A simple two-page proof of local realism

[gill1109]

PS. Joy, are you going to discuss the failure of the perfect anti-correlation property?

My analytical model predicts perfect anti-correlation.

I know. Therefore Chantal's simulation is not a simulation of your model. QED.

[Joy Christian]

Please express this in mathematical terms. Or in terms of (a) programming language.

Mathematical language:

If |C_a| = 0, then |C_b| = 1.

If |C_b| = 0, then |C_a| = 1.

Programming language:

double C_a1 = Math.cos(eta_ae + phi_op)/N_a; // ordinary channel; lambda = +1
double C_a2 = Math.cos(eta_ae + phi_op + Math.PI)/N_a; // ordinary channel; lambda = -1

double C_b1 = Math.sin(eta_be + phi_or)/N_b; // extraordinary channel; lambda = +1
double C_b2 = Math.sin(eta_be + phi_or + Math.PI)/N_b; // extraordinary channel; lambda = -1

[gill1109]

Orthogonal in the sense that the zero's of each of the functions are the +/-1's of the other?

These are functions which don't *only* take the values -1, 0 and 1. I doubt that this odd kind of orthogonality will do much for you. And since the present simulation does not exhibit perfect anti-correlation at equal settings, your present choices of phases are badly wrong.

.

[Ben6993]

Hi Joy:

No, nothing as sophisticated as that is needed. All I am saying is that when Alice detects a particle, the phase angles ensure that Bob does not end up detecting the same particle. It is a very simple criterion. I later learned from Ben that the same criterion is also used by De Raedt in his work.

The phase difference in Dr.Raedt's code was a 90 degree difference between the particles in the pairs. Here is an extract from Dr. Raedt' fortran code (I can't find the reference to his paper):
------------
twopi = 2 * Pi
pi2 = Pi / 2
...
' pick a polarization
R0 = Rnd
x1 = twopi * R0 ' polarization of particle 1
x2 = x1 + pi2 ' polarization of particle 2
------------
So particle 1 has random polarisation within 0 to 2*pi.
Particle 2 polarisation is that for particle 1 but with pi/2 added.

[Joy Christian]

Hi Joy:

No, nothing as sophisticated as that is needed. All I am saying is that when Alice detects a particle, the phase angles ensure that Bob does not end up detecting the same particle. It is a very simple criterion. I later learned from Ben that the same criterion is also used by De Raedt in his work.

The phase difference in Dr.Raedt's code was a 90 degree difference between the particles in the pairs. Here is an extract from Dr. Raedt' fortran code (I can't find the reference to his paper):
------------
twopi = 2 * Pi
pi2 = Pi / 2
...
' pick a polarization
R0 = Rnd
x1 = twopi * R0 ' polarization of particle 1
x2 = x1 + pi2 ' polarization of particle 2
------------
So particle 1 has random polarisation within 0 to 2*pi.
Particle 2 polarisation is that for particle 1 but with pi/2 added.

Thanks, Ben. Yes, I understand that the difference has to be 90 degrees. But within S^3 there is a twist in the Hopf bundle, and hence the odd looking phase angles. Nevertheless, the difference is indeed exactly 90 degrees. We can see that by noting that the effect of the phase angle is equivalent to replacing the cos function with the sin function --- i.e., shifting the phase by 90 degrees. Threre is nothing mysterious about this. It is good to see that De Raedt has been using the same criterion.

[gill1109]

So phi_o^r = -1.517 and phi_o^s = 0.663 (radians), two phase shifts in two different places, are somehow the same as one phase shift of pi/2?

How can you talk about a "phase-shift" anyway, when we're operating in S^3, represented locally as S^1 x S^2. ? Shouldn't we be talking about a rotation?

[Joy Christian]

So phi_o^r = -1.517 and phi_o^s = 0.663 (radians), two phase shifts in two different places, are somehow the same as one phase shift of pi/2?

Yes. Play around with C_a and C_b in Chantal's simulation and witness this yourself.

How can you talk about a "phase-shift" anyway, when we're operating in S^3, represented locally as S^1 x S^2. ? Shouldn't we be talking about a rotation?

