## Local Causality in a Friedmann-Robertson-Walker Spacetime

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

### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Hi Fred,

I see that you are not toeing the line on the use of "toe the line"?

Perhaps the saying has two states and the one to be used is decided by a magic random quantum process?
Perhaps it was pre-determined that you would use the "tow" version?

---------------
"Tow" or "toe" the line?
See http://www.phrases.org.uk/meanings/toe-the-line.html

Regards
Ben
Ben6993

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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

By the way, Amazon.com has reduced the price of my book to 7.70 (81% off the original price!). I am toying with the idea of publishing a third edition of the book.
Joy Christian
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Joy Christian wrote:Although Richard Gill has been banned from this forum and can no longer post a reply here, it seems important to me that I should elaborate on why he and other Bell believers are having so much difficulty in understating my simple counterexample to the so-called theorem by Bell (cf. my post here: viewtopic.php?f=6&t=55#p2222).

As I have mentioned many times before, the fundamental difficulty they are having is in switching from the traditional R^3 perspective to the S^3 perspective on which my counterexample is based (see, for example, the detailed discussion on my blog).

Their difficulty can be understood in terms of Thomas Kuhn’s celebrated comments on scientific revolutions. Namely, that switching from understanding ideas within an old paradigm to ideas within a new paradigm requires something like a Gestalt Switch. A scientist cannot operate in the old paradigm after having been converted to a completely different way of conceptualizing the world through a new paradigm. In other words, while Richard Gill and his fellow Bell believers continue to see only the mature spinster in the picture below, I and a few others who understand my work are able to see the beautiful young lady, ready to take on the new world:

It is amusing to witness how the physics community can sometime get locked into a false belief. Here is an example of an army of Bell devotees still defending their false belief in his now falsified theorem. After more than 300 comments, they are still finding evermore flimsy and tangential arguments to discredit me and my work on the Bell's so-called theorem. What is worse, it is by no means clear that they even understand Bell's work or have any real background in the subject. Sad, really.
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

A complete, numerical, event-by-event verification of the local-realistic and deterministic 3-sphere model presented in this paper can be found in this simulation.
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Joy Christian wrote:A complete, numerical, event-by-event verification of the local-realistic and deterministic 3-sphere model presented in this paper can be found in this simulation.

It is well-known and accepted that experiments with low detector efficiency cannot be used to falsify local realism, because of the detector efficiency loophole. To falsify local realism, one needs an experiment where almost all events are detected - the detector efficiency should be so good that even assigning arbitrary values to the undetected cases does not allow to recover the BI.

The simulation presented at that simulation is an example of a simulation of such an experiment with detector efficiency loophole. What it is not is a local realistic model for QM, which would be able to model also a 100% detector efficiency.

Code: Select all
f = -1 + (2/sqrt(1 + ((3 * s)/pi))) # For details see the paper arXiv:1405.2355g = function(u,v,s){ifelse((abs(colSums(u*v))) > f, colSums(u*v), 0)}
leads to a nontrivial part of the u,v with g(u,v,s) = 0, thus, correspondingly
Code: Select all
A = +sign(g(a,e,s)) # Alice's measurement results A(a, e, s) = +/-1          B = -sign(g(b,e,s)) # Bob's measurement results B(b, e, s) = -/+1
also with A,B = 0 instead of +/-1 as claimed in the comment. These zero results do not change the sum AB, because they add only zeros, but the number of events with +/-1 values is, of course, different.
Code: Select all
N = n((A*B),a,e,s,b,e,s) # Total number of simultaneous events observed
counts not the total number, but the number of the nonzero pairs, where the detection was successful for above A and B. It depends on a and b.

A local realistic model would have to present, instead, initial values (preparations) $\lambda$ with a frequency corresponding to a probability distribution $\rho(\lambda)d\lambda$ which does not depend on a and b, and functions $A(a,\lambda), B(b,\lambda)\in\{-1,1\}$ which are never zero.
Schmelzer

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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Schmelzer wrote:The simulation presented at that simulation is an example of a simulation of such an experiment with detector efficiency loophole.

