Is this new version of the CHSH inequality valid?

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

Is this new version of the CHSH inequality by Richard Gill valid? Please see paper linked.

Yes
3
33%
No
6
67%
 
Total votes : 9

Re: Is this new version of the CHSH inequality valid?

Postby gill1109 » Sat Feb 08, 2014 1:02 pm

Dear Fred

I think you haven't read my paper carefully enough to see exactly what it is that (2) , (4) and (6) are saying. You need to distinguish between <AB>, <AB>_{ave}, and <AB>_{lim}. Each is defined pretty explicitly.

And yes, by the way, my paper *has* been read by a lot of smart people (that's important) and by a lot of important people (that's pretty irrelevant, but as you bring it up...).

I would say that remarks about Joy's model are "off topic" in this thread.

Richard
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Re: Is this new version of the CHSH inequality valid?

Postby Joy Christian » Sat Feb 08, 2014 1:14 pm

gill1109 wrote:...my paper *has* been read by a lot of smart people...


Either these people you refer to are not really smart, or they are too polite to tell you that your argument is simply wrong (for the reasons given in my previous posts).
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Re: Is this new version of the CHSH inequality valid?

Postby minkwe » Sat Feb 08, 2014 7:14 pm

I'll try to summarize my issues with Gill's paper below:

The central theme of the paper is the claim that "Bell's theorem (and its experimental confi rmation) should lead us
to relinquish not locality, but realism, as a universal physical principle."

My critique is two fold:
(1) The definition of realism employed in the paper is one that can be rejected immediately without need for experiment. It is a straw-man.
(2) The claimed experimental proof of Bell's theorem is invalid. It is only apparent because statistical mistakes have been made.

Now to the details:

(1) On page 2 second paragraph, Gill says:

This idea, called locality or, more precisely, relativistic local causality, is just one of the three principles. Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual de nfiniteness.

According to this, "The principle of realism" is the idea that outcomes of measurements which were not performed, exist. Obviously, if you did not do the measurement, the outcomes can not be said to exist. So this definition of realism, is equivalent to stating that:

"Results which do not exist, exist"

We can all agree that this is untenable and we do not need any experiments in order to discard such an idea.

But further down he says
"By existence of the outcomes of not actually performed experiments, we only mean their mathematical existence within some mathematical-physical theory of the phenomenon in question"

Here he appears to be saying he is not talking about physical existence, just "mathematical existence", whatever that means, with the obvious conclusion then that his paper must then be construed as an argument against the "mathematical existence" of hidden variables, or against mathematical realism, contrary to the earlier claims of demonstrating we must relinquish "realism, as a universal physical principle."

(2) See my next post.
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Re: Is this new version of the CHSH inequality valid?

Postby minkwe » Sat Feb 08, 2014 7:21 pm

(2) As concerns the claim that experiments violate the CHSH inequality:

Gill derives the CHSH by assuming that 4 functions A, A', B, B' exist at the same time. (Whatever his definition of the word 'exist'). After doing some algebra on those 4 functions he obtains the inequality

S = <AB> + <AB'> + <A'B> - <A'B'>, -2 <= S <= 2

Then in an experiment he measures <AB'> on one set of particles {1} measures <AB'> on ANOTHER set of particles {2}, <A'B> on yet another set of particles {3} and <A'B'> on yet another set of particles {4}. Note that in the experimental data, A and B exist for the first set of particles {1}, so let's call the correlation <A1B1>, and similarly A & B' exist for set {2}, to give <A2B2'>, and A' & B exist for the set {3}, to give <A3'B3> and also A' & B' exist for the set {4}, to give <A4'B4'>. Then using these correlations from 4 different disjoint sets of pairs of particles he calculates
<A1B1> + <A2B2'> + <A3'B3> - <A4'B4'>
And obtains a violation. from this violation, he then claims that "realism", simultaneous existence of the 4 functions (A, B, C, D) is untenable. Of course they do not exist in the experiment, in the experiment what exists is A1 & B1 at the same time, A2 & B2' simultaneously but at a different time, A3' & B3 simultaneously at a different time, and same for A4' & D4'. Yet, the conclusion being made in the paper is similar to the claim that (A1, B1, A1', B1') do not exist simultaneously for the set of particles [1], nor do (A2, B2, A2', B2'), (A3, B3, A3', B3'), or (A4, B4, A4', B4').

