Hi Everyone,

I have produced yet another simulation for the EPR-Bohm correlations which is more satisfactory and faithful to my 3-sphere model than previous attempts by myself and others. But before I describe it I want to thank Fred Diether, Michel Fodje, and Albert Jan Wonnink for ongoing discussions and help, as well as to some annoying, cynical, and persistent critics (such as Richard Gill) for keeping me on my toes about this.

So, without further ado, here is the new simulation I would like to show off: http://rpubs.com/jjc/84238.

For those not familiar with my work on Bell, perhaps the best theoretical discussion to understand this simulation can be found here: http://arxiv.org/abs/1405.2355.

There is plenty of explanation in the preamble of the simulation itself, but the basic idea is to have sufficient structure of the 3-sphere (which is part of a well known solution of Einstein's field equations of general relativity) constructed in the preamble of the simulation before the actual correlations are computed. The locally explicable strong (or "quantum") correlations then follow from the structure of the 3-sphere itself, and the Bell-CHSH as well as CH inequalities are duly violated.

I don't think it is possible to improve on what I (with help) have produced in this simulation, but of course I would be delighted to be proven wrong about this.

Enjoy ,

Joy Christian

I have produced yet another simulation for the EPR-Bohm correlations which is more satisfactory and faithful to my 3-sphere model than previous attempts by myself and others. But before I describe it I want to thank Fred Diether, Michel Fodje, and Albert Jan Wonnink for ongoing discussions and help, as well as to some annoying, cynical, and persistent critics (such as Richard Gill) for keeping me on my toes about this.

So, without further ado, here is the new simulation I would like to show off: http://rpubs.com/jjc/84238.

For those not familiar with my work on Bell, perhaps the best theoretical discussion to understand this simulation can be found here: http://arxiv.org/abs/1405.2355.

There is plenty of explanation in the preamble of the simulation itself, but the basic idea is to have sufficient structure of the 3-sphere (which is part of a well known solution of Einstein's field equations of general relativity) constructed in the preamble of the simulation before the actual correlations are computed. The locally explicable strong (or "quantum") correlations then follow from the structure of the 3-sphere itself, and the Bell-CHSH as well as CH inequalities are duly violated.

I don't think it is possible to improve on what I (with help) have produced in this simulation, but of course I would be delighted to be proven wrong about this.

Enjoy ,

Joy Christian

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:I have produced yet another simulation for the EPR-Bohm correlations which is more satisfactory and faithful to my 3-sphere model than previous attempts by myself and others.

http://rpubs.com/jjc/84238.

My critic remains unchanged.

For f>0 we have g = 0 if |v.w| < f, which excludes some pairs.

"# v and w are orthogonal to each other in S^3 when abs(colSums(v * w)) < f"

Thats ok with f=0 (if you use \le instead of <) but does not make sense for f>0. But, ok, let's accept your notion of "orthogonality", it does not change anything how you name it. The point is that g(v,w) =/= 0 excludes a lot of pairs v,w.

"t = function(v1, w1, v2, w2) {abs((sign(g(v1, w1))) * (sign(g(v2, w2)))) > 0 } # Puts a topological constraint on the distance function g(v, w) on S^3"

Name it a "topological constraint" if you like, names don't matter, but this extends the exclusion: All the v1,w1 excluded by g(v1,w1) =/= 0 and, similarly, all v2,w2 excluded by g(v2,w2) =/= 0 are excluded.

"A = +sign(g(a, u)) # Alice's measurement results A(a, u) = +/-1"

Not really. I assume sign 0 is 0, not? Thus, measurement results would be A(a, u) = +/-1 or 0.

"N = length((A * B)[t(a, u, b, u)]) # Total number of simultaneous events

# Metric {g, t} forbids the results (0,+), (0,-), (+,0), (-,0), and (0,0)"

You name it "metric forbids". But what is relevant is that it is not the preparation procedure alone, which decides what is forbidden, but one needs the actual choices a, b of Alice and Bob to find out if u is forbidden or not.

Nobody doubts that if one can exclude (or "forbid") some of the preparations u using the values a and b, one can easily violate Bell's inequalities. This is part of the detector efficience loophole (where the detector "knows" and can "forbid" the corresponding u based on this information) as well as the superdeterminism loophole (where the choices of Alice and Bob are known and can be used already at preparation time). So, the simulations contains nothing which would question Bell's theorem.

- Schmelzer
**Posts:**123**Joined:**Mon May 25, 2015 1:44 am

The simulation also contains nothing that would question the Pope's belief in the immaculate conception and the Ayatollah's belief in the prophesy of Mohammad.

