Hidden Variables
Bell's theorem - for or against Hidden Variables? - Printable Version

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RE: Bell's theorem - for or against Hidden Variables? - secur - 08-23-2016

(08-23-2016, 01:25 AM)Thomas Ray Wrote: secur wrote, "Our only real disagreement concerns the results of the exploding ball experiment. With luck someone will perform it and put the issue to rest."

A non-arbitrary initial condition, without entanglement, will put the issue to rest.  That is the point.  Understand that, and everything else falls into place.

The correlation function should be classical, and not violate Bell or CHSH inequalities. Doesn't seem to matter how the initial conditions are designed. That's what Gill's CHSH proof shows. Of course the standard caveat applies: I may be missing something!

(08-23-2016, 08:25 AM)gill1109 Wrote:
(08-22-2016, 09:29 PM)secur Wrote: Anyway, you're assuming that all four combinations of the a's and b's will occur. That happens in a typical Bell experiment, allowing CHSH inequality to be derived easily. However in Christian's case he instructs us to pick only one (a, b) then use it with each of the experimental data points to produce the script-E terms.
In his experiment, you observe N particle pairs, get N values of lambda, and then compute any script-E term for any (a, b) you like. For every (a, b): the same N particle pairs, the same N values of lambda.

Ok, now I get it - you're right.


RE: Bell's theorem - for or against Hidden Variables? - Thomas Ray - 08-23-2016

(08-23-2016, 05:13 PM)secur Wrote:
(08-23-2016, 01:25 AM)Thomas Ray Wrote: secur wrote, "Our only real disagreement concerns the results of the exploding ball experiment. With luck someone will perform it and put the issue to rest."

A non-arbitrary initial condition, without entanglement, will put the issue to rest.  That is the point.  Understand that, and everything else falls into place.

The correlation function should be classical, and not violate Bell or CHSH inequalities. Doesn't seem to matter how the initial conditions are designed. That's what Gill's CHSH proof shows. Of course the standard caveat applies: I may be missing something!

(08-23-2016, 08:25 AM)gill1109 Wrote:
(08-22-2016, 09:29 PM)secur Wrote: Anyway, you're assuming that all four combinations of the a's and b's will occur. That happens in a typical Bell experiment, allowing CHSH inequality to be derived easily. However in Christian's case he instructs us to pick only one (a, b) then use it with each of the experimental data points to produce the script-E terms.
In his experiment, you observe N particle pairs, get N values of lambda, and then compute any script-E term for any (a, b) you like. For every (a, b): the same N particle pairs, the same N values of lambda.

Ok, now I get it - you're right.

The correlation function is classical.  Gill's correlation function is meaningless without a time parameter.  That's the whole point.


RE: Bell's theorem - for or against Hidden Variables? - gill1109 - 08-24-2016

(08-23-2016, 09:15 PM)Thomas Ray Wrote:
(08-23-2016, 05:13 PM)secur Wrote:
(08-23-2016, 01:25 AM)Thomas Ray Wrote: secur wrote, "Our only real disagreement concerns the results of the exploding ball experiment. With luck someone will perform it and put the issue to rest."

A non-arbitrary initial condition, without entanglement, will put the issue to rest.  That is the point.  Understand that, and everything else falls into place.

The correlation function should be classical, and not violate Bell or CHSH inequalities. Doesn't seem to matter how the initial conditions are designed. That's what Gill's CHSH proof shows. Of course the standard caveat applies: I may be missing something!

(08-23-2016, 08:25 AM)gill1109 Wrote:
(08-22-2016, 09:29 PM)secur Wrote: Anyway, you're assuming that all four combinations of the a's and b's will occur. That happens in a typical Bell experiment, allowing CHSH inequality to be derived easily. However in Christian's case he instructs us to pick only one (a, b) then use it with each of the experimental data points to produce the script-E terms.
In his experiment, you observe N particle pairs, get N values of lambda, and then compute any script-E term for any (a, b) you like. For every (a, b): the same N particle pairs, the same N values of lambda.

Ok, now I get it - you're right.

The correlation function is classical.  Gill's correlation function is meaningless without a time parameter.  That's the whole point.
Not Gill's correlation function: Christian's correlation function.


RE: Bell's theorem - for or against Hidden Variables? - Thomas Ray - 08-24-2016

(08-24-2016, 07:56 AM)gill1109 Wrote:
(08-23-2016, 09:15 PM)Thomas Ray Wrote:
(08-23-2016, 05:13 PM)secur Wrote:
(08-23-2016, 01:25 AM)Thomas Ray Wrote: secur wrote, "Our only real disagreement concerns the results of the exploding ball experiment. With luck someone will perform it and put the issue to rest."

A non-arbitrary initial condition, without entanglement, will put the issue to rest.  That is the point.  Understand that, and everything else falls into place.

