## A new simulation of the EPR-Bohm correlations

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

### Re: A new simulation of the EPR-Bohm correlations

Joy Christian wrote:They are obsessed about the number of pre-states used in the simulation and how many of these pre-states are actually selected in a given experiment for a given pair (a, b) of settings. But who cares about the pre-ensemble and the pre-states in R^3? The pre-ensemble does not exist in Nature. Only S^3 and the real states (u, s) exist in Nature. Pre-ensemble M and pre-states are like the wooden frame, and S^3 and the corresponding real states (u, s) are like the Picasso. Thus Gill and his proxy are simply barking on the wrong tree!

The problem is that in local realism the states have to be prepared and chosen without knowing a and b. Simply because they are yet undefined and unknown - at least if one excludes superdeterminism, at those places where an Einstein-local theory could define and prepare its hidden variables.

This property - independence of a and b - is the essential, key property of the local hidden variables. That's why I care about it. You may name this "obsessed", but I simply know - its trivial - that without this independence of lambda on a and b one cannot prove Bell's inequalities, thus, an example where these initial values depend on a and b is worthless and irrelevant.

Thus, the hidden variables lambda can only be those variables which are defined without knowing a and b. In the computation this property has the pre-ensemble, and the pre-ensemble only.

Once the definition of what are the "real states (u,s)" depends on a and b, they can be identified only at measurement time, because only at measurement time a and b are created by the free choices of the experimenters. The preparations should have been some element of the pre-ensemble.

What happens, if the pre-ensemble element to become a "real state" once a and b come into existence? However one names it, it will be a failure of the particular experiment. Or A(a,l) will not be +-1 but 0, or B(b,l) will be 0. This possibility is named (or equivalent to) the detector inefficiency loophole. And it is also well-known that low detector efficiency allows to obtain violations of Bell's inequalities within local realistic models.

So what I do is simply to defend Bell's theorem against "counterexamples" which are not really counterexamples but simple long ago known possibilities to obtain violations of Bell's inequalities, which in simple and obvious ways violate the conditions of Bell's theorem.

Here, again, a clear statement that one of the central points of Bell's inequality - the independence of the states lambda as well as its probability distribution rho(lambda)d lambda - is simply ignored in your "counterexample", which makes it completely worthless:
Joy Christian wrote:Therefore what is physically relevant in the simulation is the ratio of the total number N of the simultaneous events observed by Alice and Bob and the total number L of the initial states (u, s) in S^3. Whether or not the absolute numbers N and L depend on the settings (a, b) is completely irrelevant.

What you have created is a "counterexample" which could be written in the following form:

$E(AB|ab) = \int A(a,\lambda) B(b,\lambda) \rho(a,b,\lambda) d \lambda$

And what you have declared now is that this dependence on a and b is completely irrelevant. But it is relevant, for such an expression one cannot prove Bell's inequality.
Schmelzer

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### Re: A new simulation of the EPR-Bohm correlations

Complete nonsense. There is no such dependence in this simulation http://rpubs.com/jjc/84238,

or in this theoretical analysis on which it is based: http://arxiv.org/abs/1405.2355.

Please stop making bogus claims about my work. They remind me of Gill
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

There is:
http://rpubs.com/jjc/84238 wrote:Ls[i, j] = length(s[t(a, u, b, u)]) # The number of initial states (u, s) in S^3

This is the number of states used for given values a,b, in your simulation. This is, clearly, what in a numerical simulation would be proportional to the density rho(lambda). Thus, rho depends not only on lambda (this would be the case if you would use all the pre-states Ls[i, j] = length(s) instead) but also on a and b.
Schmelzer

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### Re: A new simulation of the EPR-Bohm correlations

Actually, you are worse than Gill. What you are claiming is total hogwash.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

*
I have added the following explanatory note in the simulation for the benefit of the flatlanders: http://rpubs.com/jjc/84238.
# Nota bene: The pre-ensemble M and the pre-states u do not exist in Nature.
# Only S^3 and the states (u, s) within S^3 exist in Nature. Therefore what
# is physically meaningful is the ratio N/L of the total number N of the
# simultaneous events observed by Alice and Bob and the total number L of
# the initial states (u, s) within S^3. This ratio is constant, N/L = 1, and
# remains independent of the settings a and b, as shown in the graph below.
# Consequently, the density rho(u, s) also remains independent of a and b.

