Ed, a clarification:
To be clear, that "oops" in "Gordon Watson replied on Mar. 7, 2015 @ 23:22 GMT" (or anywhere else here) refers to MY "oops". Like that equation I messed up -- and will fix when I get those further clarifications requested in the above "oops" post.
Cheers; Gordon
Ed, thanks to your recent clarifications I can at last pin-point my concerns re your model:
1. "Bell's hidden constraints" (your term; my [В±1]) are hiding in your model.**
2. Your E(AB) -- in my terms -- being simply twice* the E(AB|classical), is unphysical.**
3. *The factor of 2 arises from the value of your X being в€љ2; see notes hereunder.
4. Given #2, the component probabilities in your model will not be true.
5. I make no reference here to your "Energy Exchange Theorem".
6. I trust you will be equally analytical if my FQXi2015 is accepted. It addresses (and, I believe, resolves) concerns similar to those addressed in your essay: re Bell-v-Einstein it settles the physics in Einstein's favour. It also expresses a need to relate my notation and terminology to that of QM.
.................................
Ed, from "Edwin Eugene Klingman replied on Mar. 7, 2015 @ 20:03 GMT":
"Given the dynamics of a 3-D spin vector with a 3-D velocity in a 3-D field and a 3-D gradient, one can generate some rather complex math. But physically, one sees that, in Stern-Gerlach, the deflection is caused by the force of the gradient on the magnetic moment. If the magnetic moment is aligned with the field, the force is maximum and hence the deflection is maximum. Call this deflection X and calculate that it is given by the first term in parentheses in equation (4).
If the spin is (initially) not aligned, then the force is less than maximum, and I use energy-exchange physics to calculate how much less and show it as x in equation (4). Thus to get the actual deflection you must calculate X-x. I think you'll find that this takes care of the sign you've been so worried about.
Alice's deflection then ranges from full max to full min, based on the local angle Оё between her spin and her field, (a,О»)."
..................
Ed, with thanks for the above, I trust the following will help you understand my concerns.
In seeking to understand your deflection calculations, I introduced X and you have now (as above) introduced the term X-x = "actual deflection" -- which is what I sought to understand. So let my X now be "the first term in parentheses in equation (4)". X is therefore non-negative in your formulation.
Let Alice's 'actual deflection' be О"x; Bob's О"x'. Then we have:
О"x = X-x = X - X(1-cos(a,О») = Xcos(a,О»). (1)
О"x' = X-x' = X - X(1-cos(b,О»')) = X(cos(b,О»')) = -Xcos(b,О»). (2)
Thus, in preparing to compare the QM result with your own:
E(AB|QM) = -a.b; (3)
which yields, for b = a:
E(AB|QM, b = a) = -1; (4)
for comparison with your model, using (1)-(2):
E(О"x.О"x'|EEK) = E((Xcos(a,О»)).(-Xcos(b,О»))) = -X2.E((cos(a,О»).(cos(b,О»))); (5)
which yields, for b = a:
E(О"x.О"x'|EEK, b = a) = -X2.E(cos(a,О»)).(cos(a,О»)) (6)
= -X2N-1 ОЈ(cos2(a,О»j): ОЈ = ОЈjN; j = 1, 2, ..., N; N large: (7)
= -X2/2; since О»j is a random variable and so N-1 ОЈ(cos2(a,О»j) = 1/2. (8)
= -1: IFF X2 = 2 and your model is to match QM, per (4); (9)
X (= в€љ2) being the first term in parentheses in your key equation (4).
.................
PS: Ed, the model you use is the same as the appealing one in equations (3)-(6)** at http://viXra.org/abs/1406.0184 - version 1 version 1. But there I explained the physical significance of those (shortcut stepping-stone) equations and added the QM equations at (8)-(13). I took the short-cuts out of a later version that I also sent to you and others (11 July 2014); the shortcuts had served their purpose.
NB: **Each "Bellian constraint" [В±1] that you reject is implicit in these equations (3)-(6) -- and therefore in your model -- because:
в€љ2cos2s(a,О») is shorthand for в€љ2[+1]cos2s(a,О»)+в€љ2[-1]cos2s(a,О»'), etc., (10)
-- which is simply в€љ2 times the related classical probabilities but unphysical and therefore insufficient to deliver all the QM probabilities --
with s= 1/2 in the model you presented: replace X by в€љ2 in all the above equations and in your essay to see the underlying (but unphysical) model.