The elephant in the room is the fact that no experiment which measures <A1B1> , <A2B2'> , <A3'B3>, <A4'B4'> on different sets of particles, will ever be able to make any proclamation whatsoever about the simultaneous existence of (A1, B1, A1', B1') or (A2, B2, A2', B2') etc.
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Re: Is this new version of the CHSH inequality valid?

Postby minkwe » Sat Feb 08, 2014 7:29 pm

To further elaborate, an analogy which I've mentioned to Gill previously is the following:

Suppose I derived an inequality which related the head-size to the length of snakes in the amazon. Suppose then that an experimenter, say Gill, decides to test my inequality and he measures the head-sizes of 1 billion snakes in the amazon randomly chosen. Then he also measures the lengths of 1 billion completely different snakes also randomly chosen. From these measurements, suppose he calculates certain averages which violate my inequality. Can he then claim that his observed violation proves the suggested relationship does not exist between length and head-size? Of course not.

This is precisely the kind of statistical mistakes being made when experiments which measured <A1B1> , <A2B2'> , <A3'B3>, <A4'B4'> are being used to claim that (A1, B1, A1', B1') do not exist. Now mathematically speaking, we may agree that they do not exist in the equations, because he did not measure them. But that says absolutely nothing about the physical principle of realism. Maybe this is the sense in which Gill meant "mathematical existence". Either way, why would we expect (A1, B1, A1', B1') to exist simultaneously in the experimental data if we do not measure it. In other words, why do we expect to see a relationship between head-size and length if we never jointly measure them? As is obvious, no amount of random choice or law of large numbers can rescue us from the fatality of failing to measure what our claims are centered on.
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Re: Is this new version of the CHSH inequality valid?

Postby minkwe » Sat Feb 08, 2014 7:41 pm

Finally, let us examine the derivation to see if it holds up to the experiment. We can clearly see it if we follow Gills derivation starting with equation (1) where he does the factorization:

AB + AB' + A'B - A'B' = +/-2
A(B+B') +A'(B-B')
Obviously, the above is correct because trivially, one of the two terms (B+B) or (B-B) must be zero, while the other is 2 or -2. The terms are not independent, any two terms share a factor.

In experiments in which 4 different sets of particles are used, Gill believes we should still write:

A1B1 + A2B2' + A3'B3 - A4'B4' = +/-2

But this is false. A1, A2, A3' and A4' are 4 different random variables from 4 particle pairs, each free to have a different value, which means factorization is not possible which means we can just as easily have A1 = 1, B1 = 1, A2= -1, B2' = -1, A3' = 1, B3 = 1, A4' = 1 and B4' = -1, which would give us a value of 4 for the expression, clearly violating it. Contrary to the claims, the violation here is precisely due to the fact that we have used 8 different random variables to calculate the expression, when the original expression assumed we had just 4 with factorization possible. Proceeding to obtain the statistical version just like Gill did in proof 2, but taking into consideration the appropriate experimental fact, that we have 4 different ensembles, we end up with an inequality:

<A1B1> + <A2B2'> + <A3'B3> - <A4'B4'> <= 4

All the terms are independent. No shared factors. Revealingly, no experiment has ever been performed which violates this inequality. Note by the way that we have used the same random sampling assumptions to obtain this inequality which Gill used to obtain his, the only difference being that we have taken into consideration, the appropriate experimental facts, namely that the random variables in each set of particles are free from those in any other set disjoint to it.
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Re: Is this new version of the CHSH inequality valid?