They indeed describe rotations of the quaternions involved [cf. eqs (A28) and (A29) in my "Whither..." paper]. The expression "phase shifts" is also correct, because they shift the phases of the sine and cosine functions. The expression "phase shifts" is used also in QM, in the same context. You are welcome to call them rotations.

[FrediFizzx]

Here is a link to an improved Mathematica version of Michel Fodje's simulation by John Reed.
EPRsims/Minkwe_Reed_EPRsim2.nb

Here is a PDF file link for those that don't have Mathematica.
EPRsims/Minkwe_Reed_EPRsim2.pdf

Here is a PDF File of the graph for output of 10 million trials.
download/Minkwe.pdf

Here is a link to Joy's proof that Michel's simulation works because of 3-sphere topology.
http://libertesphilosophica.info/blog/w ... mplete.pdf

Looks like Joy's parallelized 3-sphere model works as advertised and explains quantum correlations in a local realistic way.

[gill1109]

Here is a link to an improved Mathematica version of Michel Fodje's simulation by John Reed.
..
Here is a PDF File of the graph for output of 10 million trials.
download/Minkwe.pdf
...
Looks like Joy's parallelized 3-sphere model works as advertised and explains quantum correlations in a local realistic way.

Look closely and you see the systematic deviation from the cosine curve. It does not work as advertised.

If you want perfection, I recommend the 1999 Gisin and Gisin model:

http://arxiv.org/abs/quant-ph/9905018
http://rpubs.com/chenopodium/gisin1

While you're at it, take a look at

http://rpubs.com/gill1109/JCS

[FrediFizzx]

All the deviations from the cosine curve are no big deal and are just limitations due to rounding, etc. Joy has proven that the result of his local realistic parallelized 3-sphere model is -a.b. I think we are done here.

[gill1109]

All the deviations from the cosine curve are no big deal and are just limitations due to rounding, etc. Joy has proven that the result of his local realistic parallelized 3-sphere model is -a.b. I think we are done here.

Everyone is free to ignore any evidence whatever, and to stay believing whatever they believed in advance...

I understand that Joy has agreed that both Michel Fodje's particle-based simulation and Chantal Roth's pair-based simulations (JCS, JCS2) are a little bit off target and need fixing. This is not a question of rounding errors, it is fundamental. We await Joy's proposals for the "good" phase angles.

Joy told us himself that Daniel Sabsay's javascript should not be taken seriously. In my opinion, it should be taken down from "Libertes Philosophica" - it's a fake. It is not what it is claimed to be. It's a discredit to Joy.

[Ben6993]

Richard:
In your version of Chantal's simulation, the lack of perfection of fit to the cosine curve is most noticeable at 0 deg [and 360] and 180 degrees.

Fred noted [on the FQXi site] that the rounding from real values, of radian angles, to bin values, of integer degrees, in Chantal's code will cause approximations. That kind of rounding error would not normally cause a bias though, and should get asymptotically closer to the cosine curve target with larger N? I also note that Florin's plot [on FQXi, I think] of detection efficiency is most deviant for angles 0 and 180 deg. Is there perhaps a connection?

There is also the barrier problem. The correlation cannot be more than 1 nor less than -1. Random errors can reduce the correlation below 1 but cannot increase the correlation above 1 to cancel out the random errors. This is why correlation coefficients are not averaged using a simple arithmetic average. Although there is no adding of correlation coefficients in the simulation, there is still a one way effect of rounding errors near the barrier walls where correlations are 1 and -1, i.e. at angles 0 and 180 degrees. But it should still be possible to get closer to the wall asymptotically with large N without a bias.

[gill1109]

Richard:
In your version of Chantal's simulation, the lack of perfection of fit to the cosine curve is most noticeable at 0 deg [and 360] and 180 degrees.

Fred noted [on the FQXi site] that the rounding from real values, of radian angles, to bin values, of integer degrees, in Chantal's code will cause approximations. That kind of rounding error would not normally cause a bias though, and should get asymptotically closer to the cosine curve target with larger N? I also note that Florin's plot [on FQXi, I think] of detection efficiency is most deviant for angles 0 and 180 deg. Is there perhaps a connection?