The above explaining my long-standing concerns, and happy that we share similar concerns re Bell, etc., with best regards; Gordon Watson
E & OE.
Dear Edwin
Thanks for reading and commenting on my essay. Looking through the comments on your essay I must admit to some gratitude that you kicked the hornets' nest first ;-) EPR-Bell has subtleties associated with at least the following points:
1.Local
2.Causal
3.Deterministic
4.The correlation result itself
5.Distinction between theory and experiment
It isn't possible to address all these in the essay character count, leaving every author who considers Bell hanging on at least one point. I address points 2-5 but am left hanging on the connection between points 1 and 2. I see that your model has the correct correlation result through meeting the JC result: correlation between two results involving S0 over a S2 spatial subspace from comes from S3. I also note that your consideration of point 5 has similarities to mine:
•Dirac eigenvalue map - over underlying-reality in my terms
•Pauli eigenvalue map - over experimental-reality in my terms
As you commented on my essay, my hidden propagator dynamics approach is more general than your specific example, but from your essay I cannot tell if your model would be an example of my general HPD result or not. So can I ask you about your position on:
1.Am I right in thinking that your point about the two eigenvalue maps can be characterised as a distinction between the true underlying physics and what is measured by experiment?
2.From the point of view that these is a distinction between underlying physics and what is being measured, the terms local, causal and deterministic become ambiguous unless it is made clear whether they are referring to the underlying physics or experimental measurements. Although the suppositions you make seem to be that your model is causal and deterministic in terms of the underlying physics, does that actually mean the correlation result is local and deterministic?
Best wishes,
Michael
Dear Michael,
Thanks for your well thought out comment on my essay. You're welcome re. kicking the hornets nest!
Your five points are well chosen, and, as you say, difficult to nail down in the allotted word count. You ask specifically whether the Dirac eigenvalue map, is over underlying-reality (in your terms) while the Pauli eigenvalue map is over experimental-reality.
First, the issue is covered in much more detail in Spin: Newton, Maxwell, Einstein, Dirac, Bell, which I hope you find time to look at. It is my reference (4).
The underlying reality implied by Dirac's relativistic equation is interpreted as 'spin' but, as I note, there is no exact eigenvalue equation for his 4-spinor solution. Instead, the Foldy-Wouthuysen integral transformation is imposed to produce (to any desired order in v/c) a two-component equation that can be put in one-to-one correspondence with Pauli, but does not treat spin, per se. Instead, it is a helicity eigenvalue equation with implications discussed in reference (4).
Pauli, on the other hand, is a constant-field-solution with Hamiltonian based on mu.B, which is a provisional eigenvalue, provided the field is constant; which it is not in Stern-Gerlach. To model Stern-Gerlach appropriately (which Bell does not do!) one must add the gradient term to the Hamiltonian, which does not yield the binary +/-1 eigenvalues, but instead yields a scattering continuum. Because Bell [and his legion of supporters] assume that they are measuring spin directly, and assume that Pauli's equation does apply, they force the experimental results to equal +/-1 despite that the measured scattering is clearly not a point but a continuous distribution. Thus they misinterpret the experimental reality, which is the scattering continuum, in favor of their desired result, which is the spin projection. The results of the experiment do indicate two final spin states, since, with energy exchange, the spins do either align or anti-align, whatever the initial state, but this completely discounts, in effect erases, the additional "hidden" information derived from the initial spin, which is in a random direction.
After erasing the underlying physical reality information, they cannot compute the actual correlation, and draw conclusions of non-locality from this basic mistake. I show that when the actual underlying physics [of energy exchange] is taken into account, my local model yields exactly the -a.b of quantum mechanics and of experiment.
You then ask if my causal and deterministic model in terms of the underlying physics actually means the correlation result is local and deterministic? That's a good question. I had not asked myself exactly this question, but would probably have answered yes. But I'm not sure. The inputs to the experiment are the random initial spin's, and the local outputs are causally determined. But the correlations over these outputs are still a statistical quantity, reflecting, in some manner, the random distribution of inputs. Thus, each run of 300 (a,b)-angles times 10,000 spins per angle [reflected in my results] yields the -a.b cosine shape of the curve but with the nonzero 'thickness' of the lines as shown in my figures. If instead of 3 million points I based the results on 3 billion points, the line should be much thinner. At what point does the statistical data become a cosine curve of no thickness? I don't know. In the limit that's what I would expect. Does that mean the correlation is local and deterministic? You decide.