The simulation presented at this location has nothing whatsoever to do with detector efficiency loophole or any other ridiculous loophole.

What you have written above is complete and utter garbage. There are no 0 outcomes, either in the theoretical model or in the simulation.

Bogus criticisms of my work is not going to get you anywhere.

Your comments only show that you are a closed-minded and uninformed Bell-fanatic who is incapable of understanding any rational argument.

I repeat:

A complete, numerical, event-by-event verification of the local-realistic and deterministic 3-sphere model presented in this paper can be found in this simulation.
Joy Christian
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

It may be instructive here to make a rather general comment about an elementary logical fallacy (or deception) that is repeatedly and universally used by all of the Bell-believing critics of my refutation of Bell's theorem since 2007. Rather surprisingly, this logical fallacy is committed even by philosophers who should know better.

The elementary logical fallacy the critics commit is the well known straw-man fallacy. You can clearly see its blatant manifestation in the above comments by Ilja Schmelzer --- See how selectively he presents what he claims to be my simulation. The actual simulation is of course dramatically different from what he presents.

The usual form of this logical fallacy is the following: If a proposed physical model (or argument) is X, then the critic surreptitiously replaces it with his or her own grossly distorted, much weaker misrepresentation Y. And since the surrupticious and deceitful replacement Y of the original argument X is deliberately chosen to be much weaker, the critic is able to easily refute or discredit it, thus giving the false impression that he or she has refuted the original pristine model or argument X.

As we know, such a deceitful and dishonest strategy is often used in politics. But, sadly, some supposed scientists also use it in defending their own vested interests.

I will name names here so that there remains no ambiguity in exactly who I am blaming. The people who have used such a dishonest and deceitful strategy against my refutation of Bell's theorem include Philippe Grangier, Richard Gill, Scott Aaronson, James Owen Weatherall, Ilja Schmelzer, and coutless number of other lesser known "scientists", including endless number of anonymous reviewers of my papers employed by some of the top physics journals such as Nature and Physical Review.

It seems that physicists, philosophers, and statisticians will go to whatever length to protect their vested interests, regardless of the cost of their actions to physics.
Joy Christian
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Once Joy Christian decided to attack me again, with a long post which contains essentially nothing than an unbased accusation that I fighted a strawman instead of his simulation, I decided to consider this posting as the one which at least contains the claims what I have misrepresented:
Joy Christian wrote:The simulation presented at this location has nothing whatsoever to do with detector efficiency loophole or any other ridiculous loophole.
What you have written above is complete and utter garbage. There are no 0 outcomes, either in the theoretical model or in the simulation.
Bogus criticisms of my work is not going to get you anywhere.
Your comments only show that you are a closed-minded and uninformed Bell-fanatic who is incapable of understanding any rational argument.
I repeat:
A complete, numerical, event-by-event verification of the local-realistic and deterministic 3-sphere model presented in this paper can be found in this simulation.

Also only a lot of furor, but at least one claim: There are no 0 outcomes. But the code of the simulation contains the following:

Code: Select all
g = function(u,v,s){ifelse((abs(colSums(u*v))) > f, colSums(u*v), 0)}# g(u, v, s) = 0 if |u.v| < f(s)

This means, the function g(u,v,s) gives colSums(u*v) when abs(colSums(u*v))) > f, and else 0. Thus, if at least sometimes abs(colSums(u*v))) <= f, then g has 0 outcomes.

Maybe, this never happens? Not probable. But to test this is easy - if this never happens, then the function g(u,v,s) always gives colSums(u*v). Thus, one can easily simplify the code, and, by the way, prove that there are really no 0 outcomes (or, if there are, that they would be irrelevant) by replacing the code with
Code: Select all
g = function(u,v,s){colSums(u*v)}

Fortunately, we do not even have to do it - Joy does it himself:
Code: Select all
# For completeness we now calculate the correlations for two special cases:f = 0   # Switching back the geometry and topology from S^3 to R^3

with everything else unchanged. Now, with f=0, the expression {ifelse((abs(colSums(u*v))) > f, colSums(u*v), 0)} is already equivalent to colSums(u*v).