Postby Joy Christian » Sat Feb 08, 2014 10:22 pm

Nice arguments, minkwe. The 500-pound canary in Gill's supposed "proof" is sitting in this mathematical step of his:

AB + AB' + A'B - A'B' = A(B+B') + A'(B-B')


In addition to your arguments, it is also worth stressing that B and B' are NOT occurring at the same time, or even in the same experiment. To be sure, B' could indeed occur instead of B in a given experiment, but it is complete nonsense to add or subtract counterfactually possible events in this manner. That would be equivalent to asserting that going either to New York or to London is equivalent to going to (New York+London). Need we say more how ridiculous Gill's mathematical step is? :lol: :lol:
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Re: Is this new version of the CHSH inequality valid?

Postby jdfriedgen » Sat Feb 08, 2014 10:42 pm

It seems to me that followings are ultimately won by political means, often and unfortunately regardless of the merit of the work. But I'm still curious as to Richard Gill's response to Joy Christian's:

"I DID NOT compute a different correlation to the usual one. I derived correlation E(a, b) = -a.b between measurement results A(a, L) = +1 or -1 and B(b, L) = +1 or -1, in a completely standard manner."
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Re: Is this new version of the CHSH inequality valid?

Postby Joy Christian » Sat Feb 08, 2014 10:54 pm

jdfriedgen wrote:It seems to me that followings are ultimately won by political means, often and unfortunately regardless of the merit of the work. But I'm still curious as to Richard Gill's response to Joy Christian's:

"I DID NOT compute a different correlation to the usual one. I derived correlation E(a, b) = -a.b between measurement results A(a, L) = +1 or -1 and B(b, L) = +1 or -1, in a completely standard manner."


To understand my statement you have to understand at least eq. (29) of this paper: http://arxiv.org/abs/1203.2529.

EPR-Bohm correlations are correlations among the binary points of a parallelized 3-sphere, no matter which representation of the 3-sphere you use to compute them.
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Re: Is this new version of the CHSH inequality valid?

Postby gill1109 » Sun Feb 09, 2014 2:22 am

jdfriedgen wrote:It seems to me that followings are ultimately won by political means, often and unfortunately regardless of the merit of the work. But I'm still curious as to Richard Gill's response to Joy Christian's:

"I DID NOT compute a different correlation to the usual one. I derived correlation E(a, b) = -a.b between measurement results A(a, L) = +1 or -1 and B(b, L) = +1 or -1, in a completely standard manner."


The answer depends what you consider to be Joy Christian's model.

(A) There is a two page summary on Christian's blog:

http://libertesphilosophica.info/blog/w ... 1/EPRB.pdf

(B) There is a computer implementation by Michel Fodje

https://github.com/minkwe/epr-simple/

(Note: Michel has two different simulations: a port of Chantal Roth's, and his own epr-simple; I refer to the latter).

(C) There is Christian's one page paper

http://arxiv.org/abs/1103.1879

which I analysed in http://arxiv.org/abs/1203.1504; Joy responded in http://arxiv.org/abs/1203.2529

In (A) and (B) the conventional (physicists') correlation is used: the average of the product of the outcomes. Since these are binary (+/-1) and since on average + and - 1 occur equally often, the means are zero and the standard deviation is 1, so the physicst's correlation is a statistician's corrleation too. I'll come back to some interesting differences between (A) and (B) in a moment.

In (C), see formula (5), the correlation is defined as the average of the product of the outcomes, divided by theoretical bivectorial standard deviations.

In (A), according to (A.9.2) and (A.9.3), it appears that the outcomes can take the value 0 as well as +/-1. The probabilities (A.9.4) - (A.9.5) should therefore be written as conditional probabilities: not only is eta_ab given, one also must condition probabilistically on non-zero values. Now the question is, on which?

Christian wants us to understand that the 0's don't occur at all because *before* choosing measurement directions a and b, one chooses a state, which corresponds to a pair (e0,theta0) which satisfies |cos(eta_xe0)| >= sin^2(theta0) for all x.

According to this reading there is no point at all in writing A(...) = 0 if ... since this never ever occurs.

However Michel only tests the criterion with x=a on one particle and with x=b on the other particle, and he computes correlations (for directions a, b) by collecting the pairs of particles from which both measurements had non-zero outcomes. Thus his correlation is taken over outcomes of measurements of plenty of non-states as well as of states.