My very best regards,
Edwin Eugene Klingman
Gordon,
Above, you claim that "Your E(AB) ... being simply twice* the E(AB|classical), is unphysical."
First, you are deriving a non-local equation by including a, b, λ, and λ' in your equation. These never appear in the same place in a local solution. In my model they are calculated locally and only the numeric result is sent to the statistical module. To understand this, assume that Alice calculates [according to the energy exchange physics] the number 36. Did this come from 1x36, or 2x18, or 3x12, or 4x9, or 6x6? These are local numbers that no one but Alice knows. Similarly for Bob. So when you derive an expectation value with all of the local values in one place, as you do, you have already lost locality in favor of non-locality.
My local model only correlates the actual results, which do not contain explicit local information, but only the results of the local physics. Your analysis, both here and in your other work, always yields a non-local calculation of the correlation.
You are showing exactly the behavior to be expected when the focus shifts from physics to math. Of course the math has to be correct! Bell's math is correct, and my math is correct. It is Bell's physics where the problem lies. And it is your unwillingness to focus on physics, while worrying the math to death that is the distraction.
Do you believe that, for every experiment Bell considers, that (ignoring the actual spread) the experimental results are +1 or -1? Of course not. Instruments must be calibrated, and, in some instances, normalized.
By focusing only on math, you set X = sqrt(2) and claim my result, proportional to X-squared, is off by a factor of two. But if you bothered to think about what X is, you would see your error. X is the term calculated by dividing the field strength by the gradient, and these are not only not known exactly, but extremely difficult to measure, and vary from experiment to experiment, and this does not in any way affect the interpretation of the experiment.
So your assumption that X is constant, which supposedly leads to an error in my analysis, is a mistake you make due to ignoring the physics. A major theme of this essay contest is how math leads physicists astray. Your math is leading you astray. Please stop and think about the physics, before making more such claims.
Bell's theorem mistakenly forces the outcomes to +/-1, but he does correctly insist, per EPR, that when a = b, there is perfect correlation, -1. It should be obvious that this is possible for any gradient only if the result of the correlation calculation is normalized to fit this known data point. When I normalize the data the actual form and strength of the field and its gradient are effectively adjusted (as Bell does!) to yield the physically meaningful correlation. Your math is not physically meaningful, and in fact, by ignoring the physics and focusing on the tool, you have tricked yourself.
FQXi is to be congratulated for choosing a topic that, in many essays, focuses attention on the fact that, as Alma Ionescu says,
"Mathematical physics is only as good as physical insight."
Edwin Eugene Klingman
Gordon,
There is so much confusion above and so many mistakes in your work that I'm breaking the chain of this thread and summarizing it below at the Mar. 10, 2015 @ 00:17 GMT. Please, before filling my thread with further confusion, try to digest my response.
Edwin Eugene Klingman
Ed,
To be clear: E(AB|EEK) = 2E(AB|classical equivalent) is the correct result. That is not, and has never been, in dispute!
Here's the problem: Your model, based on deriving the classical result multiplied by 2, will also deliver the component classical probabilities times 2. These are NOT the correct (experimentally available) component probabilities, per QM. So I would be pleased if you would bring your component probabilities into the discussion.
In other words, your model satisfies only one boundary condition; that of E(AB|EEK) = 2E(AB|classical equivalent) = E(AB|QM) by deriving E(AB|classical equivalent).в€љ2.в€љ2.
I'll expand on this in my (hopefully final) comprehensive reply to your: Author Edwin Eugene Klingman wrote on Mar. 10, 2015 @ 00:17 GMT
To that end, to ensure that I can be comprehensive:
1. Could you please answer my questions at: Gordon Watson replied on Mar. 5, 2015 @ 20:35 GMT
2. Would you elaborate on the role of high-level Mathematica in your model, please. Or refer me to where this is discussed.
3. Re the neutron example (giving scattered results) at: "Author Edwin Eugene Klingman wrote on Feb. 9, 2015 @ 23:03 GMT." What was the source of the data for that please?
Many thanks; Gordon Watson
Gordon,
Please digest the information I have given you. You show no sign of understanding it.
