Bell's Theorem is too Narrow to Prove Useful to Quantum Mechanics

Bell's Theorem, that “all theories” about paired or entangled quantum information are inherently worse than quantum mechanics, is considered fundamental to physics and the philosophy of science.

The author respectfully suggests that Bell's inequality formalizes “all theories” into a narrow band, allowing “all theories” only information about the results of two experimental tests done on the quantum information and the rights to use only a hypothetical and unmeasurable angle lambda that relates to that quantum information, further requiring that “all theories” create a function in lambda that must be multiplied by the results of the two measurements. The formalism of Bell's Theorem claims to cover “all local hidden variable theories” but the physics community seems to have taken that to mean “all theories” in spite of warnings from Gerard t'Hooft and seems to have given up on causality and realism.

Ingenious experiments have verified Bell's inequality, which the author does not dispute. The interpretation and formalism are what have gotten physics into trouble. The author will take four approaches in this discussion, two theoretical and two practical. The theoretical discussions involve asking a “physicist” with programming/information theory skills and a “physicist” with statistical or bio-statistical experience to create a predictor function that will be better than the results from quantum mechanics. Discussions of experiments with polarized light and with the spin of particles follow, but cast more doubt on the interpretation of results than the results themselves.

Objections from a Object Programming Approach -or-
Dysfunction from a Functional Programming Approach -or-
Contradiction/Confounding/Clarification from a Contractual Programming Approach

Assignment: Function rho is passed one parameter, lambda, which ranges from -pi to pi inclusive. The value returned for pi will equal that for -pi. The integral of rho over the range of lambda is to be 1. We may require it to return a value 0 or greater and less than 1. The function receives no information about A, a, B, b and is not allowed to make predictions based on A, a, B, or b. When multiplied by A(a,lambda) and B(b,lambda) and the result integrated over the range of lambda, it is expected to provide a result similar to (a dot b) when we (not you) integrate rho(lambda)*A(a,lambda)*B(b.lambda) over lambda.[1]

Good luck. 
 
Failure will lead to stagnation in a field of physics to be determined later.

Programmer's Response: We cannot use a or b or A or B or A(a,lambda) or B(b, lambda) to predict rho or better yet that integral? You've prescribed how P will be calculated? Are you serious? Sounds like a setup for failure to begin with; a self respecting programmer would not accept the contract. No thanks. Stagnate. Go ask a statistician.

Statistician looks at Bell's Theorem

Assignment: We have run a few experiments that show a correlation between measurements of a physical phenomenon we can rerun. You are to create the best description of that variance using only single variable analysis: we will tell you what the correlation is with one variable and the correlation with another variable and want you to improve on the prediction results. You are expected to use those results multiplicatively with the function of your creation. Oh yes, we will tell you the main independent variable, but not the value of the other two independent variables used to determine the dependent values we will give you. You are not allowed to make predictions based on the value of those two independent variables. Analysis of variance is off limits. That is reserved for the one true theory. Failure will lead to you being banned from publication on this or any other topic within the field. Worse, failure will leave the one true theory able only to describe and without any means to discuss why; causality will be forbidden.

Statistician's Response: In statistics, especially bio-statistics, we rarely get the chance to rerun an experiment as often as we want, even when we have the money to do it. How exciting. But why, with three independent variables, are you allowing me access to only one? And why are you telling me that I must multiply by the linear results? Really? Do you want my theory to fail? It will, you know. We are used to looking for hidden variables all the time and describing results without knowing mechanisms, but to be told I won't be able to use known information in my analysis is almost a guarantee of failure. I'll pass. What is it you were trying to predict, anyway?

Conclusion to Theoretical Approaches

Bell's Inequality is ably described in Griffiths 2005 Introduction to Quantum Mechanics p425; the author even thinks he understands it. Yet Bell's Inequality is based on a straw man: if rho(lambda) is a multiplicative factor which must integrate to 1 over lambda and that cannot know anything about a or b or use them as variables, it is a pretty dumb hidden variable theory and should not be expected to do much. Quantum mechanics P is allowed to know a and b, and is rightfully proud and embarrassed that (a dot b) is as good as it can do.
Back to the statistician's question: what was to be predicted?

