## A question on Joy Christian's S^3 model

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Re: A question on Joy Christian's S^3 model

Jochen, thanks. Your posts have been very entertaining to me.

Joy et all,

--a lurker--
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### Re: A question on Joy Christian's S^3 model

Joy Christian wrote:Seriously: what appears to be non-local to the flatlanders from their perspective from within R^3, is perfectly local and realistic from the perspective from within S^3.

That is what the S^3 model is all about. That is what my theoretical papers 1 and 2 show. And that is what the simulation demonstrates spectacularly. Sorry John Bell.

OK, Joy, serious question. And this is from me and nobody else and it gets back to some of what I said about Kaluza-Klein, etc. to start the thread viewtopic.php?f=6&t=75 almost a year ago:

Does your model absolutely and unequivocally and irrevocably require using more than just the three observed three space dimensions to make what looks to be non-local in three dimensions, appear local by using the extra dimensions? That is, is there any way you can show locality of the Bob and Alice stuff if you are restricted to three dimensions and not allowed to add any more?

I am confused, because a year ago I believe you said that the extra dimensions are not needed:

Joy Christian, Wed Jul 30, 2014 2:09 am wrote:This claim can be refuted by simply demonstrating that in fact the emblematic quantum correlation, i.e., the EPR-Bohm or singlet correlation, can be explained purely locally (http://rpubs.com/jjc/16415), and without needing extra dimensions.

And yet I see persistent talk about extra dimensions throughout these threads. So, if these are not needed, then why is there so much chatter about them in these threads, and why are you now using the (rather delightful, thanks!) flatland video to try to make your points? Maybe I need to better understand exactly what you have mind by R^3 versus S^3. Is it the curvature that does the trick?

Jay
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### Re: A question on Joy Christian's S^3 model

Just to add my own angle on what Jay has said above, here's a slightly redacted reproduction of what I wrote recently 'elsewhere':

My position has been to ignore the convoluted stats argument owing to the adage 'lies, damn lies, and statistics'.
What got me doubting Joy was his definitive linkage to an intrinsic physically real torsion as 'physical explanation'. The sole example Joy could give me of a classical observable consequence of such 'intrinsic torsion' was 'gimbal lock', which seemed misplaced to me to put it mildly. Tried to get it boiled down to that any intrinsic spacetime torsion was equivalent to saying there is a uniform chirality to spacetime - as say exists within a solution of a levo-rotatory sugar. Which manifests as rotation of the plane of polarization of linearly polarized light. Or alternately, as a differential in c for RH vs LH circularly polarized light. Classically easily observable. Joy would not comment on such suggestions from me. Nor on my observation that even allowing such existed in vacuo (contrary to observational evidence), inevitably chiral media effects (aka 'intrinsic spacetime torsion') accumulate linearly over distance and imply a periodic (phase) dependence thereby. Whereas EPRB situations and similar are totally independent of spatial separation.

Still, I cannot swallow the implied magic literally at the heart of physics that entanglement implies. Hence keep hoping someone like Hans De Raedt et al will finally provide a convincing resolution preserving both locality and realism.
Q-reeus

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### Re: A question on Joy Christian's S^3 model

Yablon wrote:Does your model absolutely and unequivocally and irrevocably require using more than just the three observed three space dimensions to make what looks to be non-local in three dimensions, appear local by using the extra dimensions? That is, is there any way you can show locality of the Bob and Alice stuff if you are restricted to three dimensions and not allowed to add any more?

I am confused, because a year ago I believe you said that the extra dimensions are not needed:

Joy Christian, Wed Jul 30, 2014 2:09 am wrote:This claim can be refuted by simply demonstrating that in fact the emblematic quantum correlation, i.e., the EPR-Bohm or singlet correlation, can be explained purely locally (http://rpubs.com/jjc/16415), and without needing extra dimensions.

And yet I see persistent talk about extra dimensions throughout these threads. So, if these are not needed, then why is there so much chatter about them in these threads, and why are you now using the (rather delightful, thanks!) flatland video to try to make your points? Maybe I need to better understand exactly what you have mind by R^3 versus S^3. Is it the curvature that does the trick?

Hi Jay,

Yours is indeed a serious question, and a rather delightful one! Let me separate it out in two parts, to make clear what I have in mind: (1) EPR-Bohm or the standard singlet correlations, and (2) All other more complicated quantum correlations, involving more than two particles etc.