To sum up:

Christian seems to me now to be propagating a different model (two page summary, A) from his earlier one (one page paper, C). I think of them as Christian 1.0 and Christian 2.0.

There are some mathematical obscurities in his two page summary which need to be cleared up.

There appears to be a serious mismatch between Christian's two page summary and Fodje's simulation.
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Re: Is this new version of the CHSH inequality valid?

Postby gill1109 » Sun Feb 09, 2014 3:09 am

I suggest to Minkwe that he carefully reads sections 2 and 9 of my paper. They are about event-based simulations of rigorous Bell-CHSH type experiments. No need to get into a philosophical muddle discussing what realism should or should not mean. Section 9 explains how, given a computer program like his, we would be able to construct the Nx4 spreadsheet discussed in Section 2, and deduce that CHSH should apply to the output of the computer experiment.

Why is his able to violate CHSH? It is not a *rigorous* experiment. The outcome "0" is allowed as well as +/-1. The observed correlations are computed on the post-selected samples, post-selected according to both particles getting detected. He needs to get rid of this bug. It will be a difficult job.

If he wants to use a "rigorous" (loophole free) inequality, he should consider using the Clauser/Horne (Eberhard) inequality. It corresponds simply to merging the outcomes 0 and -1 so that we have a proper experiment with binary outcomes and no missing particles. Unfortunately his statistics do not violate the Eberhard inequality.

Experiments were done on photons last year which did violate Clauser-Horne / Eberhard. I'm afarid that minkwe is not able to reproduce the statistics of those experiments.

For a careful discussion, in the context of quantum entanglement, of the notions of realism, locality and freedom, I refer you to Boris Tsirelson's exposition on citiziendium,

http://en.citizendium.org/wiki/entanglement_(physics)
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Re: Is this new version of the CHSH inequality valid?

Postby Joy Christian » Sun Feb 09, 2014 3:43 am

gill1109 wrote:To sum up:

Christian seems to me now to be propagating a different model (two page summary, A) from his earlier one (one page paper, C). I think of them as Christian 1.0 and Christian 2.0.

There are some mathematical obscurities in his two page summary which need to be cleared up.

There appears to be a serious mismatch between Christian's two page summary and Fodje's simulation.


The comments which led Gill to his sum up once again reveal that he has no understanding of the basic mathematical fact that one can use different representations to describe one and the same underlying structure. There is only one model---the one I constructed back in 2007. The rest are my attempts to explain the model to the uninformed and uninitiated by using different representations. There is absolutely no mathematical obscurity in any of my papers or their summaries. There is no mismatch of any kind between my two-page summary or the simulations of the model described in it. As I have already noted, the bottom line is the following:

EPR-Bohm correlations are correlations among the binary points of a parallelized 3-sphere, no matter which representation of the 3-sphere you use to compute them.
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Re: Is this new version of the CHSH inequality valid?

Postby Joy Christian » Sun Feb 09, 2014 4:01 am

gill1109 wrote:If he wants to use a "rigorous" (loophole free) inequality, he should consider using the Clauser/Horne (Eberhard) inequality. It corresponds simply to merging the outcomes 0 and -1 so that we have a proper experiment with binary outcomes and no missing particles.



THERE ARE NO ZERO OUTCOMES, either in my model, or in its simulation by Michel. The state is (e, t). The state is NOT e.

Since the joint probabilities of observed events predicted by my model are exactly the same as those predicted by quantum mechanics, the Clauser-Horne inequality is rigorously violated by both my model and its simulation by Michel. The violation of this inequality by my model has been explicitly discussed in this paper (see section A.3.2 on page 352): http://libertesphilosophica.info/blog/w ... hapter.pdf.
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Re: Is this new version of the CHSH inequality valid?

Postby Joy Christian » Sun Feb 09, 2014 4:19 am

gill1109 wrote:No need to get into a philosophical muddle discussing what realism should or should not mean.