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:The simulation also contains nothing that would question the Pope's belief in the immaculate conception and the Ayatollah's belief in the prophesy of Mohammad.

This remark would have been necessary, if the title would have been "A new simulation of the Pope's theory of immaculate conception" or "A new simulation of the Ayatollah's belief of Mohammed's prophesy".

- Schmelzer
**Posts:**123**Joined:**Mon May 25, 2015 1:44 am

Joy Christian wrote:The simulation also contains nothing that would question the Pope's belief in the immaculate conception and the Ayatollah's belief in the prophesy of Mohammad.

Since the true believer in Bell's by now decisively refuted "theorem" has not even been able to understand my simple comment, let me point out that his seemingly scientific comments on the simulation above are actually factually incorrect. One only needs to test the mathematical properties of the metric {g, t} defined in the simulation to recognize that the true believer is talking nonsense. It is abundantly clear that the metric mathematically excludes the results (+,0), (-,0), (0,+), (0,-) and (0,0), and as a result reproduces the strong correlations entirely as a consequences of the geometrical and topological structures of the 3-sphere as advertised.

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:One only needs to test the mathematical properties of the metric {g, t} defined in the simulation to recognize that the true believer is talking nonsense. It is abundantly clear that the metric mathematically excludes the results (+,0), (-,0), (0,+), (0,-) and (0,0), and as a result reproduces the strong correlations entirely as a consequences of the geometrical and topological structures of the 3-sphere as advertised.

The "true believer" does not doubt that "the metric" (whoever this is) excludes the results (+,0), (-,0), (0,+), (0,-) and (0,0) mathematically, and not, say, physically, metaphorically, or philosophically.

This does not change the fact, that "the metric" for this purpose uses the knowledge of the choices a, b, of Alice and Bob. The part of the u which has not been "mathematically excluded" by "the metric" can be seen in Gill's variant http://rpubs.com/gill1109/ChristianSampleSizes .

- Schmelzer
**Posts:**123**Joined:**Mon May 25, 2015 1:44 am

Schmelzer wrote:The part of the u which has not been "mathematically excluded" by "the metric" can be seen in Gill's variant http://rpubs.com/gill1109/ChristianSampleSizes .

Well, well. Gill has once again found a proxy to speak for him here, since he has been banned from this forum for unruly behaviour, just as he has been banned from several other internet sites (such as, for example, from Paul Snively's blog). Also worth noting is this paper of mine where I have exposed Gill's mathematical mistakes.

As for Gill's "variant" linked above, it only exhibits once again that neither of the two true believers in Bell have actually understood the details of the simulation, let alone the details of the analytical 3-sphere model. Over the years both of the true believers have persistently exhibited a mental block which prevents them from switching off their flatland --- R^3 --- prejudices and appreciate the geometry and topology of the 3-sphere. They are still arguing that if Earth is a sphere as I claim, then why aren't we all sliding off its curves. The u in question are in fact mathematically excluded by the metric, but the flatlanders are unlikely to understand that.

It is also important to record here the dishonesty in what Gill claims is my simulation code and he has only added two lines to it. In fact he has deliberately omitted the words "pre-ensemble" from my code to mislead the scientific community. This is not the first time Gill has employed this kind of dishonest strategy. Two other examples of such dishonesty by Gill are worth noting. In his very first critique of my work he attributes his equation (2) to me, but it has nothing to do with my model. Gill's purpose in doing this is simply to mislead the scientific community in broad daylight. Another example (actually several instances) is in his recent preprint which was rejected even by the arXiv moderators. In that preprint at various places he attributes several equations and other details to me, but in fact they are all either subtly or blatantly altered by him to discredit my actual model and mislead the scientific community. Such a dishonest strategy is an insult to the scientific process.

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:... it only exhibits once again that neither of the two true believers in Bell have actually understood the details of the simulation, let alone the details of the analytical 3-sphere model. Over the years both of the true believers have persistently exhibited a mental block which prevents them from switching off their flatland --- R^3 --- prejudices and appreciate the geometry and topology of the 3-sphere. They are still arguing that if Earth is a sphere as I claim, then why aren't we all sliding off its curves. The u in question are in fact mathematically excluded by the metric, but the flatlanders are unlikely to understand that.

The problem is that I do not even see a necessity to "understand" something about S^3, and in considering Bell's theorem even R^3 does not play any role.

The point is that a counterexample for Bell's theorem has to present two functions, A(a,u) and B(b,u), with values +-1. In the experiments, the a, b are elements of S^2, but to get the point it is sufficient to restrict this not only to S^1, but even to three or four values.

