Thank you Georgina, very much.
The Nature of the Wave Function by Edwin Eugene Klingman
Dear Edwin and Georgina,
Georgina: I assure you my objections to Edwin's model have nothing to do with my ego. It has to do with understanding the powerful logic of Bell's theorem and the actual physics, mathematics, and experimental facts about the EPR correlations. These facts are against Edwin's ideas.
Edwin: Precisely because I did not want to hurt your chances in the contest and because I did not want to start another heated debate, earlier I avoided commenting on your model too critically. However, I cannot agree with your remark that: "[ I ] have had a number of years to meet others challenges, and still have not met their objections, although I give you full credit for the yeoman-like efforts you have put forth."
I *have* met every single challenge put to me over the past five years. The reason I have been able to meet these challenges is not because I am some super-smart genius, but because my ideas are in complete harmony with the choices made by Nature herself. I am sorry to note that you have taken the silly and ignorant objections to my efforts by some less-than-qualified individuals very seriously. But more importantly, you have not yet appreciated the simple fact that Bell's theorem cannot be overcome as naively as you are trying to do. As a result, your model fails at the very first hurdle. Please do not take my word for this. Ask any experimentalist who have had some experience in the matter. Or simply check on a piece of paper what quantum mechanics predicts. As I explained above, it certainly does not predict what your model predicts.
Nevertheless, it is only fair that you explore your ideas in your own way and reach your own conclusions. I genuinely wish you best of luck with your efforts.
Joy
[deleted]
Hi Edwin,
Something that bothered me early on, when I was introduced to Joy's model, is what I perceived to be a carefully buried assumption that one could perform a Bayesian type analysis on the experimental results the model generates. This is not trivial, for if true, it would destroy the foundation of the framework. This is because Bayesians cannot avoid the assumption of a definite probability on the interval [0,1]. To get this probability, one must apply a degree of personal belief dependent on previous outcomes.
I had to be convinced that Joy's statistical analysis was based purely on a frequentist interpretation -- that every measurement trial is independent of every other (i.e., Bernoullian). This is what got me into some hot exchanges with Richard Gill, over the law of large numbers -- he insists that the central limit theorem that guarantees 0.5 in the interval proves that Joy's prediction is wrong, because no matter how many trials, the upper bound is set by the middle value based on faith in the law of large numbers (this is what gets us the upper bound in Bell-Aspect). Gill misses the point. Joy's framework does not address a single interval of probability in a unified series of trials; it deals with discrete non-probabilistic outcomes on both sides of the singularity that exists in every measurement function continuous from an initial condition (Lamport).
As a consequence, discrete measurement outcomes, 1 or - 1, are not equally likely for every orientation of the measurement apparatus (the observer) choosing from a continuous range of possible measurement values of a fixed input argument (- a.b). For a run of trials in one probability interval [0,1], in some orientation that outputs some value, we're going to get a unitarily corresponding value on the oppositely oriented interval. Joy explains this in terms of trigonometric functions, though I prefer to think of it in analytical terms; i.e., angle-preserving conformal mapping to infinity. We don't need all the tools of complex analysis that the link describes, because geometric algebra simplifies and reduces the calculation to all real values. The only way this is possible, however, is by continuing the inherently 2-dimensional complex analysis to a 4-dimension domain (where the toplogy of S^3 lives). And from there, we get the sigificance of Joy's parallelizability: S^0, S^1, S^3, S^7. The topology is complete and self-limiting.
So when it comes to Alice and Bob and the measurement angles they choose, though they record their results on a 1-dimension line in a 2-dimension space, the continuous range of those values actually lives in 8 dimensions, from which Joy derives the (CHSH) upper bound 2sqrt2, which is identical to sqrt8 and gives us an integral norm. Which leads to Joy's statement in his "What really sets the upper bound ..." paper:
" ... we have proven that the upper bound of 2sqrt2 on the strength of all possible quantum correlations is derived from the maximum of parallelizing torsions within all possible norm-composing parallelizable manifolds."
Please take this for what it's worth. My support for Joy's program is based almost entirely on mathematical completeness. That opinion in turn is taken from Einstein's conviction that no probabilistic framework can lead to a mathematically complete theory of how nature works. Since your premise is the same -- there's nothing to say you can't get there by a different road.
Best,
Tom
Tom,
Edwin is of course free to explore whichever road he wants to explore. At this stage I am only asking him to take the first step.
Quantum mechanics predicts the following correlation function for the singlet state:
E(a, b) = -a.b.
