Eckard, hoping this helps when I comment on your essay, this is carried-over from my answer to you at More realistic fundamentals: quantum theory from one premiss.
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Thank you Eckard, hope this helps:
EB: Your horrible formalism will deter less qualified readers like me.
GW: With every pointed critical comment most welcome, I will whole-heartedly welcome your suggestions.
nb: my preliminary notation is meant to be physically significant and to helpfully include every relevant beable and every relevant interaction. Even to the point of charting the dynamics of interactions (see the little arrows). [ps: I've lived with such since 1989 when I first read about Bell's theorem, thanks to Mermin (1998); old habits die hard.]
Thus a polariser is represented by a "delta" denoting "change" -- akin to a delta-function -- its orientation and output channels identified. Even an analyser (often a multiplier) is represented by a multiplication (a scalar-product). How about what's yet to come: a fancy-q for qon, a quantum particle; saving 4 syllables? A fancy-P denoting probability (subjective) and/or prevalence (objective) -- to thus rescue "probability" from much modern nonsense, eg, Fuch's QBism? (At the same time leaving ordinary P and q unchanged in ordinary physics.)
Please have another look at ¶4.1 and the exercise there; knowing that we're on a steady heading to more conventional representations -- see eqn (21). And please make critical suggestions for improvement.
EB: I am unhappy with the lacking readiness to fundamentally clarify the issue of entanglement.
GW: Yes, me too, so thanks for this. Entanglement is nothing mysterious. Under the R-F theorem [and what I call Born's Law: see the law of eponymy], the probability interpretation of QM needs to be more clearly understood. The entanglement brought about by angular-momentum conservation (with the added information that the sum for the two particles is zero), is a physical (and therefore a logical) constraint on all probabilities and observations. This has nothing to do with AAD [nonlocality], nor remote piloting, etc. Rather, if the total angular-momentum is zero in EPRB, then λi = μi pair-wise.
An arbitrarily-oriented polarising interaction with one pristine twin yields thus, by logical inference, a related equivalence-class for the other pristine twin. (And this conclusion, tested any time, always gives the expected result.) There is thus no need to invoke anything mysterious: rather, an understanding of entanglement is crucial to any non-mysterious understanding of EPRB, Aspect's experiments, QM, and our world in general.
EB: Was Dirac possibly wrong when he believed "that this concept of the probability amplitude is perhaps the most fundamental concept of quantum theory"? If my doubt is justified, then it [the Fourier-based R-F theorem; RFT] is even more fundamental.
GW: Not to diminish Dirac, but to acknowledge R and F: for me, RFT is a more soundly-based argument, with applications beyond QM. For those who see mystery in the superposition of states, or in the preparation of superimposed states, RFT demonstrates this: the superposition principle is a mathematical tool (thus logical constraint), valid for all none-negative distributions; whether of probability, mass, charge, etc.
nb: under TLR, Planck's a quantum-of-action is not mysterious either. It is required for the description of extended particles (in contrast to mathematical points).
EB: Errare humanum est.
GW: And to our friends: Errare humanum est, perseverare autem diabolicum.
EB: I cannot finally judge John Hodge's "opposite approach" because I didn't yet read his essay. ... I am sure that in reality there is no supersonic acoustic wave speed greater than the speed of sound. According to my knowledge, the propagation of light in vacuum was also never measured to exceed c.
GW: I expect to respond to John Hodge tomorrow.
EB: [Edited, as my response] If I understand Gordon Watson correctly, he [with Fröhner] is aligned with the power, centrality and generality of the RFT.
GW: Yes.
EB: I consider my own suspicion much more radical and invite all of you to show in what I am wrong.
GW: I will comment soon, but make this point now: I agree with the second sentence in your essay, but would ask you to reconsider some of your positions in the light of RFT; for many other statements in your pristine essay resonate-in-harmony [verschränkt = entangled] with mine.
PS: With my thanks again, and hoping to be helpful, I will post this on your site too.
Gordon
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Gordon Watson
More realistic fundamentals: quantum theory from one premiss.