Now, u can be, of course, whatever you like, S^3 or S^7 or E_8 or the Monster Group, whatever it is, I have to care only that u is defined without knowledge of a or b. This is, fortunately, quite easy even without understanding the formulas. All one has to do is to look if some incomprehensible formula somehow depends on a or b. In this case, the result depends on a or b, thus, should not be used to compute u. This may be, at worst, a little bit unfair, if the dependence on a reduced to a dependence on a/a, thus, does in fact not exist, but such is life. If it is claimed that the result does not depend on a and b, then, please, write the program in a way that the computation does not use the values of a or b.

Then, there is the second simple thing I have to check, which is that A(a,u) and B(b,u) have values +-1, always, for every value of u which has been prepared without knowing a and b. The values should be, indeed, in {-1,1} = S^0, thus, the only topology I have to consider here is that of S^0, much easier than even your "flatland" R^3. And the only mathematics I need to check correlation formulas are the mathematics of computing the product A(a,u) B(b,u), which is also not a product of some S^3 or S^7 or some Monster group, but of S^0.

So, even if the simple math of S^3 would be too high for me (LOL), the point is that it is not even necessary to find the errors in your programs, which make them irrelevant as counterexamples to Bell's theorem.

The book "The True Believer" you have linked is, by the way, a nice, interesting book, I can recommend it too. And, I would guess, you know yourself that naming those who don't accept your "refutation" "true believers" is cheap polemics without a base nor in reality, nor in the book. Because the book is about participants in mass movements which want to change society, while the few defenders of Bell defend an accepted mainstream theorem, thus, in this question quite conservative.

- Schmelzer
**Posts:**123**Joined:**Mon May 25, 2015 1:44 am

Schmelzer wrote:The problem is that I do not even see a necessity to "understand" something about S^3, and in considering Bell's theorem even R^3 does not play any role.

Then there is nothing further I could possibly discuss with you. You simply do not get it, and you will never get it. You are welcome to your flatland.

I have explained my reasoning many times before, so anyone who wishes to understand my model can visit this page of my blog.

Here I simply want to stress that what Gill has produced at the above link is complete nonsense. It has nothing to do with my model. It is his yet another dishonest attempt to discredit my work (for example, just look at "expand = 4" in the picture he has produced; just replace it with "expand = 1" and you will see what I mean).

Finally, if anyone wishes to truly understand the above simulation should actually read the theoretical analysis present in this paper: http://arxiv.org/abs/1405.2355.

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

http://libertesphilosophica.info/blog/disproof-of-bells-theorem-book/ wrote:... this mistake lies in the formulation of the very first equation of his famous paper. The correct form of his proposed functions to reproduce the quantum correlations local-realistically must be

instead of

for them to provide a complete local description of the physical reality demanded by Einstein.

S^3 contains, of course, also a subgroup S^0 = {-1,1}, and if the values would be in this subgroup, nothing would change at all. You could as well use some embedding of S^0 into whatever group one likes. So, behind this replacement is, in fact, the trick that the values are not in the subgroup Z_2 of SU(2) created by {E,-E}, but in some direction depending on a resp. b. And, then, the multiplication gives something different from +-1, thus, we have something completely different from the experiment.

Because Bell's theorem is about are the results of the measurements, which are simply numbers, and, when the correlations are computed, multiplied like numbers. To compare with these experiments, and the way the experimenters handle the results A, B of the experiments, one has to do what the experimenters do with the measurement results - write down numbers +1 or -1 and then multiply them following the rules of Z_2 = S^0.

- Schmelzer
**Posts:**123**Joined:**Mon May 25, 2015 1:44 am

Schmelzer wrote:S^3 contains, of course, also a subgroup S^0 = {-1,1}, and if the values would be in this subgroup, nothing would change at all. You could as well use some embedding of S^0 into whatever group one likes. So, behind this replacement is, in fact, the trick that the values are not in the subgroup Z_2 of SU(2) created by {E,-E}, but in some direction depending on a resp. b. And, then, the multiplication gives something different from +-1, thus, we have something completely different from the experiment.

Please do not make bogus claims like these (they remind me of Gill) without actually reading what I have written and explained on my blog page I have linked above.

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

In response to the bogus criticism of my simulation by Gill linked above, I have revised the simulation. I have added a new figure which correctly displays the ratio of the total number N of the simultaneous events observed by Alice and Bob and the corresponding initial states (u, s) of the spin system: http://rpubs.com/jjc/84238.

As one can see, the correct figure is somewhat different from what Gill claims it should be! It exposes the fact that Gill has no understanding of my local model.

As one can see, the correct figure is somewhat different from what Gill claims it should be! It exposes the fact that Gill has no understanding of my local model.