This is odd. On the one hand Gill wants to make an *extraordinary claim* that there is a magic of non-realism in the world, and on the other had he wants us to remain muddleheaded about the very notion of realism. Why? Obviously because he wants to trick us into accepting a total nonsense like

AB + AB' + A'B - A'B' = A(B+B') + A'(B-B'),

where B and B' are not actual events but only counterfactually possible events. The quantity (B+B') here is saying that either going to New York or going to London is the same thing as going to (New York+London)! But, hey, let us not get into the philosophical muddle of the city called (New York+London). Just take his word for it.
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Re: Is this new version of the CHSH inequality valid?

Postby gill1109 » Sun Feb 09, 2014 6:18 am

(1) I do not make any extraordinary claim. The claim I make was made by Heisenberg, Schrödinger and Bohr long before Bell's work: namely that quantum mechanics brings intrinsic (irreducible) randomness into physics. The claim is accepted by many, many notable physicists today (Gisin, Zeilinger, Werner, Weihs, ...). John Bell himself agreed that quantum mechanics violated either locality, or realism, or no-conspiracy. His personal inclination was to reject locality, but he accepted that either of the other two alternatives were logical possibilities.

(2) Christian keeps repeating "there are no zero outcomes" but a glance at the output from minkwe's model shows there are lots. A glance at minkwe's description of his simulation affirms their presence.
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Re: Is this new version of the CHSH inequality valid?

Postby gill1109 » Sun Feb 09, 2014 6:46 am

It seems that many people have difficulty understanding how the CHSH inequality could possibly apply to experiments in which, in each run, a different pair of measurement settings are in use. I suggest they focus their attention on event-based computer simulation of such experiments. And carefully read sections 2 and 9 of my paper, together.

Sections 2 and 9 are both about event-based computer simulation of Bell-CHSH experiments. I concentrate on the memoryless case. (For simulations which use the memory of past runs to create new ones, a more complicated analysis is possible, using martingale theory, which I published earlier).

Here is a passage from Section 9, the emphasis is new:

"Suppose someone has invented a local hidden variables theory. He can use it to simulate N = 800 runs of a CHSH experiment. Typically he will simulate the source, the photons, the detectors, all in one program. Let us suppose that his computer code produces reproducible results, which means that the code or the application is reasonably portable, and will give identical output when run on another computer with the same inputs. In particular, if it makes use of a pseudo random number generator (RNG), it must have the usual “save” and “restore” facilities for the seed of the RNG. Let’s suppose that the program calls the RNG the same number of times for each run, and that the program does not make use in any way of memory of past measurement settings. The program must accept any legal stream of pairs of binary measurement settings of any length N. In particular then, the program can be run with N = 1 and all four possible pairs of measurement settings, and the same initial random seed, and it will thereby generate successively four pairs (A,B), (A′,B), (A,B′), (A′,B′). If the programmer neither cheated nor made any errors, in other words, if the program is a correct implementation of a genuine LHV model, then both values of A are the same, and so are both values of A′, both values of B, and both values of B′. We now have the first row of the N × 4 spreadsheet of Section 2 of this paper. The random seed at the end of the previous phase is now used as the initial seed for another phase, the second run, generating a second row of the spread- sheet. This is where the prohibition of exploiting memory comes into force. The second row of counterfactual outcomes has to be completed without knowing which particular setting pair Alice and Bob will actually pick for the first row."

minkwe's code is beautifully written, clearly structured. It is easy to adapt it to satisfy all of my requirements ... except for the requirement that the measurement outcomes can only be +1 or -1.

As long as the simulation also generates "no detections", it is not appropriate to use CHSH: one should use a Clauser-Horne or a chained CHSH inequality. The measurements have ternary, not binary, outcomes.

His simulation is a nice illustration of how the singlet correlations can be generated in a perfectly local realistic way if detectors do not always detect particles. So far, a loophole-free CHSH type experiment still has not been performed. The experts consider that it is within grasp (it is suggested that we will have to wait for about five years). At this moment, every experiment done till now can be given a local realistic explanation. I find it an exciting prospect that the definitive breakthrough may occur in our lifetimes. If it happens and is succesful, it will perhaps be the experiment of this century.