This correlation function says that, given two fixed directions a and b, if the angle between them happens to be equal to 30 degrees, then the quantum correlation predicted by the singlet state is
E(a, b) = -cos(30) = -0.866...
This is a result from Quantum Mechanics 101. Any would be modeller of quantum mechanics is therefore obliged to reproduce at least this number. All I am asking Edwin for now is to reproduce this number for the fixed directions a and b, before he sets out to explore other roads. If he cannot reproduce this elementary prediction of quantum mechanics, then his efforts to overcome Bell are doomed.
Joy
Let me make sure you understand my worry. As it stands, Edwin's model predicts exactly zero correlation, E(a, b) = 0, not E(a, b) = -a.b as he is claiming. Because the cosine angle averages out to zero just as the sine angle does (remember that ab = cosine B sine in geometric algebra). On the other hand, if somehow the cosine angle does not average out to zero, then neither does the sine angle, and then again there is a contradiction with the quantum prediction. In other words, as it stands, there is simply no model.
Dear Joy Christian,
There are several issues, but let me dispose of the 'personal' first. I did not interpret Georgina's very nice compliment to me as in any way reflecting on you.
Second, I did not mean to imply that I have "taken sides with" your critics from the Disproof blogs, most of whom argue about a mathematical step. Although it is probably poorly worded, it is still true that you have not "met their objections", in the sense that they still object. You also know that I have defended you against their attempt to apply mathematics in a 'same-time' fashion that is explicitly against the spirit of your physics. In fact, you have posted my defense at least a half dozen times. Therefore I think you overstate the case to say, "I am sorry to note that you have taken the silly and ignorant objections to my efforts by some less-than-qualified individuals very seriously."
As I have remarked to you a number of times, I do not find higher-dimensional physics theories credible. Of course I could be mistaken in this. I am perhaps more open to unusual topologies, but I cannot conceive of a likely case in which handedness switches between experiments in a 50/50 fashion while remaining (as I interpret it) fixed for the duration of an indefinitely long experimental run (in theory Alice and Bob can be in different galaxies.)
Therefore I have, rightly or wrongly, divided your approach into a mathematical framework and a physics portion. The math is based on geometric algebra (appropriately so, in my view) and upon physics that is represented in this framework. As stated, I have a hard time accepting the physics of higher dimensions and synchronized switching topologies of space-time, so I instead have attempted to express my own physics in your framework.
I will address this physics in following comments.
Edwin Eugene Klingman
Dear Joy,
In a comment you first claim that I should hold the angle fixed ("let Alice and Bob choose to keep their respective measurement directions *fixed* for all runs of the experiment. They are perfectly entitled to do so under the "free will" requirement.") Then in the last comment you claim that ("Because the cosine angle averages out to zero just as the sine angle does ... Edwin's model predicts exactly zero correlation, E(a, b) = 0, not E(a, b) = -a.b "
But assume that Alice and Bob agree to hold the angle fixed, but then decide to flip a coin (or in some other way) decide whose angle will be the clock-wise-most angle. The average, as I understand it will in this case be cos (30) since cos(30) = cos(-30) and the sine components cancel, since sin(30) = -sin(-30). So I don't understand your comment that my model always obtains an answer identically zero. This, as I understand it, is simply the same result that you get by claiming synchronized switching topology.
Edwin Eugene Klingman
Dear Joy,
I may be confused about this, but I understand the problem to be one of showing whether or not Bell's theorem leads to 'hidden variable'-based calculations that yield the same predictions as quantum mechanics calculations. Because, as I clearly state in my essay, my wave function *is* the quantum mechanical wave function, then I should reproduce the same quantum mechanical results as quantum mechanics. The question is why Bell does not, given his assumptions. You have claimed that Bell makes a complicated topological error: "Bell's prescription is not only false, it is breathtakingly naive and unphysical." (your book, page 3).
In a way we agree on this. In an earlier paper ("Physics-based Disproof...") referenced in my essay, I claim that Bell's use of a unit vector (a or b) to represent the inhomogeneous Stern-Gerlach field is unphysical. But of course the only way to actually compare any result to Bell's calculation is to use this unit vector, so we are to some degree stuck between a rock and a hard place.
As I have continued to ponder Bell's theorem, I also realized that his use of a simple unit vector to represent the actual physical spin (due to a finite particle and associated fields) is a similar error, since the particle induces fields that do *not* have the character of a simple unit vector. For this reason I believe that his two unit vectors vastly oversimplify the situation in which an inhomogeneous spin field traverses an inhomogeneous magnetic field, and therefore his oversimplified calculation ("Bell's inequality") is not to be taken seriously. At least not seriously enough to change all of our ideas of local realism.