The correlation function should be classical, and not violate Bell or CHSH inequalities. Doesn't seem to matter how the initial conditions are designed. That's what Gill's CHSH proof shows. Of course the standard caveat applies: I may be missing something!

(08-23-2016, 08:25 AM)gill1109 Wrote: In his experiment, you observe N particle pairs, get N values of lambda, and then compute any script-E term for any (a, b) you like. For every (a, b): the same N particle pairs, the same N values of lambda.

Ok, now I get it - you're right.

The correlation function is classical.  Gill's correlation function is meaningless without a time parameter.  That's the whole point.
Not Gill's correlation function: Christian's correlation function.

Christian's correlation function has a large enough defined measure space to accommodate nonlinear time reversibility.  Gill's non-defined measure space of linear superposition is what Einstein called " ... an attempt to breathe in empty space", a meaningless game with numbers.


RE: Bell's theorem - for or against Hidden Variables? - secur - 08-24-2016

BTW there's no need to quote all of the posts all of the time.

The Script-E correlation function defined in Section IV "Proposed Experiment" doesn't depend on a measure space, it's just an algebraic function, derived from measurements in the lab of the spins of the two halves of the exploding balls. But Gill assumes (as I do) that those measurements take place in an SO(3) world, while Christian assumes SU(2), quaternionic or spin space. The actual numbers which result would tell which is correct.

Christian's preferred space is indeed "larger" (a double cover). Maybe you can say, loosely, quaternions "accommodate nonlinear time reversibility". The internal half-angle can "remember the history of rotation": from which direction an angle was approached. But again this has nothing to do with the correlation function calculations, only with the results expected.

My comment to Gill, "you're right", referred specifically to the "mistake" I thought he'd made. I think he's right in general also, but haven't studied his paper enough to say that. 

IMHO Christian should present the paper as simply a tutorial on SO(3) vs. SU(2). His fig. 4, the discussion around it, and the appendices, are worthwhile, AFAIK.

Einstein said that quantizing gravity was like attempting to breath in empty space. Gravity has nothing to do with this problem, although Christian does bring it in via FLRW, to motivate use of quaternions.


RE: Bell's theorem - for or against Hidden Variables? - Thomas Ray - 08-24-2016

" ... Gill assumes (as I do) that those measurements take place in an SO(3) world, while Christian assumes SU(2), quaternionic or spin space. The actual numbers which result would tell which is correct."

Here's what Christian defines as measure space: "It is also crucial to appreciate that the spin angular momenta L(s, λ) (i.e., the bivectors) trace out an su(2) 2-sphere within the group manifold SU(2) ∼ S3, not a round S2 within IR3 as Gill has incorrectly assumed." http://arxiv.org/pdf/1501.03393v6.pdf

"Einstein said that quantizing gravity was like attempting to breath in empty space."

Here's what Einstein said about breathing in empty space: "It is maintained that perhaps the success of the Heisenberg method points to a purely algebraical method of description of nature, that is to the elimination of continuous functions from physics. Then, however, we must also give up by principle, the space-time continuum. It is not unimaginable that human ingenuity will someday find methods which will make it possible to proceed along such a path. At the present time, however, such a program seems like an attempt to breathe in empty space. (The Theory of Relativity and Other Essays.)

"At the present time, the opinion prevails that a field theory must first, by 'quantization' be transformed into a statistical theory of field probabilities according to more or less established rules. I see in this method only an attempt to described relationships of an essential nonlinear character by linear methods." (The Meaning of Relativity)

Has anything changed that would eliminate spacetime? No.


RE: Bell's theorem - for or against Hidden Variables? - gill1109 - 08-24-2016

(08-24-2016, 03:52 PM)secur Wrote: Gill assumes (as I do) that those measurements take place in an SO(3) world, while Christian assumes SU(2), quaternionic or spin space. The actual numbers which result would tell which is correct.
I don't assume anything. I read Christian's instructions to the experimenters. They are completely explicit. The actual numbers which result from the experiment will generate correlations which, with absolute certainty, will satisfy the CHSH inequality, whatever kind of world we live in. Hence the desired "singlet correlations" will certainly not be obtained.

Christian's response http://arxiv.org/pdf/1501.03393v6.pdf to my paper does not answer this criticism. Instead it contains yet another mish-mash of the same theory as in all the other papers, including the same errors.


RE: Bell's theorem - for or against Hidden Variables? - secur - 08-24-2016

Einstein wrote: Then, however, we must also give up by principle, the space-time continuum.

AFAIK he's referring to the space-time continuum of GR, so the quote is more-or-less about gravity. If I'm wrong, I'll happily concede the nit.

Thomas Ray wrote: Here's what Christian defines as measure space: "It is also crucial to appreciate that the spin angular momenta L(s, λ) (i.e., the bivectors) trace out an su(2) 2-sphere within the group manifold SU(2) ∼ S3, not a round S2 within IR3 as Gill has incorrectly assumed."