As I have expressed to you several times, and has been proved on other FQXi threads over thousands of comments, as soon as one gets into the mathematical details the physics goes out the window and all comments begin to focus on irrelevancies. If you doubt this go back and review the thousands of JC comments.
My essay in this contest is intended to present a local model that I have described in full detail and that I have shown the results of in figures on page 7. Those results produce the cosine correlation curve that Bell claims to be impossible. They were derived from the equations and in the manner that I have described here numerous times. If you believe that is not a cosine curve correlation on page 7 simply state so and we can terminate this series of exchanges. Otherwise, none of these suggestions and criticisms that you have made above bear any relevance to that curve. My focus in this essay contest is not upon convincing you that I know how to do math. It is on convincing physicists who believe that Bell proved it is impossible to derive that curve. The important aspects of the problem have to do with the physical reasoning that led to Bell's mistake, not with any mathematical questions. No math, and probably not even experiments, will convince the Bell believers unless and until they understand the error in physical reasoning that Bell made. That is where I intend to keep the focus. No one besides you is questioning the math. They are arguing the physics. That is where the appropriate argument lies.
As for questions at 20:35 on March 5: 1.) No. 2.) Yes, it uses the same random inputs. Each run of the model is with and without the constraints applied. 3.) I generate random a, b, and λ. That is merely the distribution in this run based on 3 million random numbers. It will change slightly with each run. 4.) Theta has already been discussed, as well, I believe, as the 3D nature of a and b.
For the reasons I have explained several times I am not going to go into the Mathematica code in this forum.
I do not recall the exact source of the neutron data, and it has zero relevance to my essay. My essay does not in any way depend on the neutron data which I found by googling "neutron and Stern-Gerlach" in response to a comment from Tim.
Your insistence stated above in "Here's the problem" tells me that you have not in any way understood my answer to your previous comments. You inject square roots of two into a model that has no such entities. Please take a little time to understand the answers I have already given you. It is not yet clear to me that you have the slightest comprehension of the model that I describe in my essay and have described to you, because your comments bear little relevance to my model.
You state above: "I would be pleased if you would bring your component probabilities into the discussion." I do not use "component probabilities" in my analysis or in my calculations, other than the random distribution of a, b, and λ. Apparently you wish to formulate my model in terms of your model, which is a nonstandard model, and this is of no interest to me. As you know I was much taken with your symbolism that represented the transformation from the initial state to alignment with the final state, (λ -> a) and I still think that it is a bridge between classical and quantum mechanics that has much to recommend it. But I have no interest in comparing my model to your paper 1406.0184, which is one I never signed off on. In your #13 on page 3 in that paper you constrain Alice's output to +1 and -1. I have explained dozens of times in this series of comments that that is a problem. Your nonstandard treatment of the problem changes nothing with respect to my essay and my local model. As I explain in the following comment your model is non-local because you bring all of the parameters together in a way impossible for a local model. My local model does not ever bring these parameters into one place. It does not deal with the probabilities other than the actual post-experiment probability distribution of correlated local results.
In an earlier series of comments someone wanted to compare my model to his nonstandard theory treating spin as simply 'a bit of information'; my response was that we can just agree to disagree. If you feel the need to bring more arguments from your nonstandard treatment into this thread I would ask that you present it in-line here. I do not intend to expend any more effort on irrelevant comparisons to your nonstandard treatment. My focus is and will continue to be the physical reasoning that led Bell to his false conclusions about non-locality.
Edwin Eugene Klingman
The Klingman Model (TKM). Problem 1: Alice's calculation.
In all Bell-tests known to me, Alice is the agent (human or robot) that freely sets the direction a of detector A. So Alice is correctly shown "out of sight" in top figure, p.6: for she (normally) has no other role to play.
However, at p.6, Alice calculates local deflection ﾎ"xj via eqn (4): which may be written
ﾎ"xj = X - X(1-cos(a,ﾎｻj)) = Xcos(a,ﾎｻj); (1A)
where X is the first term in parentheses in (4).
Given that Alice knows a: how does she make this calculation?
PS: On p.6 it says that "Bob will see initial spin ﾎｻ' = -ﾎｻ ...". I'm taking this to be a colloquialism and that such variables cannot be seen?
Gordon Watson: a local realist interested in the physics behind TKM.