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

Schmelzer wrote:Because Bell's theorem is about are the results of the measurements, which are simply numbers, and, when the correlations are computed, multiplied like numbers. To compare with these experiments, and the way the experimenters handle the results A, B of the experiments, one has to do what the experimenters do with the measurement results - write down numbers +1 or -1 and then multiply them following the rules of Z_2 = S^0.

Except the quantum experiments don't ever really violate Bell-CHSH. The bound that those experiments are constrained by is 4 not 2. Basically, Bell-CHSH is "rigged" against local hidden variables so it is false. Easy to see by simple inspection of how Bell derived CHSH. If each CHSH term is independent, the bound is 4; if they are not independent, the bound is 2. And the experiments use independent terms in their CHSH calculations. The whole Bell thing is completely bogus. You can even see by simple inspection that the 3 term inequality is bogus.

- FrediFizzx
- Independent Physics Researcher
**Posts:**1154**Joined:**Tue Mar 19, 2013 6:12 pm**Location:**California, USA

Joy Christian wrote:Please do not make bogus claims like these (they remind me of Gill) without actually reading what I have written and explained on my blog page I have linked above.

I have not only read, but even quoted what I have considered the most important error.

If the +-1 are only the subgroup defined by {-E,E} of SU(2), then explain please why in the picture there are three obviously different points (one for A, one for B, another one for AB) assigned with labels +-1. And this:

http://libertesphilosophica.info/blog/disproof-of-bells-theorem-book/ wrote:That is to say, his argument simply does not go through without the assumption of totally disconnected set \cup\,S^0 as the set of all possible measurement results (actual as well as counterfactual).

also presupposes the use of something different than -+1 as a measurement result.

http://libertesphilosophica.info/blog/disproof-of-bells-theorem-book/ wrote:Because then the measurement results \pm\,1 occur as points of an absolutely parallelized 3-sphere, which is the set S^3 of unit quaternions. As a result, we must specify the joint probability distribution for the occurrence of the four pairs of measurement results on such a 3-sphere,

Of course, not, because the measurement results, factual as well as counterfactual ones, are +-1, and the only operations which matter to compute E(a,b) are multiplication, which gives a result inside +-1, and then addition to obtain averages. If Z_2 is somehow embedded into whatever group you like which contains a Z_2 subgroup, the remaining part of the group plays no role at all.

So, or you introduce at some point values of A(a,l) which are not +-1, then the whole game has nothing to do with the experiments, where the results are always +-1, even the counterfactual ones. Or they are always +-1, then the remaining part of SU(2) is as irrelevant as would be the remaining part of the Monster group if you would have embedded it there.

- Schmelzer
**Posts:**123**Joined:**Mon May 25, 2015 1:44 am

Joy Christian wrote:In response to the bogus criticism of my simulation by Gill linked above, I have revised the simulation. I have added a new figure which correctly displays the ratio of the total number N of the simultaneous events observed by Alice and Bob and the corresponding initial states (u, s) of the spin system: http://rpubs.com/jjc/84238.

As one can see, the correct figure is somewhat different from what Gill claims it should be! It exposes the fact that Gill has no understanding of my local model.

It only exposes the fact that you don't get the elementary point that the initial states should not depend on a and b, because a and b are unknown. But your computation of the number of "initial states" depends on a and b:

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.

- Schmelzer
**Posts:**123**Joined:**Mon May 25, 2015 1:44 am

Schmelzer wrote:It only exposes the fact that you don't get the elementary point that the initial states should not depend on a and b, because a and b are unknown.

The initial states do not depend on a and b, because --- as anyone can see from the simulation --- they are unknown to both Alice and Bob, living in S^3, not R^3.

I have no interest in convincing either you or Gill. The only reason I respond to you and Gill is to prevent other onlookers from being hoodwinked by your nonsenses.

Also,

please do not make bogus claims like the above (they remind me of Gill) without reading what I have written and explained on my blog page I have linked above.

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

By the way, as a quick check one can add the following few lines in the simulation (at appropriate places) to see that the claims made by Gill and his proxy are false:

M = 1000

(N = length(A[t(a, u, b, u)]))

## [1] 673

(L = length(s[t(a, u, b, u)]))

## [1] 673

(J = length(t(a, u, b, u)))

## [1] 1000

The lengths of N and s in S^3 are the same, as they must, but the length of t(a, u, b, u) is equal to the length of the pre-ensemble M in R^3, independent of a and b.