As far as the standard EPR-Bohm or singlet correlations are concerned, no extra dimensions are needed. As the notation suggests, S^3 is a three dimensional space, just as R^3 is. Intuitively the difference between S^3 and R^3 is similar to that between S^2 (e.g., the surface of earth ) and R^2 (e.g, a football field). Jut as we recover R^2 from S^2 by removing a single point at infinity, R^3 can be recovered from S^3 by removing a single point at infinity: S^3 = R^3 U {$\infty$}. Topologically, however, there are profound differences between R^3 and S^3. The former, R^3, is flat, open, and multiply-connected, whereas the latter, S^3, is curved, compact, and simply-connected. Thus curvature does play an important role in what I am suggesting with regard to singlet correlations. There is, however, a further subtlety that is crucially significant. S^3 can be rendered flat as far as its Riemann curvature is concerned by expressing it as a set of unit quaternions, in which case it is homeomorphic to the group SU(2). Its "curviness" is then entirely captured by torsion, which turns out to be responsible for extending the bound on the Bell-CHSH inequality from $2$ to $2\sqrt{2}$. But none of these require any extra dimensions. The latter properties of S^3 can be better appreciated within the embedding space R^4, but the embedding four dimensional space is not the real space. It is just an auxiliary mathematical space. The actual space is still only three dimensional space, S^3.

So far so good. But what about the more complicated quantum correlations? Well, it turns out that even for the simplest extension of the singlet correlations to more than two particles, such as in the GHZ state, extra dimensions become indispensable if we are to seek local-realistic explanation along the line I have provided for the singlet correlations. It is unfortunate that the relentless attacks on me by the Bell mafia since 2007 (leading to academic ostracism, on and off-line harassments, withdrawal of research funds, blocking of publications, insults, and abuse) has distracted me from pursuing the issue of extra dimensions in greater detail, beyond studying the simplest cases like the GHZ or Hardy states. I do have a rather formal theorem, however, about a local-realistic explanation of ALL quantum correlations in terms of large extra dimensions (more precisely, in terms of the octonionic 7-sphere embedded in eight large dimensions): http://arxiv.org/abs/1201.0775.

So, in sum, although extra dimensions are not needed to explain the standard singlet (or EPR-Bohm) correlations local-realistically, they seem to be indispensable for the local-realistic explanation of the more complicated quantum correlations. I hope this answers your question.

Best,

Joy
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### Re: A question on Joy Christian's S^3 model

Unless I am on ignore, seem to have made the mistake of not specifically addressing my last post here (currently 3rd post, p5) to Joy as a query rather than just comments. So, Joy, having raised (again), some specific issues, please be good enough to convincingly deal with each, one-by-one, within the appropriate context. Given the imo reasonable assumption there should be a correspondence principle at play that somehow connects your postulated torsion to both QM stats AND physically consistent classical physics observables. Thanks in advance for any useful response, as Americans like to put it.
Q-reeus

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### Re: A question on Joy Christian's S^3 model

Q-reeus wrote:Unless I am on ignore, seem to have made the mistake of not specifically addressing my last post here (currently 3rd post, p5) to Joy as a query rather than just comments. So, Joy, having raised (again), some specific issues, please be good enough to convincingly deal with each, one-by-one, within the appropriate context. Given the imo reasonable assumption there should be a correspondence principle at play that somehow connects your postulated torsion to both QM stats AND physically consistent classical physics observables. Thanks in advance for any useful response, as Americans like to put it.

I cannot address a question that I don't understand. Torsion is a tensor, locally defined at every point of the physical space, as explained here. So I don't understand what your worry is. As for the Gimbal lock, this post by Paul Snively may be helpful in addressing your question: http://psnively.github.io/blog/2015/01/22/Fallacy/.
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### Re: A question on Joy Christian's S^3 model

Q-reeus wrote:Just to add my own angle on what Jay has said above, here's a slightly redacted reproduction of what I wrote recently 'elsewhere':

My position has been to ignore the convoluted stats argument owing to the adage 'lies, damn lies, and statistics'.
What got me doubting Joy was his definitive linkage to an intrinsic physically real torsion as 'physical explanation'. The sole example Joy could give me of a classical observable consequence of such 'intrinsic torsion' was 'gimbal lock', which seemed misplaced to me to put it mildly. Tried to get it boiled down to that any intrinsic spacetime torsion was equivalent to saying there is a uniform chirality to spacetime - as say exists within a solution of a levo-rotatory sugar. Which manifests as rotation of the plane of polarization of linearly polarized light. Or alternately, as a differential in c for RH vs LH circularly polarized light. Classically easily observable. Joy would not comment on such suggestions from me. Nor on my observation that even allowing such existed in vacuo (contrary to observational evidence), inevitably chiral media effects (aka 'intrinsic spacetime torsion') accumulate linearly over distance and imply a periodic (phase) dependence thereby. Whereas EPRB situations and similar are totally independent of spatial separation.