Two possibilities: he means this theoretically, or practically.

Theoretically he defined his bivectors as quaternions that square to -1. So theoretically, he's right.

But practically he's using them to represent directions in real space (the spins of the exploding ball halves). In real space you can use quaternions for this purpose, but must (according to normal thinking) consider any unit vector equal to its negative. Thus removing the double cover and "collapsing" to SO(3). But he claims the "normal thinking" is false, and it's possible to distinguish between 2 pi and 4 pi rotations. That's the whole point of the paper, as you can tell from the title. Following normal thinking I don't buy this, without some proof or at least justification.

[EDIT] reading Christian's response to Gill, I see the bivectors are angular momenta, pseudo-vectors, and not equal to their negatives, as I said. I have to think about that. Still it doesn't seem to affect Gill's point which, after all, is simple algebra ...

secur wrote previously: Gill assumes (as I do) that those measurements take place in an SO(3) world, while Christian assumes SU(2), quaternionic or spin space.

Gill wrote: I don't assume anything.

Hard to believe. Everyone assumes that if they turn in a circle, they're back where they started. You don't think you need to turn once again to restore initial state, do you? So, you assume real space is SO(3) not SU(2). With the appropriate caveats: local tangent space, whatever.

Gill wrote: I read Christian's instructions to the experimenters. They are completely explicit. The actual numbers which result from the experiment will generate correlations which, with absolute certainty, will satisfy the CHSH inequality, whatever kind of world we live in. Hence the desired "singlet correlations" will certainly not be obtained.

Ok, that's not nit-picking. Your point is that no matter what the N values of lambda are, no matter how they're obtained, the Script-E correlation function must satisfy CHSH, by simple algebra.  You've said this before, and I admit it's been hard to wrap my head around this apparent fact. It's such an egregious mistake on his part, I keep thinking I'm missing something. I'll read his response and see if it makes any sense.


RE: Bell's theorem - for or against Hidden Variables? - secur - 08-25-2016

In http://arxiv.org/pdf/1501.03393v6.pdf Christian seems to get confused in eqns 11, 12, 13. As eqn 11 shows script-E is simply a (finite) sum of products of script-A and script-B terms. BTW there seems no need for introducing these script A and B symbols, elsewhere the exact same equation uses regular A and B. Anyway, eqn 11 then introduces a new symbology: expectation value of script-A-sub-A times script-B-sub-B, which is simply another way of writing the script-E summation. Eqn 12 shows CHSH equation written with this new symbology. Then he says Gill's mistake is to take the expectation brackets outside of the four terms, as shown in eqn 13.

With this new expectation-value symbol it looks, superficially, like he has a point. It looks exactly like a typical mistake one can make in QM. There, you can't in general treat expectations that way because of non-commuting observables. However if we just replace the expectation-value symbols with their equivalent summations from eqn 11, it's clear that the step, Gill's step, from 12 to 13 is not a mistake. We're simply removing the (identical) summations outside of the four terms which are combined by addition and subtraction - perfectly legal.

So it seems a deliberate attempt to obfuscate a very simple point, to rebut Gill. It's hard to accept that Christian, obviously an intelligent person, who knows his geometric algebra, would do this. But that's the way it looks.

Earlier he makes an interesting point about psuedo-vectors, which change upon reflection. Therefore it could be said that O(3) is the correct group for them, not SO(3). (BTW I'm sure this whole topic is very well understood by some people but can't find a good reference.) Now both O(3) and SU(2) are "double covers" of SO(3). So - this is pure conjecture on my part - is Christian trying to say that pseudo-vectors are properly represented as SU(2), or quaternions? But of course O(3) and SU(2) are not isomorphic, even though they have similar elements (two copies of SO(3)). O(3)'s covers are not connected like SU(2)'s so they are definitely very different groups. Maybe you could make something of this idea, however - if, indeed, that's what he's trying to do. I'll think about it.

In conclusion my opinion is unchanged although, certainly, there are subtleties here I haven't grasped to my satisfaction. Gill is right, the CHSH proof is simple algebra - according to Christian's own equations for script-E. The fact that he substitutes this new expectation-value symbology (nothing like it in the original paper), in the crucial eqns 11-13, might mean there is an important point that he simply is not expressing well. He's making a mistake; but if I understood what he's really getting at, perhaps there's real meat here. Or, it might just mean he's deliberately obfuscating. Either way Gill is right, based on what Christian actually wrote. Perhaps if he could write clearly, without mistakes, what he's really thinking, Gill's objection would be answered. I wish Christian himself would comment.


RE: Bell's theorem - for or against Hidden Variables? - Thomas Ray - 08-25-2016

(08-24-2016, 10:46 PM)secur Wrote: Einstein wrote: Then, however, we must also give up by principle, the space-time continuum.