M = 1000

(N = length(A[t(a, u, b, u)]))

## [1] 673

(L = length(s[t(a, u, b, u)]))

## [1] 673

(J = length(t(a, u, b, u)))

## [1] 1000

The lengths of N and s in S^3 are the same, as they must, but the length of t(a, u, b, u) is equal to the length of the pre-ensemble M in R^3, independent of a and b.

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:By the way, as a quick check one can add the following few lines in the simulation (at appropriate places) to see that the claims made by Gill and his proxy are false:

M = 1000

(N = length(A[t(a, u, b, u)]))

## [1] 673

(L = length(s[t(a, u, b, u)]))

## [1] 673

(J = length(t(a, u, b, u)))

## [1] 1000

The lengths of N and s in S^3 are the same, as they must, but the length of t(a, u, b, u) is equal to the length of the pre-ensemble M in R^3, independent of a and b.

First of all, thanks for acknowledging in this way that the length of N = length(A[t(a, u, b, u)]) and L = length(s[t(a, u, b, u)]) is 673 and not 1000.

To understand why (J = length(t(a, u, b, u))) gives 1000, let's look at the definition of the length in R. t is not an array, but a function. What could be

the length of a function or expression? The tutorial http://cran.r-project.org/doc/manuals/r ... -intro.pdf helps:

p. 7 wrote:the value of the expression is a vector with the same length as the longest vector which occurs in the expression

Thus, the vector computed by t(a, u, b, u) has the same length as the longest vector in the argument list, which is u, with length 1000.

Why, then, we get a smaller length for L = length(s[t(a, u, b, u)])? Here, we have to check what is the meaning of s[t(a, u, b, u)]. Let's see:

p.10 wrote:A logical vector. In this case the index vector is recycled to the same length as the vector from which elements are to be selected. Values corresponding to TRUE in the index vector are selected and those corresponding to FALSE are omitted. For example

> y <- x[!is.na(x)]

creates (or re-creates) an object y which will contain the non-missing values of x, in the same order. Note that if x has missing values, y will be shorter than x.

Thus, s[t(a, u, b, u)] is a new vector, which consists of those elements of s for which t(a, u, b, u) is true. Let's look what is s itself:

s = runif(M, 0, pi) # Initial states of the spins are the pairs (u, s) in S^3

A vector of length M, described as the initial value.

Instead, s[t(a, u, b, u)] is a vector of much shorter length, 673<1000, which denotes those initial values which are accepted after one knows the values of a and b.

So, please don't sell us an expression like length(s[t(a, u, b, u)]), which obviously depends on a, b, as an initial value s which does not depend on a,b.

So, everything as expected, the most difficult thing was to google for an intro into the language R which I have never used before, to clarify if my naive guesses about the meaning were correct.

- Schmelzer
**Posts:**123**Joined:**Mon May 25, 2015 1:44 am

Although I have said this many times before, it seems important to me that I should elaborate on why Bell devotees like Richard Gill and his proxies continue to have so much difficulty in understating my simple counterexample to Bell's "theorem", and in particular this current simulation. The fundamental difficulty they are having is in switching from the conventional R^3 perspective to the S^3 perspective on which my counterexample is based (see, for example, the discussions 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 devotees 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:

Needless to say, the previous post with its seemingly scientific content is very much a victim of having been locked up in deeply entrenched R^3 prejudices.

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 devotees 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:

Needless to say, the previous post with its seemingly scientific content is very much a victim of having been locked up in deeply entrenched R^3 prejudices.

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

OK, so Gill is now sending me private emails about the current simulation, because he is banned form this forum. He is sending me emails about what he perceives to be an issue with the current simulation. I am, however, as unimpressed by his concerns as by the above comments by his proxy.

The bottom line is that both Gill and his proxy are confusing the Picasso with a wooden frame on which it has been mounted. 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!

What exists, according to my model, is S^3 and the real states (u, s). 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. Only the ratio N/L has a physical meaning. And when N/L is plotted as in my simulation, we find that it is always constant and equal to 1, regardless of the settings. So, please, the pre-ensemble does not exist! And therefore what Gill has been plotting, namely N/M, is completely meaningless.

The bottom line is that both Gill and his proxy are confusing the Picasso with a wooden frame on which it has been mounted. 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!

What exists, according to my model, is S^3 and the real states (u, s). 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. Only the ratio N/L has a physical meaning. And when N/L is plotted as in my simulation, we find that it is always constant and equal to 1, regardless of the settings. So, please, the pre-ensemble does not exist! And therefore what Gill has been plotting, namely N/M, is completely meaningless.

- Joy Christian
- Research Physicist
**Posts:**1625**Joined:**Wed Feb 05, 2014 3:49 am**Location:**Oxford, United Kingdom

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