Gordon,
Bell states that "since the quantum mechanical wave function does not determine the result of an individual measurement, this predetermination [ i.e., a = b => -1 ] implies the possibility of a more complete specification of the state." In my local model that more complete specification is the initial spin, λ, which has dynamical significance. What is in question is the physics of this "hidden" variable which is 'hidden' from quantum mechanics. It may or may not be hidden from Alice and Bob. Whether or not it is measurable is not specified by Bell's theorem. There are several cases possible. If Alice knows the value of λ, she can compute the deflection. If she does not know λ, the deflection will still be determined by the laws of energy exchange physics, and will be the result as I have specified. In that case, in principle, Alice can recover the value of λ (or at least the value of angle (a, λ) that the spin makes with the local field) from the actual deflection, which she measures and sends to the statistical unit. Same for Bob. It is these measured values, determined by the energy exchange physics, that determine the correlation. In addition the theory can be checked by preparing a known λ and presenting it to Alice, and -λ to Bob.
Edwin Eugene Klingman
Thanks Ed; it's good to see some agreement returning between us. I hope to show that I understand the physics of your local model very well ... and that some clarifying simplification is possible. Since we each proclaim ourselves to be "local realists", I suspect that we might only differ when it comes to a definition of "realism".
Now, re simplification: I would have your Alice be exactly the Alice that is discussed in Bell-tests. She simply sets a once -- ie, once for each each experimental run -- and has a snooze.
While she sleeps your "black-box" A will send each ﾎ"xj to your module D until an experimental run of N paired-tests has been conducted (N large). Similarly Bob's box B sends each paired ﾎ"x'j to your module D.
I accept: (i) independent of Alice and Bob, it is these paired ﾎ"s that determine the correlation; (ii) in addition your theory can be checked by preparing a known ﾎｻj and presenting it to Alice, and a paired ﾎｻ'j to Bob.
I must run right now (so E & OE), but if you'd let me have your views on the above simplification (I believe it avoids unnecessary complications), I'm keen to move to another.
Best; Gordon
Gordon,
Your 'simplification' is what my model does already. For each pair of settings [ a , b ] there are 10,000 experimental runs, i.e., 10,000 random λs are sent, and the paired results correlated. Every point in the curves on page 7 represents the correlation of 10,000 λs for a fixed [ a , b ] pair, so I don't believe that a "known" λ adds anything to my model. Actually, each λ is known to me, if I wish to print it out. The fact that it is randomly generated does not prevent my knowing it if I wish to do so. In fact, I dynamically generate the vectors shown in the middle of page 6 just so I can see for myself that random spins are occurring. Further, that is definitely the way the physical experiment must be run to test my theory. The point of the experiment to test my theory is not to produce any correlation; it is to show that the A(a,λ) is not ±1, but depends on (a,λ) in the manner I state.
Edwin Eugene Klingman
Ed, your responses often represent the exact opposite of my position or statement; some to the point of nonsense. Maybe this reflects your past experience at the hands of Bell's supporters -- but (NB; like you) I too am a local realist.
Now, until now, I've refrained from addressing the issue. But we have here another example: You say: Your 'simplification' is what my model does already.
However, in line with my concern above, the simplification that I proposed (the first of several on offer; see my earlier posts) was specifically this: To solve what I defined as Problem 1 with your model: Alice's calculation, my simplification was to eliminate any hint of, or need for Alice (and, of course, Bob) to do any calculations at all.
An immediate consequence of that simplification was to revert Alice and Bob back to the roles that they have forever occupied in the Bell literature: they would thus be the agents responsible for the settings a and b, respectively; with no other responsibilities, and certainly none to do with calculations!
Your essay has this (p.6): "Alice chooses a as the direction of her Stern-Gerlach magnetic field; she will calculate a scattering angle with a component given by eqn (4). Bob will see initial spin λ' = -λ with angle θ' =(b,λ') and calculate the local deflection predicted for his SG apparatus."
Then there are the complex arrangements that you present so recently at "Klingman replied on Mar. 11, 2015 @ 00:31 GMT", "Bell states that "since the quantum mechanical wave function does not determine the result of an individual measurement, this predetermination [ i.e., a = b => -1 ] implies the possibility of a more complete specification of the state." In my local model that more complete specification is the initial spin, λ, which has dynamical significance. What is in question is the physics of this "hidden" variable which is 'hidden' from quantum mechanics. It may or may not be hidden from Alice and Bob. Whether or not it is measurable is not specified by Bell's theorem. There are several cases possible. If Alice knows the value of λ, she can compute the deflection. If she does not know λ, the deflection will still be determined by the laws of energy exchange physics, and will be the result as I have specified. In that case, in principle, Alice can recover the value of λ (or at least the value of angle (a, λ) that the spin makes with the local field) from the actual deflection, which she measures and sends to the statistical unit. Same for Bob. It is these measured values, determined by the energy exchange physics, that determine the correlation. In addition the theory can be checked by preparing a known λ and presenting it to Alice, and -λ to Bob."