Last year the detection loophole was closed in experiments on polarization of photons, by two leading experimental groups (Vienna; Colorado). Those experiments did not yet have the necessary separation and timing of the two measurement stations in order to ensure against the locality loophole or the no-conspiracy loophole. However other experiments with photons did not have those two defects. Thus the photon polarization system is the first quantum system for which all three of the major experimental loopholes have been closed, albeit not yet simulataneously.
Last edited by gill1109 on Sun Feb 09, 2014 6:59 am, edited 1 time in total.
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Re: Is this new version of the CHSH inequality valid?

Postby Joy Christian » Sun Feb 09, 2014 6:57 am

gill1109 wrote:I do not make any extraordinary claim. The claim I make was made by Heisenberg, Schrödinger and Bohr long before Bell's work: namely that quantum mechanics brings intrinsic (irreducible) randomness into physics. The claim is accepted by many, many notable physicists today (Gisin, Zeilinger, Werner, Weihs, ...). John Bell himself agreed that quantum mechanics violated either locality, or realism, or no-conspiracy. His personal inclination was to reject locality, but he accepted that either of the other two alternatives were logical possibilities.


"Argument from authority" is a logical fallacy. The opinions of authorities is besides the point. You are indeed making extraordinary claims in your paper. You are explicitly making claims about the physical reality, and you are using questionable mathematics to justify these claims. Authorities have nothing to do with this.

gill1109 wrote:Christian keeps repeating "there are no zero outcomes" but a glance at the output from minkwe's model shows there are lots. A glance at minkwe's description of his simulation affirms their presence.


There are no "zero outcomes" (whatever you mean by "zero outcomes") either in my model or in Michel's simulation. The initial state is (e, t). It is not just e.
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Re: Is this new version of the CHSH inequality valid?

Postby gill1109 » Sun Feb 09, 2014 7:06 am

Joy Christian wrote:There are no "zero outcomes" (whatever you mean by "zero outcomes") either in my model or in Michel's simulation. The initial state is (e, t). It is not just e.


Yes the initial state is (e, t) in both your model and in Michel's simulation.

There are zero outcomes in Michel's simulation. Look at his description of his code. Look at the results which I posted at the beginning of this thread.

I ran his code with N = 1 million and extracted the data from the runs with Alice's angle 0 or 45 degrees, Bob's angle 22.5 or 67.5 degrees. (Angles are binned, bin-width = 7.5 degrees).

Setting combination 1, 1

Code: Select all
     -1   0   1
 -1   5  20 169
 0   26  24  24
 1  148  11   6


Setting combination 1, 2

Code: Select all
     -1   0   1
 -1  46  36 103
 0   36   0  35
 1  106  41  42


Setting combination 2, 1

Code: Select all
     -1   0   1
 -1   4  20 173
 0   24  24  27
 1  167  15   8


Setting combination 2, 2

Code: Select all
     -1   0   1
 -1   5  19 137
 0   15  52  25
 1  137  22   5
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Re: Is this new version of the CHSH inequality valid?

Postby Joy Christian » Sun Feb 09, 2014 7:46 am

gill1109 wrote:Yes the initial state is (e, t) in both your model and in Michel's simulation.


Good. So we agree at least about this much. I am no expert in programing, so I will let someone else respond to that part. From the perspective of my analytical model what we agree about is all I needed you to agree about. I am not too concerned about how one implements the above fact in the actual numerical simulation.
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Re: Is this new version of the CHSH inequality valid?

Postby minkwe » Sun Feb 09, 2014 11:27 am

gill1109 wrote:I suggest to Minkwe that he carefully reads sections 2 and 9 of my paper. They are about event-based simulations of rigorous Bell-CHSH type experiments. No need to get into a philosophical muddle discussing what realism should or should not mean.

I have read the paper carefully, my arguments are based on the content of the paper, which includes claims of "mathematical existence". I haven't brought up any argument which the paper does not prompt. It is odd to write a paper claiming that "realism as a physical principle is not tenable" and then not want to talk about philosophical issues.
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