What do we obtain? The picture named "The linear correlations predicted by Bell's local model". No violation of the BI, nix, nada. Thus, it appears not only that there are 0 outcomes of g(u,v,s), but they make the difference.

So, what is the "strawman" I create? I simply care about the actual results of the function g(u,v,s) (and, consequently, also of the functions
Code: Select all
A = +sign(g(a,e,s)) # Alice's measurement results A(a, e, s) = +/-1          B = -sign(g(b,e,s)) # Bob's measurement results B(b, e, s) = -/+1

which are zero if g gives 0). And if the code tells me that the result is 0, I name this 0 outcome instead of
Code: Select all
# Defines an inner product on S^3, thus changing the space from R^3 to S^3

This is, obviously, a main error: Not to accept what JC writes in the comments, but to care about what the code does.
Schmelzer

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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Joy Christian wrote:
It may be instructive here to make a rather general comment about an elementary logical fallacy (or deception) that is repeatedly and universally used by all of the Bell-believing critics of my refutation of Bell's theorem since 2007. Rather surprisingly, this logical fallacy is committed even by philosophers who should know better.

The elementary logical fallacy the critics commit is the well known straw-man fallacy. You can clearly see its blatant manifestation in the above comments by Ilja Schmelzer --- See how selectively he presents what he claims to be my simulation. The actual simulation is of course dramatically different from what he presents.

The usual form of this logical fallacy is the following: If a proposed physical model (or argument) is X, then the critic surreptitiously replaces it with his or her own grossly distorted, much weaker misrepresentation Y. And since the surrupticious and deceitful replacement Y of the original argument X is deliberately chosen to be much weaker, the critic is able to easily refute or discredit it, thus giving the false impression that he or she has refuted the original pristine model or argument X.

As we know, such a deceitful and dishonest strategy is often used in politics. But, sadly, some supposed scientists also use it in defending their own vested interests.

I will name names here so that there remains no ambiguity in exactly who I am blaming. The people who have used such a dishonest and deceitful strategy against my refutation of Bell's theorem include Philippe Grangier, Richard Gill, Scott Aaronson, James Owen Weatherall, Ilja Schmelzer, and coutless number of other lesser known "scientists", including endless number of anonymous reviewers of my papers employed by some of the top physics journals such as Nature and Physical Review.

It seems that physicists, philosophers, and statisticians will go to whatever length to protect their vested interests, regardless of the cost of their actions to physics.

Joy Christian wrote:
Schmelzer wrote:The simulation presented at that simulation is an example of a simulation of such an experiment with detector efficiency loophole.

The simulation presented at this location has nothing whatsoever to do with detector efficiency loophole or any other ridiculous loophole.

What you have written above is complete and utter garbage. There are no 0 outcomes, either in the theoretical model or in the simulation.

Bogus criticisms of my work is not going to get you anywhere.

Your comments only show that you are a closed-minded and uninformed Bell-fanatic who is incapable of understanding any rational argument.

I repeat:

A complete, numerical, event-by-event verification of the local-realistic and deterministic 3-sphere model presented in this paper can be found in this simulation.
Joy Christian
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Those with unbiased interest in my work --- i.e., those without any vested interests in maintaining Bell's now falsified claims --- may also wish to study this paper to understand the basic properties of the 3-sphere. It is important to note, for example, that locally S^3 is identical to R^3, and a null rotation by definition is 1, not 0.
Joy Christian
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Joy wrote that:
locally S^3 is identical to R^3

Yes, I remember that from previous work.

But how local is local?
~ planck length & Planck time ...
~ millimetre & millisecond ...
~ metre & second ...
~ kilometre & hour...
~ parsec& aeon ...
or is local any value of closeness?