For exactly this reason I believe that your framework in which 'volume forms' are employed instead of unit vectors is both ingenius and appropriate, and I have, as explained in my essay, described a volume form that is appropriate to my theory of the wave function.
To summarize, my wave function, being a solution to the Schrodinger equation, should provide the same results as quantum mechanical calculations. As Feynman stated: "The same equations have the same solutions." But your clever reformulation of Bell's theorem, based on replacing overly simplistic unit vectors with more appropriate volume forms, should also produce the QM results. It is my expectation that my volume form will accomplish this, in the end.
Edwin Eugene Klingman
Dear Tom,
I very much appreciate your recognition that Joy and I apparently agree in a number of ways. I fully respect your mathematical capability and also your physics insight, although you and I may have fundamental differences here.
I do not dismiss your conviction that Joy's math agrees with your conceptions. But let me repeat a story here that may be more meaningful now that it may relate to the problem at hand. As you know Kaluza-Klein proposed a fifth dimension to unite gravity and electromagnetism, and ended up explaining the charge of an electron as related to a 'small circle' in the fifth dimension. Elsewhere (see "Chromodynamics War") I invoke a field, the C-field, and also derive charge as related to a 'small circle', but in 3 (or 4 space-time) dimensions. Lee Smolin has remarked that:
"A property of an extra dimension -- the radius of the extra circle in Kaluza-Klein theory -- can be interpreted as a field varying over the other dimension."
This implies to me that perhaps the "extra dimensions" that Joy invokes can be interpreted as a "field varying over the other dimensions", in which case, as you say, we might reach the same place by different roads.
Best regards,
Edwin Eugene Klingman
Dear Edwin,
We have all gone through all the various issues you mention, in several blogs, so let me not pollute your author's blog with them again.
The bottom line is this:
Quantum mechanics predicts the following correlation function for the singlet state:
E(a, b) = -a.b.
This correlation function says that, given two fixed directions a and b, if the angle between them happens to be equal to 30 degrees, then the quantum correlation predicted by the singlet state is
E(a, b) = -cos(30) = -0.866...
This is a result from Quantum Mechanics 101. You cannot possibly dispute this result. Any would be modeller of quantum mechanics must reproduce this number, just to get started. All I am asking you for now is to reproduce this number---not in words, or hopes, or intentions---but by explicit calculation---for the fixed directions a and b. If you cannot reproduce this basic prediction of quantum mechanics, then your program---despite all of its worthy intensions---has failed already.
You need not take this as a criticism. If you accomplish this, then it would be a massive boost to your program. According to Bell, as well as me, you will not be able to.
Joy
Hi Joy, Edwin,
I have to agree with Joy here. It is pretty well known that particle spins can be parallel or anti-parallel to a particles direction of motion plus it is also well known that EM radiation can be left or right circularly polarized.
So you really need to figure out how to get your C field to be both left and right handed. Nature is that way, so there must be a way. You would need to get the +/- 1 factor in your eq. 11.
Best,
Fred
[deleted]
Well yes, I guess I didn't understand completely. I see now that applying the law of large numbers to zero out the bivector terms (eqn 12 et seq) leads us into the same algebra morass that generated much of the acrimony of the past two years. Ouch.
I've not been able to conceive of any but a topological derivation of -a.b, for the simple reason that if this term is anything other than an input argument to a function continuous from the initial condition, it can't give us twin results (argument and value) and must be given a linear interpretation which obviously won't fit the analytical case. This probably isn't clear -- and I will produce a detailed explanation if required or requested -- relevant to Edwin's presentation, though, the average of experimental correlations (eqn 12) is not the same as the covariant correlation of argument and value. Here is where I have been able to grasp the extraordinary utility of geometric algebra for the Christian model -- because it eliminates complex values of a real continuous function without losing continuity, by appealing to the octonionic space.
Because quantum correlations in the Christian framework are explained solely in terms of topological initial condition and orientability, we don't need (and can't use) any tools of probability -- not the equally likely hypothesis, nor averaging nor central limit. All that remains is regression to the mean, which is expressed as the complete set of norms on a finite space.
Edwin, I still think it's possible for you to take a different road toward the same conclusions though I personally think it is unlikely to succeed -- for the reason that it's the road I abandoned after years of finding no means to obviate extra dimensions. It's important to understand that we can use mathematical artifacts of extra dimensions to describe manifestly local results without rejecting scientific realism, a case I am firmly convinced that Joy has demonstrated. If one goes back to the very beginning of the dialogue, one can see that my first response to Joy's claim that "Bell made a topological error," was "So what? He wasn't doing topology." It took a lot more to convince me that Bell *should* have been doing topology.
