory, and an incomplete one that assumes randomness from the beginning.
Reply
FrediFizzx: That quote was me, not Tom.

Sorry

FrediFizzx: There is no "collapse of the wave function" problem in EPR. That is a very common misconception.

I've never even heard of this misconception, and it's hard to believe it's common. I'm somewhat curious why anyone would think it was a problem? ... but it's not really worth going into.

FrediFizzx: We know what the explanation is for the "new" phenomena; space has unique spinor properties.

Ok, but this is a vague statement. Please give a reference explaining what space having "unique spinor properties" has to do with Bell's theorem.

Thomas Ray: ... Karl Hess ...

You mentioned that Hess paper a while ago, didn't seem convincing, perhaps I should look at it again
Reply
Secur,

That was a quote from Hess's book (which makes reference to the papers of Hess-Philipp).

My review: https://www.amazon.com/gp/review/R30ZF0S...imp_1rv_cl
Reply
Thanks Thomas Ray, I remember that book is at my local library so I'll read it, sounds entertaining. But looking on the 'net I find Richard Gill already found a mistake in the Hess-Philipp paper. He says Hess's idea is, at best, a version of a known loophole which has been ruled out by the latest experiments. So obviously there's nothing earth-shaking here.
Reply
Richard Gill's criticism is refuted. http://arxiv.org/pdf/quant-ph/0212085.pdf

[...]
Reply


Forum Jump:


Users browsing this thread: 2 Guest(s)