The point is that everything must be viewed and calculated from within S^3. Stepping out of S^3 is like stepping into nowhere. There is nothing "outside" S^3.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

Joy Christian wrote:*
I have added the following explanatory note in the simulation for the benefit of the flatlanders: http://rpubs.com/jjc/84238.
The point is that everything must be viewed and calculated from within S^3. Stepping out of S^3 is like stepping into nowhere. There is nothing "outside" S^3.

The point of the "flatlander" remains unchanged, together with the formula: "Ls[i, j] = length(s[t(a, u, b, u)]) # The number of initial states (u, s) in S^3".

The choice (and the number) of the "initial states" depends on a and b, which are unknown at the moment where a local realistic model could define initial states. Thus, this model is not a local realistic one.

You say that it is independent, I say it is dependent, it is up to the reader to decide. I support my vision with a formula "Ls[i, j] = length(s[t(a, u, b, u)])" found in your code, as well as "N = length((A * B)[t(a, u, b, u)])"

Let's also note that it would be quite trivial to prepare initial states in S^3 or whereever without using a and b.
Last edited by Schmelzer on Mon Jun 08, 2015 4:48 am, edited 2 times in total.
Schmelzer

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### Re: A new simulation of the EPR-Bohm correlations

Joy Christian wrote:Actually, you are worse than Gill. What you are claiming is total hogwash.

The simulation, together with the theoretical analysis on which it is based, speak for themselves. Anyone can see from the simulation and the theoretical analysis that the probability density rho(u, s) is independent of the settings a and b. However, if someone wants to remain in denial of this evidence, then they are free to do so.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

Joy Christian wrote:The simulation, together with the theoretical analysis on which it is based, speak for themselves. Anyone can see from the simulation and the theoretical analysis that the probability density rho(u, s) is independent of the settings a and b. However, if someone wants to remain in denial of this evidence, then they are free to do so.

Indeed, the simulation speaks for itself. Anyone can see that "Ls[i, j] = length(s[t(a, u, b, u)])" and "N = length((A * B)[t(a, u, b, u)])" do not depend on a and b.
Schmelzer

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### Re: A new simulation of the EPR-Bohm correlations

Joy Christian wrote:The simulation, together with the theoretical analysis on which it is based, speak for themselves. Anyone can see from the simulation and the theoretical analysis that the probability density rho(u, s) is independent of the settings a and b. However, if someone wants to remain in denial of this evidence, then they are free to do so.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

Within S^3, does the idea of counterfactual realism re-emerge? It doesn't work within R^3, but does it work within S^3?
I.e. if one reverses the lambda sign, keeping a, b and theta constant, do the real outcomes A and B swap values to become the counterfactual outcomes, when the real data are "good"?
Ben6993

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### Re: A new simulation of the EPR-Bohm correlations

Ben6993 wrote:Within S^3, does the idea of counterfactual realism re-emerge? It doesn't work within R^3, but does it work within S^3?
I.e. if one reverses the lambda sign, keeping a, b and theta constant, do the real outcomes A and B swap values to become the counterfactual outcomes, when the real data are "good"?

Yes, Ben, it does, just as you describe it. All actual as well as counterfactual measurement results of Alice and Bob exist as +/-1 limiting points of the elements of S^3.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

Thanks. That's good.

And also, because the outcomes in a real experiment analysed in R^3 will always have missing data (because some of the outcomes are not realisable in S^3) then that is why real experiments can beat the saw tooth pattern to become the -cos pattern.
Ben6993

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### Re: A new simulation of the EPR-Bohm correlations

Ben6993 wrote:And also, because the outcomes in a real experiment analysed in R^3 will always have missing data (because some of the outcomes are not realisable in S^3) then that is why real experiments can beat the saw tooth pattern to become the -cos pattern.