I think Anton Zeilinger is utterly wrong that events are not in need of interpretation. Theory *is* the interpretation of events. We do not do objective science inductively. I give as an example Penzias' and Mitchell's discovery of microwave background radiation. The data mean absolutely nothing unless interpreted by theory, in this case the Big Bang cosmology, though I acknowledge that other theories may fit the same data.
Tom
Dear Tom,
Your comments are interesting, and may yet shed light on what's happening. You said a lot, so I'll bite off small pieces.
First, you remark that we can use mathematical artifacts of extra dimensions to describe manifestly local results without rejecting scientific realism. Of course I have no objection to mathematical artifact. In my essay I explain how Hilbert space in an energy basis is appropriate, and how it correlates with probability. But you aren't implying that Joy's 7 (or 8) dimensions are only artifactual, are you?
In a comment above I explain that Bell's use of unit vectors to represent interaction along the path of one inhomogeneous region of field through an extended region of another inhomogeneous field might be viewed as a topological problem, in that inhomogeneous fields might be mapped into equivalent space-time curvature, and one can view the problem in terms of parallel transport. Anyway, whether you agree that this is topology or not, we both agree that Bell formulated his problem incorrectly. He "should" have been taking the interaction of two inhomogeneous fields (in relative motion) into account, and he failed to. No wonder his results don't match reality.
You said more, but I'll stop here. We do agree about "probability" in QM. But you seem to want to banish it, while I'm trying to explain why it works for a physical wave function.
Edwin Eugene Klingman
Dear Fred,
The wave function is *not* the spin your are talking about. The spin, whether for electrons or photons, is measured by its electromagnetic properties. From de Broglie on, it's been understood that the wave function is not the electromagnetic field. On the other hand the wave function *does* correspond to neutrino spin (and Z and W bosons) and here Nature most certainly does do it my way (i.e. lefthanded).
Thanks for the comment. I still hope to bring you around!
Edwin Eugene Klingman
Joy,
You keep asking me to produce a quantum mechanical calculation with my model, which indicates to me you haven't understood my model. My model yields Schrodinger's equation and the solutions to Schrodinger's equation, so I get identically the same results that quantum mechanics gets.
All I do is claim that the wave function is physical, *not* information only. By the way, I received in the mail this morning my latest issue of Physical Review Letters, which seems to agree with me. The article, (PRL 108, 260404 29 June 2012) "Implications of the Pusey-Barrett-Rudolph Quantum No-Go Theorem" undermining the quantum state as "mere information" (or "knowledge") about the real physical state of a system. As I understand it, my model is compatible with this theorem.
You have spent thousands of words telling others that they did not understand your approach, and to read it again. I don't believe that you understand my approach, or you would not keep telling me to use QM to achieve a QM result. I can't achieve anything else, since my equation and solutions are the same as QM. Please try to understand this.
However, like you, I believe that Bell got the wrong answer, and so I take advantage of your framework to reformulate Bell's problem -- using the volume forms that you proposed and that I find very appropriate. In this case I *do* depart from standard QM, since the standard QM does not use trivectors. The intent here is to show that, properly formulated Bell's approach matches QM, not his inequality. I may fail in this regard, but please try to understand what I am doing. Your repeated challenge to derive a QM result is proof that you haven't yet understood my approach.
Edwin Eugene Klingman
Hi Edwin,
You wrote: "You keep asking me to produce a quantum mechanical calculation with my model..."
No. I am *not* asking you to do that. I am *not* asking you to produce a quantum mechanical calculation. I am asking you to *reproduce* one of the most basic predictions of quantum mechanics within your own model. I am not concerned about what your model is or whether or not I understand it. Whatever your model is, it MUST reproduce the number -0.866 as a singlet correlation along two fixed directions a and b, 30 degrees apart. This number is a well established empirical fact. But you are unable to reproduce it within your model. I claim that you will *never* be able to reproduce this empirical fact---which also happens to be a prediction of quantum mechanics---unless you embrace my framework in its entirety.
Now you can prove me wrong quite easily. All you have to do is to calculate the number -0.866 explicitly, for the fixed directions a and b, within your own model.
Best,
Joy
[deleted]
Hello,
You confound really Joy what is the Universal dynamic and its irreversibility and the programmation by computing.
1 is not equal to -1 at my knowledge, the symmetries are bad understood in their pure physicality.The calsulations are just a mirror in fact, the same results for the same equations, but ....
all functions do not go to the FUNCTIONS.