Still, I cannot swallow the implied magic literally at the heart of physics that entanglement implies. Hence keep hoping someone like Hans De Raedt et al will finally provide a convincing resolution preserving both locality and realism.

A fairly simple way of thinking about parallelized 3-sphere topology, is that space has unique spinor properties.

You don't need to wait for Hans De Raedt; both Joy and Michel (minkwe) have thoroughly demolished Bell's theorem right here on this forum.
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### Re: A question on Joy Christian's S^3 model

Joy Christian wrote:I cannot address a question that I don't understand. Torsion is a tensor, locally defined at every point of the physical space, as explained here. So I don't understand what your worry is. As for the Gimbal lock, this post by Paul Snively may be helpful in addressing your question: http://psnively.github.io/blog/2015/01/22/Fallacy/.

Sorry Joy but see no meaningful answer there to the issues I raised. Just did a quick search to find something in the literature connecting torsion to chirality, and found this:
http://iopscience.iop.org/1367-2630/13/ ... 053053.pdf
see e.g. last 2 para p1 there to get the basic drift. I have no expertise in tensor maths but do understand that:

In order to somehow connect to Bell-type Alice-Bob experiments that can be performed reliably anywhere and in any lab orientation, logically a postulated intrinsic spacetime torsion must ab initio have the property of homogeneity, isotropy, linearity and so on. I can conceive of only one property fulfilling that bill - uniform chirality. Of course in the example I gave of a levo or dextro-rotatory sugar solution, such chirality is confined to the solution and has just EM coupling to photons, and over a limited frequency range at that. Whereas an intrinsic thus necessarily uniform spacetime torsion aka chirality presumably couples to all physical phenomena.

Granted even such exists, for the reasons I gave in post #3 p5, one has to sensibly explain how such torsion effects things yet so as to be independent of separation between any parts of an experimental setup.
Now, it would be helpful if you could run me over each of those issues in that post (leave out 'gimbal lock' at least for now), with a dumbed-down yet coherent explanation/resolution that a layman can follow. Cheers.
Last edited by Q-reeus on Fri Jul 10, 2015 11:38 pm, edited 1 time in total.
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### Re: A question on Joy Christian's S^3 model

FrediFizzx wrote:A fairly simple way of thinking about parallelized 3-sphere topology, is that space has unique spinor properties.

You don't need to wait for Hans De Raedt; both Joy and Michel (minkwe) have thoroughly demolished Bell's theorem right here on this forum.

Fred - I'm sure you are trying to be helpful there, but the specific issues I have raised need addressing in detail. Hopefully Joy will do that.
Q-reeus

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### Re: A question on Joy Christian's S^3 model

Q-reeus wrote:Sorry Joy but see no meaningful answer there to the issues I raised. Just did a quick search to find something in the literature connecting torsion to chirality, and found this:
http://iopscience.iop.org/1367-2630/13/ ... 053053.pdf
see e.g. last 2 para p1 there to get the basic drift. I have no expertise in tensor maths but do understand that:

In order to somehow connect to Bell-type Alice-Bob experiments that can be performed reliably anywhere and in any lab orientation, logically a postulated intrinsic spacetime torsion must ab initio have the property of homogeneity, isotropy, linearity and so on. I can conceive of only one property fulfilling that bill - uniform chirality. Of course in the example I gave of a levo or dextro-rotatory sugar solution, such chirality is confined to the solution and has just EM coupling to photons, and over a limited frequency range at that. Whereas an intrinsic thus necessarily uniform spacetime torsion aka chirality presumably couples to all physical phenomena.

Granted even such exists, for the reasons I gave in post #3 p5, one has to sensibly explain how such torsion effects things yet so as to be independent of separation between any parts of an experimental setup.
Now, it would be helpful if you could run me over each of those issues in that post (leave out 'gimbal lock' at least for now), with a dumbed-down yet coherent explanation/resolution that a layman can follow. Cheers.