I have seen in old discussions on s.p.f that some folk think it is the last on this list. (Based on an extra dimension being very large .)
But if it is the first on the list, what good is being very close if we cannot label a locality or have no ability to find it. Sometimes being too close is just as difficult as being too far away? (Based on an extra dimension being microscopic and maybe 'rolled up'. ) Also, knowing where the observer stands is important. If the locality is too close, as in the first on the list, how does the observer know which cover s/he is on/in/at?
Ben6993

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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Ben6993 wrote:But how local is local?

Good question, Ben. By "locally R^3" I mean in an infinitesimal neighbourhood of S^3 the space is identical to R^3.

Before you ask what do I mean by that, let me be more precise. Please have a look at Eq.(114) of the paper I linked above. It expresses the metric tensor, g, in terms of the Riemann curvature tensor, $\cal{R}$, at any point $x$ of S^3, where $\delta$ is the usual "flat" metric on R^3. With this expression we can now see what local means. It means a neighbourhood of S^3 where the value of the curvature tensor is effectively zero. This makes the notion of "any value of closeness" very precise. It is not necessary to invoke Planck length in this context. EPR-B experiments are not done at Planck scale. All EPR-B experiments to date are done at the laboratory or terrestrial scales.
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Thanks Joy.

Ok. Thinking of the extra dimension as compactified into 1 or -1; or say 'in pointing' or 'out pointing' in Fred's helpful early GA graphic; or convex or concave; then each of the two particles stays in their shared starting trivector (say) 'out pointing' subset of the world until their next interactions, which could be miles away. Presumably they are unable to interact with any other particles they encounter which are inhabiting an 'in pointing' trivector.

Any idea of the particles cycling round from one trivector to another en route is barred, as lambda is constant during the experiment. But, given long enough and far enough, the trivector could take the properties of its inverse (c.f. Fred's ice skaters old analogy), though that might take a large-scale journey around the universe to accomplish. Its not going to happen within a lab experiment.
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Nice thoughts, but speculative. The model applies to EPR-B experiments performed in a lab, or at most across the lake Geneva. It should not be starched beyond that.
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

In response to some of the comments in this thread, let me point out that I have now revised the simulation slightly and included explicit calculations showing that "0 outcomes" simply do not exist within S^3. Here is the essential part of the code, specifying A(a, L) = +/-1 = B(b, L), which in turn only use the metric g(u,v,s) in S^3:

Code: Select all
        A = +sign(g(a,e,s))  # Alice's measurement results A(a, e, s) = +/-1                  B = -sign(g(b,e,s))  # Bob's measurement results B(b, e, s) = -/+1                Cuu = length((A*B)[A > 0 & B > 0])   # Coincidence count of (+,+) events                Cdd = length((A*B)[A < 0 & B < 0])   # Coincidence count of (-,-) events                Cud = length((A*B)[A > 0 & B < 0])   # Coincidence count of (+,-) events                Cdu = length((A*B)[A < 0 & B > 0])   # Coincidence count of (-,+) events                corrs[i,j] = (Cuu + Cdd - Cud - Cdu) / (Cuu + Cdd + Cud + Cdu)

The above calculation produces the strong EPR-B correlation, as can be seen in the simulation. But the persistent claim is that A(.) and B(.) also produce "0 outcomes."

So now, in the revised version, I have added the following new lines in the code (which, again, only uses the metric g(u,v,s) in S^3), for the benefit of the flatlanders:

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

We can now see in the simulation that the above calculations explicitly prove Cou = Cod = Cuo = Cdo = Coo = 0. Thus there are simply no "0 outcomes" within S^3.
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

So here is a simple picture to illustrate the above simulation of my 3-sphere model. It shows S^3 and its tangent space R^3 at a given point (shown as a plane at a "dot"). One of the dimensions of S^3 is supressed, because although it is a three dimensional space like R^3, it is difficult to draw it on a two dimensional surface.