There is also the barrier problem. The correlation cannot be more than 1 nor less than -1. Random errors can reduce the correlation below 1 but cannot increase the correlation above 1 to cancel out the random errors. This is why correlation coefficients are not averaged using a simple arithmetic average. Although there is no adding of correlation coefficients in the simulation, there is still a one way effect of rounding errors near the barrier walls where correlations are 1 and -1, i.e. at angles 0 and 180 degrees. But it should still be possible to get closer to the wall asymptotically with large N without a bias.

(1) There is no binning in my simulation. No binning at all. The settings are exact, they are known, there is no approximation. I only look at finitely many different setting pairs.

(2) The prediction from QM of the singlet state is perfect anti-correlation at equal settings. I simulate at exactly equal settings and I do not get perfect anti-correlation. It's easy to see why not. It is not rounding error. The model which is being simulated does not predict perfect anti-correlation at equal setting angles.

[Joy Christian]

The prediction from QM of the singlet state is perfect anti-correlation at equal settings. I simulate at exactly equal settings and I do not get perfect anti-correlation. It's easy to see why not. It is not rounding error. The model which is being simulated does not predict perfect anti-correlation at equal setting angles.

My analytical model, just like quantum mechanics, predicts perfect anti-correlation at equal setting:

(1) http://arxiv.org/abs/1103.1879

(2) http://arxiv.org/abs/1106.0748

(3) http://arxiv.org/abs/1201.0775

(4) http://arxiv.org/abs/1203.2529

(5) http://arxiv.org/abs/1211.0784

(6) http://arxiv.org/abs/1301.1653

(7) http://libertesphilosophica.info/blog/w ... 1/EPRB.pdf

(8) http://libertesphilosophica.info/blog/w ... hapter.pdf

In R^3 based simulations of my analytical model, or in any such simulation for that matter, an additional practical issue arises. For example, Richard Gill's version of Michel Fodje's simulation is off by some 0.001. This is because Alice and Bob are not careful enough in his simulation to not end up detecting each other's particles in addition to their own. I have now been able to correct this deficiency of his simulation. The corrected version now matches with the (negative) cosine curve exactly. I will report on this latest version as soon as it is ready to be published. Imperfections in simulations like these have no baring on the perfection of my analytical model.

[gill1109]

In R^3 based simulations of my analytical model, or in any such simulation for that matter, an additional practical issue arises. For example, Richard Gill's version of Michel Fodje's simulation is off by some 0.001. This is because Alice and Bob are not careful enough in his simulation to not end up detecting each other's particles in addition to their own. I have now been able to correct this deficiency of his simulation. The corrected version now matches with the (negative) cosine curve exactly. I will report on this latest version as soon as it is ready to be published. Imperfections in simulations like these have no bearing on the perfection of my analytical model.

I am very glad that all those efforts by so many dedicated scientists from various different backgrounds are leading to refinements to the theory. The attempts at verification of the model by computer simulation, forced on Joy against his will by the constant stream of criticism from various detractors, led to his discovery of the necessity for those phase shifts. Values were initally found by trial and error in order to make the simulated curves appear close to the negative cosine. This is not yet a satisfactory state of affairs. Maybe the discovery of the phase factors is akin to Einstein's discovery of the cosmological constant - what initially looks like a fudge factor, turns out later to be of fundamental physical significance.

But the step of converting the "bug" into a fully fledged "feature" still has to be taken. We look forward to the new publication and new simulation experiments.

[FrediFizzx]

This doesn't matter anymore. You have already seen the updated explanation.

Here is a graph of six different outputs of John Reed's Mathematic version of the Minkwe simulation going from theta_0 = 0 to equal to pi/2.



This illustrates the cases that Joy mentions on page 258 to 259 here. The first graph is when theta_0 = 0 and we can see we get the Bell case of straight lines. Then the graphs increment in tenths of pi until we get to pi/2 which is the optimal case. So we can see that gradually we are going from straight lines to more and more towards the cosine curve. Now another thing to mention is that these graphs are generated with 5 million trials at one degree increments (rounded to that). So the finer that we make the degree intervals to round to, the better we will fit to the cosine curve. But the simulation will never actually get all the way there because we would have to go to zero degree intervals.

[gill1109]

When the sample size is large enough and the increments small enough, and when you zoom in and look at the graph at, say, 30 degrees, you'll see a small but systematic deviation.

