More realistic fundamentals: quantum theory from one premiss. by Gordon Watson

NB: This post was formatted correctly in preview. I've reported it for correction.

Gordon

Dear Boris, I'm replying here because your comment is currently missing.

NB: if you saw me in the penthouse of Towerblock-101, that's because I am the Chief Maintenance Mechanic there, 24/7. The basement, where the foundations are exposed, is where "I live, move and have my being" -- even sleeping there beneath my desk.

Thus, relatedly, my essay begins with two axioms and a consequent premiss: true local realism. I then study EPRB, identifying beables and interactions in a related notation.

There follows --- from first principles, in my "neo-classical" terms and concretely --- the Laws of Malus, Bayes, and Born (the last thanks to Fourier and the R-F theorem).

Though not shown (for space reasons, and from any good textbook), the consequent confirmatory QM-style application of Born's Law (now concretely established, as above; and without mystery) to EPRB and DSE (+++) is immediate.

Reproducing the correct results -- without mystery -- you can thus see that we are well on our way to reformulating QM ++ from elementary fundaments, absent mystery.

With thanks for your comment, more may follow on its return; I write here from recall.

Gordon

ADDENDUM: in-part prompted by the last line of your [Boris'] essay.

Dear Boris, captured by your opening paragraph and your Cartesian emphasis (and being, as you know, a Maintenance-Mechanic specialising in FOUNDATIONS) -- [oops, caps = Freudian slip] -- I was delighted to see you using [see my essay] Born's Law on your p.6. And more intrigued when I saw your closing line: "Physical space is the body of God in which we exist and in which wander on the way to it."

For this line triggered a corrective recollection from my years of teenage rationalism (as yet undiminished)! Though, at that time, I was not aware of (and therefore was independently following, in my terms) Descartes' Dictum (DD):

"Never accept anything for true which you do not clearly know to be such; that is to say, carefully avoid precipitancy and prejudice, and bring nothing more to your judgment than what is presented to your mind so clearly and distinctly as to exclude all ground of doubt."

For I immediately recalled, from the KJV English Bible --- Acts 17:28 --- For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring.

My own translation, from the Greek [so keen was I to understand such things] was: "In God we live, emote, and develop [our will and intellect]."

And when I looked for those poets, I found a related verse from an invocation to Zeus! As google now tells me: Zeus, in ancient Greek religion, chief deity of the pantheon, a sky and weather god who was identical with the Roman god Jupiter. His name clearly comes from that of the sky god Dyaus of the ancient Hindu Rigveda. Zeus was regarded as the sender of thunder and lightning, rain, and winds, and his traditional weapon was [electromagnetic] the thunderbolt. He was called the father (i.e., the ruler and protector) of both gods and men.

Thus, in this way, we arrive at a true fundament; in my view suited to the rationalist and the religious alike. It goes something like this: "God: in whom we live, emote, and develop our will and intellect; and, as a certain poet has said, From whom we are all related."

I look forward to your comments on this joint enterprise.

As for your ideas re Descartes ideas, I must (at the moment, subordinating space and mass to God) invoke DD.

With my thanks and best regards,

Gordon

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.)

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

Thanks Juan [= JA below]. Welcoming your comments, some seeming ambiguities [or maybe typos] need to be resolved before we properly focus on technical issues. Let's see what preliminary agreements we can come to:

JA-1: "I do not see any derivation of "quantum theory" [QT] in this work."

GW-1: Under the classicality of true local realism (TLR) -- and without mystery -- we find the Laws of Malus, Bayes and Born; plus real dynamic functions in 3-space that the Bell-literature does not. All of this from TLR and EPRB, totally absent any nonlocality [NL] -- see your next.

Without recourse to Born, TLR also provides the correct answers for Aspect's experiments, GHZ, GHSZ, etc. Thus TLR links to QT at the most fundamental level by using Malus' and Bayes' Laws in quantum contexts. We can then validate Born's Law in these experiments; THEN continue on to similar validation in double-slit experiments [DSE], etc.

See Fröhner in my references for ongoing (deeper) connections to QT. Thus, from such links, do you not now see QT derived classically? If your answer is in anyway in the negative, how come?

JA-2: "It must be recalled that quantum theory is nonlocal and this nonlocality [NL] is well established in experiment.

GW-2: ?? To recall NL I would need to recall conflicted interpretations, typically associated with the colloquialism "collapse of the wavefunction". There is no such collapse in my work, hence no such NL. So what does your claim mean? Where is the NL in QT (as opposed to interpretations)? And what experiments are you referring to, please? And what, in them, do you define as NL?

JA-3: "The idea that nonlocality must violate special relativity because it implies superluminal propagation of influences is a common confusion. The nonlocality of quantum mechanics is fully equivalent with special relativity and its causal structure."