Now you say it's you that wants to talk physics (not maths) but by any standard the job you have Alice and Bob doing is both confusing and unnecessary.
Thus, to be clear: my simplification was intended to eliminate my Problem 1 with your model: Alice's calculation by saying: Alice makes NO calculation! May I proceed on that (hopefully agreed) basis?
PS: To finish on this issue, your state: "In my model they [the numbers] are calculated locally and only the numeric result is sent to the statistical module. To understand this, assume that Alice calculates [according to the energy exchange physics] the number 36. Did this come from 1x36, or 2x18, or 3x12, or 4x9, or 6x6? These are local numbers that no one but Alice knows."
Question: Could you clarify for me please, the range of values that Alice generates via such calculations? An approximate range will do for, to my mind, they will now be the direct outputs of A-module; top figure, p.6. Also, what are these modules physically, please?
For this might make a nice segue to my next problem -- for which I see a similar simplification.
Gordon Watson: a local realist interested in the physics behind the EEK model.
Gordon,
You are correct that there is some nonsense going on, but we differ as to the source of it. There are physical phenomena, a.k.a. "reality" and there is physics, a.k.a. "a model of reality". The behavior of magnetic dipoles in an inhomogeneous field scatters the particles as shown in the iconic postcard and as described in classical mechanical textbooks.
Bell addresses the question of whether a physical model exists that allows computation of local results, that also yields the relevant correlations. Whether Alice does the local calculations or someone else does the local calculations is a piece of nonsense that I am not concerned with. A physical model that cannot calculate local results is incomplete. You insist that you understand my model and you understand the physics, but that is not apparent in your communications. I am open to reasonable questions, but I do not see much reason in your comments, and as there are many new essays posted, and only finite hours in the day, I am uninterested in devoting too much time trying to change your mind, which gives all appearance of already being made up.
Edwin Eugene Klingman
Ed, There's a bit here that's not clear to me: "I am uninterested in devoting too much time trying to change your mind, which gives all appearance of already being made up."
Where do your believe that we differ, please? In other words: what part of my thinking would you like to see change?
That will enable me (if we differ) to summarise my case so that I too can get on with other things.
Thanks; Gordon
Gordon,
Your focus on whether Alice does the calculations, or someone else does the calculations, strikes me as foolishness. If you have a point, make your point.
Edwin Eugene Klingman
Excellent job Ed!
You definitely made your point here. I think it's absolutely true that Dirac's approach to helicity is both general and fundamental, while the expression used by Pauli is a special case. I like that you use the word provisional. The subtlety of the error you point out, and its self-concealing nature, mean that you probably have as many objections to deal with as Joy did. But you seem to be up to the challenge, and perhaps with enough of an even temper to refrain from pushing your detractors into defensive posturing.
Good Luck!
Jonathan
Dear Jonathan,
Thank you very much for your kind comment and your encouragement. You definitely understand the point, and you clearly also see the problem.
And of course the problem is subtle, as your brilliant use of the term "self-concealing nature" shows. Only something as "self concealing" as this would keep it hidden from physicists for 50 years. So thank you again. Your clear, clean, wise comment is most appreciated.
I read your essay today, and find that we are in even more agreement than usual. I will comment on your thread soon.
With best regards,
Edwin Eugene Klingman
Good show!
I am glad that my insights are valuable. But your paper is deserving of kind attention.
All the Best,
Jonathan
Hi Edwin,
Through forty years of monthly doses of Scientific American, I've been led to believe that Bell, supported experimentally by Aspect, had a knock down riposte to EPR, so I am very interested to see you have taken him on. I like to think I might one day put the effort into mastering the mathematics required to understand your argument technically, but in the mean time I find the idea of Bell "using the wrong map" persuasive. As you know, I am passionate about reaching beyond instrumentalism in understanding this universe of ours, and I believe you are extending into that realm. I thoroughly enjoyed your essay Edwin,
Cheers,
Rowan