This is the value at 30 degrees, to three decimals: -0.849

This is negative cosine of 30 degrees, to three decimals: -0.866

Please show us pictures, not of the whole curve, but just the bit between, say, 29 and 31 degrees. On the vertical scale: between -0.9 and -0.8

If you take the measurement angles all to be whole numbers of degrees then all differences between measurement angles are whole numbers too. You can plot just three points on the curve for us.

I'm running Mathematica from the command line on a server, did not yet find out who to get pdf files of plots out of it, so I can't show you the picture myself just now. Should be able to do it tomorrow.

[FrediFizzx]

Can you prove that the deviation is "systematic"? I don't think you can. But we really don't care about the finer details of these simulations since Joy has already proven that his model gives the predictions of quantum theory exactly. You would be better off to try to understand why.

[gill1109]

Can you prove that the deviation is "systematic"? I don't think you can. But we really don't care about the finer details of these simulations since Joy has already proven that his model gives the predictions of quantum theory exactly. You would be better off to try to understand why.

Yes I can prove that the deviation is systematic, though my proof is statistical.
How many standard deviations would convince you?
For the Higgs Boson, five standard deviations were considered sufficient proof.
I think we are already there, regarding the differences between the various versions of Minkwe's model and Chantal's model and the negative cosine. They're all different. Only the Gisin and Gisin model, so far, is spot on. And that can be proved analytically.

If you don't care about the truth then obviously you have no need to read or write anything.

I do care about the finer details of these simulations. It's my job. Science is a multi-disciplinary, multi-person activity. You would be wise to make use of complementary expertise in areas where your own expertise is clearly lacking.

I notice that you still haven't posted a "zoom in" picture of the graph, where the deviation between the curves is most painfully obvious. What's the problem?

[gill1109]

Over on the fqxi forum http://fqxi.org/community/forum/topic/812, some of us were earlier discussing the elephant in the room which the small but real discrepancies between these various attempts to simulate Joy's model seem to have introduced.

But is there an elephant in the room? Since all these various simulations come very close to the cosine curve, who cares? They all exhibit resounding violation of the CHSH inequality... (By the way, *only* the Gisin and Gisin model hits it exactly. That can be proven analytically for Gisin and Gisin, and statistically - five standard deviations good enough for you? It was good enough for the Higgs Boson - for all the others). See http://rpubs.com/gill1109 and http://rpubs.com/chenopodium for proofs.

The problem is in the heart of the simulation. In order to generate outcomes for A and B (or in Chantal's model, A times B) we need values of the settings a and b, and we need a realization of the hidden state lambda.

In both simulations, lambda is effectively generated by the rejection method: an initial randomization can generate both states lambda and non-states (points lambda outside of the domain of A(a, .) and B(b, .)). So we just keep picking a lambda from the big set of states and non-states, till we are lucky to get a state.

In both simulation models, the criterion for rejection depends on a and b. In other words, the domain of the hidden state and hence also its probabilty distribution, depends on a and b.

Maybe this only appears to be so? Maybe if you have checked some criterion involving a and b is satified, then it is also satisfied for all possible a' and all possible b', hence it not actually "measurement setting dependent"? Well, that is what Joy claims, but the fact of the matter is that Bell's theorem shows that this selection *must* be measurement setting dependent. You can only violate Bell's inequality by violating one of locality, realism, or no-conspiracy. In this case the simulation is evidently local realist. So it violates "no-conspiracy", aka "freedom".

Either the original S^3 Joy's model is wrong, or the deductions from that model to the simulation models are wrong.

In my opinion, the real elephant in the room is the attempt to simulate Christian's mathematics within the confines of local realism on classical computers. That enterprise is doomed to failure ... by Bell's theorem. Earlier, Joy always admitted this. He always said: you have to *circumvent* Bell. He then did a U-turn and is now suffering the dire consequences.

Joy's model cannot be reproduced in flatland. It needs a real physical S^3. It needs a kind of Möbius strip in space-time which alters the measurement outcomes (the measurement outcomes which Alice and Bob saw and collected in their respective labs) as they bring them back in their space-ships, from their labs on distant planets on distant galaxies, back to Christian's head office on Planet Earth.