Ok. The only problem is that it gives a model only to an experiment which has also missing data, thus, one which would be considered as not loophole-free because of insufficient detector efficiency. And a detector-efficiency-loophole-free experiment could not be modeled.
Schmelzer

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### Re: A new simulation of the EPR-Bohm correlations

Sorry Ilja, you still don't understand how S^3 space affects what happens in Nature.
FrediFizzx
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### Re: A new simulation of the EPR-Bohm correlations

Ben6993 wrote:And also, because the outcomes in a real experiment analysed in R^3 will always have missing data (because some of the outcomes are not realisable in S^3) then that is why real experiments can beat the saw tooth pattern to become the -cos pattern.

I don't quite understand the parenthetical part of your remark. In any case my analytical Clifford-algebraic 3-sphere model as well as at least the latest simulation of the 3-sphere model have nothing to do with the missing data or loopholes. There is one-to-one correspondence between the simultaneously observed events by Alice and Bob and the initial states (u, s). So the model does not depend on detection or any other funny loophole. It is a true and final nail in the coffin of Bell's theorem.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

Hi Joy,

Yes I seemed to mangle my last post. I was reviewing it when you replied. I did not mean to imply the S^3 model depended on missing data and I don't think I wrote that. But I did mix up what a real experiment was doing.

For a real experiment the thetas and lambdas are generated by nature in S^3. So real experiments should be able to obtain the cos curve even with all pairs counted in.
Ben6993

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### Re: A new simulation of the EPR-Bohm correlations

Ben6993 wrote:For a real experiment the thetas and lambdas are generated by nature in S^3. So real experiments should be able to obtain the cos curve even with all pairs counted in.

Yes, that is correct.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

FrediFizzx wrote:Sorry Ilja, you still don't understand how S^3 space affects what happens in Nature.

This is not the point. You think if Joy includes the Monster group into his construction, it would be an argument that I do not understand the Monster group? My points do not depend on the particular choice of the model of the space \Lambda of the hidden variables. What I look for is if the model fulfills the conditions of Bell's theorem. So, I look if the \rho(\lambda) d \lambda do not depend on a,b. Or that A(a,\lambda) does not depend on b. Or that it always has values +-1 (and not sometimes 0, which would be the detection loophole). These are things I can check even without understanding the Monster group.

But, of course, S^3 is not the Monster group, so, don't worry, I understand it good enough. But it plays no role - as long as there are claims which are simply wrong - the claims that this construction is a counterexample for Bell's theorem - particular questions about S^3 do not matter very much.
Schmelzer

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### Re: A new simulation of the EPR-Bohm correlations

Joy Christian wrote: In any case my analytical Clifford-algebraic 3-sphere model as well as at least the latest simulation of the 3-sphere model have nothing to do with the missing data or loopholes. There is one-to-one correspondence between the simultaneously observed events by Alice and Bob and the initial states (u, s). So the model does not depend on detection or any other funny loophole. It is a true and final nail in the coffin of Bell's theorem.

So why you do not produce a simulation which makes this obvious? By creating elements (u,s) without any use of a,b during the computations? To create sets of random elements u or (u,s) in S^3 or TS^3 or so, which have a distribution \rho(u,s) du ds which does not depend on a, b, would be easy. Simply define this set before you define the a, b. If your claim is correct, this would be possible, even easy.
Schmelzer

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### Re: A new simulation of the EPR-Bohm correlations

I have made no claims that are even slightly wrong.

My analytical model and its latest simulation, namely http://rpubs.com/jjc/84238, are unequivocal counterexamples to Bell's theorem.

If someone does not see this, then it is their loss. Physics will move on whether or not they see the light. Their blindness is not my problem.
Joy Christian
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