Q-reeus,

None of your worries seem to have any relevance to what I am saying. A manifold, such as S^3, can be described by either curvature or torsion. Both are tensors, thus defined locally, at each point of S^3. In other words, they are just fancy "vectors". The effect of the curvaute or torsion manifestes when you consider all four terms of the Bell-CHSH inequality, as shown in Eqs. (20) to (22) of this paper. So, again, I am not sure what your worry is. If you don't like torsion in this context, then think of the strong correlations as curvature effects. That will do just fine. It is, however, more natural to use torsion in this context, as I have shown in the linked paper.
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### Re: A question on Joy Christian's S^3 model

Q-reeus wrote:
FrediFizzx wrote:A fairly simple way of thinking about parallelized 3-sphere topology, is that space has unique spinor properties.

You don't need to wait for Hans De Raedt; both Joy and Michel (minkwe) have thoroughly demolished Bell's theorem right here on this forum.

Fred - I'm sure you are trying to be helpful there, but the specific issues I have raised need addressing in detail. Hopefully Joy will do that.

Have you read Joy's book yet?
http://www.brownwalker.com/book/1612337244
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### Re: A question on Joy Christian's S^3 model

Joy Christian wrote:Q-reeus,

None of your worries seem to have any relevance to what I am saying. A manifold, such as S^3, can be described by either curvature or torsion. Both are tensors, thus defined locally, at each point of S^3. In other words, they are just fancy "vectors". The effect of the curvaute or torsion manifestes when you consider all four terms of the Bell-CHSH inequality, as shown in Eqs. (20) to (22) of this paper. So, again, I am not sure what your worry is. If you don't like torsion in this context, then think of the strong correlations as curvature effects. That will do just fine. It is, however, more natural to use torsion in this context, as I have shown in the linked paper.

Rrrright. Joy, can I just get a simple yes no answer to this question:
We presumably agree that flatness in S^3 (or R^3) implies zero curvature or torsion. Yet there is a postulated non-zero torsion existing - presumably, sans localized e.g. gravitational effects - uniform everywhere. Is such torsion synonymous with, and otherwise able to be accurately termed a uniform spacetime (or just spatial) chirality? [If not, what other term would best describe it's classical physics observable effects?] OK - that's potentially two questions.
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### Re: A question on Joy Christian's S^3 model

FrediFizzx wrote:Have you read Joy's book yet?
http://www.brownwalker.com/book/1612337244

No Fred, but once all the many new points recently raised this forum have been digested, I will definitely be in the mood for a signalled up-coming 3rd edition!
Q-reeus

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### Re: A question on Joy Christian's S^3 model

Q-reeus wrote:Rrrright. Joy, can I just get a simple yes no answer to this question:
We presumably agree that flatness in S^3 (or R^3) implies zero curvature or torsion. Yet there is a postulated non-zero torsion existing - presumably, sans localized e.g. gravitational effects - uniform everywhere. Is such torsion synonymous with, and otherwise able to be accurately termed a uniform spacetime (or just spatial) chirality? [If not, what other term would best describe it's classical physics observable effects?] OK - that's potentially two questions.

Sorry, Q-reeus, I can't make a head or tail of your question(s). You will have to try again. And please be more specific about why this is relevant at all to my model.
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### Re: A question on Joy Christian's S^3 model

Joy Christian wrote:Sorry, Q-reeus, I can't make a head or tail of your question(s). You will have to try again. And please be more specific about why this is relevant at all to my model.

Well Joy, can't think how to make earlier posted queries any clearer so guess it's time I called it quits this thread. You or other interested members might though like to at least consider the imo clear corresondence made in particular between torsion and the case of homogeneous chirality in e.g. first section of part 6 of that article I linked to earlier:
http://iopscience.iop.org/1367-2630/13/ ... 053053.pdf
As noted earlier, while the usual application is to EM, generalizing the correspondence to intrinsic spacial torsion seems pretty obvious, even trivial. Maybe I'm alone in thinking along such lines. Best.
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### Re: A question on Joy Christian's S^3 model

Q-reeus wrote:
Joy Christian wrote:Sorry, Q-reeus, I can't make a head or tail of your question(s). You will have to try again. And please be more specific about why this is relevant at all to my model.

Well Joy, can't think how to make earlier posted queries any clearer so guess it's time I called it quits this thread. You or other interested members might though like to at least consider the imo clear corresondence made in particular between torsion and the case of homogeneous chirality in e.g. first section of part 6 of that article I linked to earlier:
http://iopscience.iop.org/1367-2630/13/ ... 053053.pdf
As noted earlier, while the usual application is to EM, generalizing the correspondence to intrinsic spacial torsion seems pretty obvious, even trivial. Maybe I'm alone in thinking along such lines. Best.