Now in the simulation S^3 is modelled by the metric $g(u,v,s)$. This metric is a generalization of the standard Euclidean metric $\delta(u,v) = u\cdot v = cos(u,v)$ we normally use on R^3. In other words, it is a generalization of the standard dot (or inner) product on R^3. As such, it reduces to the standard Euclidean metric $\delta(u,v)$ on the tangent space, R^3, at any local point on S^3. Thus, locally, if you are Alice or Bob, you wouldn't notice anything unusual. You would simply think that you are living in R^3, and carry on your measurements and calculations using the standard dot product, oblivious to the fact that you are actually living in S^3. Your apparent sense that you are living in R^3 would thus be just an illusion. Globally, however, the space you are living in is S^3, and the metric defining this space is actually not the standard Euclidean metric but its generalization $g(u,v,s)$. Consequently, if you compare the events you have observed in an EPR-Bohm experiment with events observed by your remotely located colleague, then you would be in for a surprise. This is the essense of my model, and the above simulation is a fine illustration of it.

There is also an amusing toy model discussed in the first appendix of this paper which illustrates the same points without needing to know anything about a "metric."
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Joy, small point but above (at Thu Jul 09, 2015 11:09 am) you have written: "Here is the essential part of the code, specifying A(a, L) = +/-1 = B(b, L), …"

That, to me is not correct. In my opinion it should be written: "Here is the essential part of the code, specifying A(a, L) = +/-1, B(b, L) = +/-1, …"

Perhaps I am missing something, but to me the above are two different expressions.

I expect you need to satisfy the second expression to coincide with Bell's formulation? And I am guessing that you do?
Guest

### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Guest wrote:Joy, small point but above (at Thu Jul 09, 2015 11:09 am) you have written: "Here is the essential part of the code, specifying A(a, L) = +/-1 = B(b, L), …"

That, to me is not correct. In my opinion it should be written: "Here is the essential part of the code, specifying A(a, L) = +/-1, B(b, L) = +/-1, …"

Perhaps I am missing something, but to me the above are two different expressions.

I expect you need to satisfy the second expression to coincide with Bell's formulation? And I am guessing that you do?

Yes, you are quite right. Thank you. It was sloppy of me to write "A(a, L) = +/-1 = B(b, L), ..."

As you say, I should have written: "Here is the essential part of the code, specifying A(a, L) = +/-1, B(b, L) = +/-1, …"

The second expression is indeed the one that must be satisfied, and the model and its above simulation do satisfy it.
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

I should add here for those not familiar with my work that I haven't stopped with just a theoretical model and an event-by-event simulation confirming the theoretical model. I have also proposed a macroscopic experiment to test the hypothesis that we do live in a parallelized 3-sphere (S^3). The details of this proposed experiment can be found at the following links:

http://arxiv.org/abs/1211.0784 (the preprint of the above paper)

http://arxiv.org/abs/1501.03393 [see, especially, Eq. (B10)]

viewtopic.php?f=6&t=115#p3763 (discussion at this forum)

http://libertesphilosophica.info/blog/e ... taphysics/ (my blog)
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### Re: Local Causality in a Friedmann-Robertson-Walker Spacetim

Hi Everyone,

I have substantively expanded the paper being discussed in this thread. The expanded version is now on the arXiv: http://arxiv.org/abs/1405.2355.

Here is the revised abstract of the paper:

A local, deterministic, and realistic model within a Friedmann-Robertson-Walker spacetime with constant spatial curvature (S^3) is presented which describes simultaneous measurements of the spins of two fermions emerging in a singlet state from the decay of a spinless boson. Exact agreement with the probabilistic predictions of quantum theory is achieved in the model without data rejection, remote contextuality, superdeterminism, or backward causation. A singularity-free Clifford-algebraic representation of S^3 with vanishing spatial curvature and non-vanishing torsion is then employed to transform the model in a more elegant form. Several event-by-event numerical simulations of the model are presented, which confirm our analytical results with the accuracy of 4 parts in 10^4 parts.

On the page 8 of the expanded paper I have included the new, simplified local-realistic derivation of the singlet correlation, which I have also published elsewhere:

The main novelty here is that I have avoided using the concept of standard scores, which has been a stumbling block for some. I now calculate the singlet correlation E(a, b) = -a.b directly using the raw scores A = +/-1 and B = +/-1 within S^3 ( which is of course one of the well known solutions of Einstein's field equations of GR ).

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