GW-3: ??? How do you define locality AND NL? How do YOU clarify matters for people with such "confusions" please?

Gordon: to be continued.

Gordon to Juan; continuing:

JA-4: "So not only attempts to derive "quantum theory from the premiss of true local realism [TLR]" are incorrect, but they are not really needed, because there is no contradiction."

GW-4a: "Incorrect"? Please: what are the errors? And as for your claim re "no contradiction" -- please -- be sure that your answer to GW-3: is clear.

I agree with the thrust of your comment re "Bohr's idea ... " and "Entanglement implies the existence of a correlation between systems." But, since the implications go far beyond that: GW-4b: How do you define entanglement in technical terms?

JA-5: "And correlation is a function of interaction."

GW-5: ?? Is this a typo? Why is the primary twinned-pairwise-correlation in EPRB not already existing as the PRISTINE particles leave the source: ie, existing before any interaction?

JA-6:[/b ] "I am not going to write here explicitly the full expression for the correlation g because it is relatively complex and latex script here is broken, but it is a function of the interaction Hamiltonian V: g ~ V|Psi> higher order terms in V."

GW-6: LaTeX is working again, so I'd welcome the full expression; or attach it.

HTH. With my thanks again, and best regards; Gordon

PS: FQXi -- note formatting errors; no bold, and see JA-6: [/b ]

Responding to Peter Jackson (above) -- with thanks -- re:

"Juan et al,

Eckard is correct, apparent 'non-locality' only arose from our inability back then to classically explain output. I agree Gordon's essay isn't a complete classical formulation, he doesn't claim that, but it's an important move in that right direction. ... ."

..........................

PJ, imho, Eckard has it wholly correctly and your are partially correct. That is, in relation to my work, I often talk in terms of my "neo-classical" approach: but that's because many others see QT (with its quantum) as a non-classical theory. However, in my terms: my theory is wholly classical.

Background to this engineer: I hold fast to three classical mantras:

(i) Reality makes sense and we can understand it.

(ii) Correlated tests on correlated things produce correlated outcomes without mystery.

(iii) Only the impossible is impossible.

Background to my theory: Wholistic Mechanics (abbreviation WM; logo w@m, pronounced wham) began in 1989: against Mermin's "Spooky action at a distance; mysteries of the quantum theory" (Britannica's GBWW 1988).

WM is a wholly classical theory that brings QM into the classical family of physical theories: WM = unification = {classical mechanics, QM, special relativity, general relativity}.

As for the logo (poorly rendered here) its origin is this:

[math]A*\leftarrow$w_i\,@\,m_i$\rightarrow\,B*[/math]

Preparing for my initial phone-call to David Mermin, I pictured two separating particles 'wi' and 'mi' and used the analogy of entangled twinned "worms" separating -- wi (womanly, heading toward womanly Alice's locale A*) and mi (manly, heading toward manly Bob's locale B*) -- ie, heading in opposite directions from their common source, a one-off twin-producing worm-egg @ [see its spin]. Thus each twinned-pair is correlated by their common DNA and anti-correlated via their sex.

And while most analogies are unsuccessful in explaining entanglement, those with a nod to mysteries have difficulty rebutting the arguments with our worms. Thus, if Alice finds pristine 'wi' to be a female, is it any wonder [whatsoever] that she knows Bob will find a male if he does the related test. Likewise, if Bob tests pristine 'mi' for its DNA, is it any wonder [whatsoever] that he knows the DNA Alice will find if she does the related test; and so on! Of course, QM with its entanglements entails many more correlated relations: and GHZ worm-eggs produce triplets; GHSZ worm-eggs produce quads; etc.

Now, to be clear: I see my role at this stage to be the one advocating for CLASSICAL approaches (like yours; against all others who use non-classical approaches) to understand and reformulate QM, without mystery.

[ps: Alan Kadin uses the term neoclassical; perhaps like I have used "neo-classical". I believe that Alan (with many others on this path to reformulation) will deliver a classical theory if he is successful. Moreover, I do not see WM's basic classical principles being negated by such. Comments welcome.]

Cheers; Gordon

Boris,

Your mention of "wave-functions, the unit-imaginary and rotations" should take you to equation (21) in my essay AND the link [at #12 in my References] to the Riesz-Fejér paper by my friend Fritz Fröhner (1998).

So, for you, the next Law is Born's (named historically after Born's fumblings, c1926), whereas the Riesz-Fejér theorem [c1915; the R-F theorem, or RFT] derives more general results in a wholly classical manner (thanks to Fourier) AND WITHOUT MYSTERY.

As for Fritz's essay (unlike mine): that you will happily read more than 5 times for its depth.

Sincerely; Gordon