Ans also , the informations are encoded in a pure 3D dynamic !!!The waves and the informations.....=......rotations of spheres !!!
Edwin, I agree about your words, that said don't forget that the rotating 3D spheres asnwer to all.So the spin and the waves are linked.
You are right about the physicality of these waves, furthermore the informations also can be encoded in this mass. All is a pure physicality even the informations are under a specific universal dynamic.
Regards
[deleted]
Let's play
Let's speak about the entropy and the information ok ?
well
and you speak about predictions ??? and empirical facts ???? you are not rational you know ???
I ask me how is the model implied to an isothermal system with N molecules like in the ideal gas for example with a volume precise .The increase of information ..."is it proportional with entropy ?"
You can speak about the maxwell demon you know. And after we shall link with the disorder and the order !
Dear Joy,
You say: "Whatever your model is, it MUST reproduce the number -0.866 as a singlet correlation along two fixed directions a and b, 30 degrees apart. This number is a well established empirical fact. But you are unable to reproduce it within your model. I claim that you will *never* be able to reproduce this empirical fact---which also happens to be a prediction of quantum mechanics---unless you embrace my framework in its entirety."
It's pretty clear that you don't understand what I am saying, which is that I calculate the correlation EXACTLY the way it is done in quantum mechanics. But since the implication seems to be that I don't know how it's done in quantum mechanics, I will tell you how I would do it.
Beginning with equations (4) and (5) in my essay for the time evolution operator and Schrodinger's equation, I would use the appropriate Hamiltonion for the electron spin 'u' in a magnetic field 'B'
U(t) = exp (iHt/h) => exp (iu.B/h)
where U(t) is the evolution operator, t is the time, h is Planck's constant, u is electron spin and B is the external magnetic field and the period is the dot operator and the Hamiltonion becomes time independent. This would be applied to the singlet states to evolve the states to Alice's and Bob's respective directions of the magnetic field and the correlation found in the usual way by calculating the expectation value between initial states and the evolved states, where Bob's evolution operator does not affect Alice's particle and Alice's evolution operator does not affect Bob's particle. The result will involve a term of the form
< singlet | s.a s.b | singlet >
where s is the Pauli spin matrix and a is the direction of Alice's field and b is the direction of Bob's field.
Then I would make use of the identity (s.a)(-s.b) = -a.b plus -is.(axb) and Bell (equation 3) claims this results in -a.b
There may be other ways to explain this, but I believe they are equivalent. Most explanations will involve ensembles and the density matrix, with density rho=(I plus a.s)/2 for an ensemble of spin one-half particles, but the above is about as succinct as I can manage for a text-based comment.
Joy, it's pretty clear that you will never accept any statement that does not agree that you have the only possible way, and it's also clear that you have not understood what it is that I am saying. I do not wish to turn this into an extension of your 'Disproof' blog, so as far as I'm concerned we can leave it that you do not accept the ideas put forth in my essay. For anyone who has followed all of your blogs, that was a foregone conclusion.
Best,
Edwin Eugene Klingman
Dear Edwin,
I am sorry, but we cannot leave it at that. As far as I have understood, you are making a claim that your model reproduces quantum mechanical correlations in every respect, but at the same time your model is both *local* and *realistic*, thus providing, in particular, a local-realistic explanation for the singlet correlation, in contradiction to Bell's theorem . If this is not the claim you are making, then I do apologize and withdraw all my comments from this blog.
However, what you have described above, and in your paper, is neither a local model, nor does it reproduce the observed singlet correlation, -a.b, for the fixed observation directions a and b of Alice and Bob. It is pretty clear that you have not understood Bell's theorem at all. The fact that "Bob's evolution operator does not affect Alice's particle and Alice's evolution operator does not affect Bob's particle" DOES NOT make your model local in any way. Nor does your use of the identity (s.a)(-s.b) = -a.b plus -is.(axb) reproduce the scalar result -a.b for the fixed directions a and b.
I am forced to say this because you are making a use of my framework and implying that you have improved upon it. As grateful as I am to you for that, I cannot possibly let you misuse my framework the way you are misusing it and not make a comment. So I assert, as clearly as I can: your model is not a local model, and it does not reproduce the singlet correlation for the fixed observation directions of Alice and Bob (or even for the unfixed directions as far as I can see). Therefore your model is not a counterexample to Bell's theorem.
Having said that, I have no objections to your model explaining---in a different and perhaps more enlightened (but ultimately *non-local*) way---some of the physics usually described by quantum theory. That is very nice. But your claim of producing a local model for the singlet correlation is simply false. You are nowhere near accomplishing that.
Best,
Joy