AFAIK he's referring to the space-time continuum of GR, so the quote is more-or-less about gravity. If I'm wrong, I'll happily concede the nit.

Thomas Ray wrote: Here's what Christian defines as measure space: "It is also crucial to appreciate that the spin angular momenta L(s, λ) (i.e., the bivectors) trace out an su(2) 2-sphere within the group manifold SU(2) ∼ S3, not a round S2 within IR3 as Gill has incorrectly assumed."

Two possibilities: he means this theoretically, or practically.

Theoretically he defined his bivectors as quaternions that square to -1. So theoretically, he's right.

But practically he's using them to represent directions in real space (the spins of the exploding ball halves). In real space you can use quaternions for this purpose, but must (according to normal thinking) consider any unit vector equal to its negative. Thus removing the double cover and "collapsing" to SO(3). But he claims the "normal thinking" is false, and it's possible to distinguish between 2 pi and 4 pi rotations. That's the whole point of the paper, as you can tell from the title. Following normal thinking I don't buy this, without some proof or at least justification.

[EDIT] reading Christian's response to Gill, I see the bivectors are angular momenta, pseudo-vectors, and not equal to their negatives, as I said. I have to think about that. Still it doesn't seem to affect Gill's point which, after all, is simple algebra ...

secur wrote previously: Gill assumes (as I do) that those measurements take place in an SO(3) world, while Christian assumes SU(2), quaternionic or spin space.

Gill wrote: I don't assume anything.

Hard to believe. Everyone assumes that if they turn in a circle, they're back where they started. You don't think you need to turn once again to restore initial state, do you? So, you assume real space is SO(3) not SU(2). With the appropriate caveats: local tangent space, whatever.

Gill wrote: I read Christian's instructions to the experimenters. They are completely explicit. The actual numbers which result from the experiment will generate correlations which, with absolute certainty, will satisfy the CHSH inequality, whatever kind of world we live in. Hence the desired "singlet correlations" will certainly not be obtained.

Ok, that's not nit-picking. Your point is that no matter what the N values of lambda are, no matter how they're obtained, the Script-E correlation function must satisfy CHSH, by simple algebra.  You've said this before, and I admit it's been hard to wrap my head around this apparent fact. It's such an egregious mistake on his part, I keep thinking I'm missing something. I'll read his response and see if it makes any sense.

secur wrote:  "Einstein wrote: 'Then, however, we must also give up by principle, the space-time continuum.'

AFAIK he's referring to the space-time continuum of GR, so the quote is more-or-less about gravity. If I'm wrong, I'll happily concede the nit."

The quote is about relativity.  The Lorentz transformation of special relativity does not give up spacetime, merely because it is locally rigid.

"Thomas Ray wrote: Here's what Christian defines as measure space: "It is also crucial to appreciate that the spin angular momenta L(s, λ) (i.e., the bivectors) trace out an su(2) 2-sphere within the group manifold SU(2) ∼ S3, not a round S2 within IR3 as Gill has incorrectly assumed." 

Two possibilities: he means this theoretically, or practically.

Theoretically he defined his bivectors as quaternions that square to -1. So theoretically, he's right."

Well, no kidding.  Theory is primary.  This is the mistake that Bell believers consistently make -- and have to make, in order to preserve the delusion -- that one can depend on observation alone to support a mathematical theory, no matter how ugly and ad hoc.  This is acceptable in no other area of physical science.  Why the exception for 'practical' quantum mechanics?

secur wrote:  "But practically he's using them to represent directions in real space (the spins of the exploding ball halves). In real space you can use quaternions for this purpose, but must (according to normal thinking) consider any unit vector equal to its negative. Thus removing the double cover and 'collapsing' to SO(3). But he claims the 'normal thinking' is false, and it's possible to distinguish between 2 pi and 4 pi rotations. That's the whole point of the paper, as you can tell from the title. Following normal thinking I don't buy this, without some proof or at least justification.

[EDIT] reading Christian's response to Gill, I see the bivectors are angular momenta, pseudo-vectors, and not equal to their negatives, as I said. I have to think about that. Still it doesn't seem to affect Gill's point which, after all, is simple algebra ...

secur wrote previously: Gill assumes (as I do) that those measurements take place in an SO(3) world, while Christian assumes SU(2), quaternionic or spin space."

Normal thinking, as you noted, is toward 'simple algebra.'  Joy has taken great pains to show that Bell's choice of topology is deficient, and therefore simple algebra doesn't work.  Maybe you think (as I did once upon a time) that since he wasn't doing topology, we should trust the algebra.  However, when measured against the requirements of special relativity, point set topology enters by default.  If we accept Bell's theorem, we have to give up special relativity.  That will leave physics as a simple probabilistic game; Gill is perfectly happy with that.

Best,
Tom