Polarization Experiments

Freedman and Clauser's experiments suggest a “new” phenomenon of signal enhancement would be required for the tightly confined theories of local realism to do better than Bell's inequality for experiments with and without polarizers.

Yet polarization DOES lead to signal enhancement in some cases. A polarizer is oriented horizontally in front of a sensor that only senses vertically polarized light. The sensor sees no light, no matter what is sent to the first polarizer. (If the polarizers are perfect or the first is “over aggressive” and the sensor slightly imperfect.)

Yet adding a polarizer in between, oriented at 45 degrees to vertical, does enhance detection. One eighth of the incident light will be detected. So in at least one situation, a Bell's Inequality is counterproductive.

The mnp Model suggests that experiments with polarized light depend on whether the photons being tested are part of an ongoing stream of radiation (with the attendant existing attenuating fields) or if they are emitted far enough apart to not be affected by recent fields.

The author suggests Freedman and Clauser's experiments are probably fine, just that the interpretation and formalisms are flawed.

Spin Experiments

Looked at from any axis, electrons have spin (angular momentum) of h/2 “up” or “down.” Measuring one electron a second time at a different angle leads to a (more or less) random result. Measuring a paired electron after the first is measured at a different angle leads to a similarly random result. The author wonders if the distribution is any different when the spin of the first of a pair has NOT been measured but its presence merely sensed. He suggests not. Quantum mechanics sees that spin as an intrinsic property of the fermion, with no clear idea how the tiny mass of the electron could create that much angular momentum without spinning with surface faster than the speed of light. So the author needs to ask:

What is Spin? 
 
Ohanian's description of spin as circulation of energy in the fields from 1984 published 1986, following work by Belinfante in 1939 and suggestions by Gordon in 1928 is interesting. [2] Am J Phys. 54 (6), June 1986 from aforrester.bol.ucla.edu/docs/Spin_Ohanian.pdf (thanks for the reference to Griffiths [1] 2005 pg171 footnote 25) Seeing spin as a wave property works for both classical waves and quantum mechanical waves. Ohanian's treatment is compatible with (and uses) quantum field theory to quantize the effects, but is fundamentally compatible with classical wave treatments as well. In fact, the emphasis on circularly polarized fields sounds familiar. Conservation is met by circulation within a field! 
 
Ohanian's description is in keeping with the mnp Model's view of electrons as surfaces of electric charge material rotating in rings either left or right, which would create “vortexes” in the field around the electron but no net effect unless an interaction/measurement occurs. The spin measured (or captured) by the Stern Gerlach magnets is apparently not a direct reflection of the left or right spin of the electron's charge structure, but an effect on the field that then effects the electron's travel, much as polarization filters affect electro-magnetic fields (and in the mnp Model, which then affect the photon) In the mnp Model, photons have two different “halves” with the first half consisting of magnetic entities with spin in one direction and the second half with spin in the opposite direction. Why that would create, independent of the photon's mass and energy, a spin angular momentum in the field with exactly twice the magnitude of an electron's or quark's angular momentum is a question that shows the current limits of the author's understanding and education. 
 
Conclusion

Physicists should have no trouble seeing quantum mechanics as an incomplete theory. Feynman is quoted as saying “nobody understands quantum mechanics.” All hope of causality has been abandoned, prematurely in the author's estimation. Quantum mechanics is wonderful, beautiful, eminently descriptive, reasonably predictive, and may have put many physicists out of work. Quantum mechanics should be comfortable with the “incomplete” label.

Bell's Theorem need not confine theory to multiplicative factors that are distributive over addition, so quantum mechanics too has hope of expansion. The reliance of quantum mechanics on commutative relations when it suits the purposes of development and description may well be appropriate for charge based issues which seem to be symmetrical or commutative, but may not work with gravity.

To paraphrase an adventurous friend, The Education Continues

To speak for causality and realism: I'm not dead yet.

References:
[1] D. Griffiths, Introduction to Quantum Mechanics, 2nd ed. (Pearson Education, Upper Saddle River, NY, 2005).
[2] H. Ohanian, “What is Spin?” Am. J. Phys. 54 (6), 500 (1986).