OK, I looked at the linked paper and I now understand where the confusion is. At least in that paper they are talking about non-Riemannian geometry, whereas what I am talking about is simply a teleparallel interpretation of the same old Riemannian geometry (as explain on my blog page I linked earlier, see below). In other words, the torsion you have in mind is very different from the torsion I have been considering in my papers: http://libertesphilosophica.info/blog/o ... lations-2/.
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### Re: A question on Joy Christian's S^3 model

Richard Gill has suggested the following procedure (via private email) to check that there are indeed no "zero" outcomes in this simulation of my 3-sphere model:

Set, for example, i = 7.2 and j = 25.3, change the lines “for i in … { " and "for j in … { " in the simulation, and remove the closing brackets. In other words, remove the two loops and replace them with fixed i and j, with whatever pair of angles you like. Running the simulation then shows that there are no zero outcomes for this pair of angles. You can then repeat the run with any number of randomly chosen pairs of angles and confirm that there are indeed no zero outcomes for any pair of angels.

Thus, since the functions A(a; e, s) and B(b; e, s) depend only on the settings a and b (respectively) and the "shared randomness" (e, s), and since the computation of the correlation is done by coincident counts, what we have here is an unequivocal refutation of Bell's theorem, without needing to know anything about the 3-sphere.

This should finally put an end to the 50 year old Bell delusion.
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### Re: A question on Joy Christian's S^3 model

You can try any pair of angles, and follow the procedure I noted above (as suggested by Richard Gill).

Do try $i = 10$ and $j = 20$, giving $\alpha = (10 - 1) \times 7.2^\circ = 64.8^\circ$ and $\beta = (20 - 1) \times 7.2^\circ = 136.8^\circ$, and run this simulation.

It does not matter which pair of angles you try. You will always get

Cou = Cod = Cuo = Cdo = Coo = CoB = CAo = 0.

This puts THE END to the Bell delusion.
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### Re: A question on Joy Christian's S^3 model

For convenience let me post part of the code here to demonstrate that there are indeed no zero outcomes in the above simulation.

Code: Select all
Angles = seq(from = 0, to = 360, by = 7.2) * 2 * pi/360K = length(Angles)M = 10^5r = runif(M, 0, 2*pi)z = runif(M, -1, +1)h = sqrt(1 - z^2)x = h * cos(r)y = h * sin(r)e = rbind(x, y, z)s = runif(M, 0, pi)f = -1 + (2/sqrt(1 + ((3 * s)/pi)))g = function(u,v,s){ifelse(abs(colSums(u*v)) > f, colSums(u*v), 0)}

Code: Select all
i = 1   # fixing ialpha = Angles[i]a = c(cos(alpha), sin(alpha), 0)  # Measurement direction 'a'j = 20  # fixing jbeta = Angles[j]b = c(cos(beta), sin(beta), 0)  # Measurement direction 'b'A = +sign(g(a,e,s))  # Alice's measurement results A(a, e, s) = +/-1B = -sign(g(b,e,s))  # Bob's measurement results B(b, e, s) = -/+1

And the results are:

Code: Select all
> (Cou = length((A*B)[g(a,e,s) & A == 0 & B > 0]))  # Number of (0,+) events[1] 0> (Cod = length((A*B)[g(a,e,s) & A == 0 & B < 0]))  # Number of (0,-) events[1] 0> (Cuo = length((A*B)[A > 0 & B == 0 & g(b,e,s)]))  # Number of (+,0) events[1] 0> (Cdo = length((A*B)[A < 0 & B == 0 & g(b,e,s)]))  # Number of (-,0) events[1] 0> (Coo = length((A*B)[g(a,e,s) & A == 0 & B == 0])) # Number of (0,0) events[1] 0> (CoB = length(A[g(a,e,s) & A == 0]))   # Number of A = 0 events within S^3[1] 0> (CAo = length(B[g(b,e,s) & B == 0]))   # Number of B = 0 events within S^3[1] 0

Thus, it does not matter which pair of angles we try (by fixing i and j as done above). We will always get

Cou = Cod = Cuo = Cdo = Coo = CoB = CAo = 0.

Thus there are simply no "0 outcomes" in the 3-sphere model, or in the above simulation.

This puts an end to the Bell delusion.
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### Re: A question on Joy Christian's S^3 model

Hi Joy,

For completeness would you show the print out of cuu, cdd, cud, cdu and N along with the other variables already printed. All these variables are incremented together wrt index looping, so that should be a final nailing of the missing-or-not zeros.

(I had the R language on my old computer but it is not on my new computer, so I have not been able to run that code myself.)
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