• FQXi Essay Contest - Spring, 2017

  • Space and Time, Geometry and Fields: An Historical Essay on the Fundamental and its Physical Manifestation by Michaele Suisse and Peter Cameron

Dean,

Glad you like the review. Are you familiar with the algebra?

re unobservability of phase, particles are little oscillators. When you dephase them, break them apart, you get a lump of energy. incoherent. The coherent phase information of the coupled modes that comprised the oscillator is gone.

this is what gauge invariance is about. One's model has to permit local phase shifts (so unfortunate that weyl's 1918 paper ended up with the word gauge in place of phase) without changing the physics. For this to be true phase cannot be a single measurement observable.

one might consider the phase difference to be a measure of how precisely one can define simultaniety. Need two things for them to be simultaneous. How does one make just one measurement of two things when those to thing are at separate locations?

this is basis of special relativity. Need three things to get special relativity. The two objects plus the observer. Lorentz transform is just trigonometry, Pythagoreus.

quantum logic at foundational level is just two things, two interacting wavefunctions. To assume logic beyond that is epistemologically incorrect imo. Phase is not a single measurement observable.

Peter,

Looked at Watson and Trail, didn't find much i could relate to.

Liked the appearance of your interferometer experiment. You have access to hardware?

This article discusses an interesting time symmetry experiment in the nested Mach-Zender interferometer

https://physics.aps.org/articles/v6/133

If you look at my author page on vixra, you will see a delayed-choice variant on this experiment. Any thoughts on how to get it done?

Pete

Hello Mr Cameron,

You are welcome.No I have not made this contest, I have serious problems in Belgium and my mind is not focus and also my English is not good.I will publish several white pappers this year in logic about my equation, the spherisation and quant and cosm sphères, about DM, the quantum gravitationa also, this and that,about also the spherical geoemtrical algebras that I have invented but I must admit it is not easy to formalise all these spherical volumes and their motions with the vectors and scalars, I study and read the book of Hestenes and it is not easy , I try to respect our mathematical laws but I am not a mathematician and I am obliged to study things that I don't know.Not easy is even a weak word lol , Hestenes is so relevant and his book is so difficult to understand.

About the ratio, I have never said this but I lmike your generality and the fact to try finding this QG.I liked your papper Mr Cameron you know, but I see differently simply about this QG.I am wishing you all the best in this contest,

Dear Michaele Suisse and Peter Cameron,

My less formal comments, including a couple of strategy suggestions, are provided in reply to under your kind comments on my essay. Here I want to be a bit more formal and put on my technical editor hat, because I think your ideas are not getting as much traction as you would like in part because of your paper writing style.

The biggest problem is pretty simple: In your frustration to get your message across, you are trying to jam far too much content at every level -- into your papers, tables, figures, charts, pretty much whatever. Or to put it another way, you are doing something that is very common in bad government technical presentations, which is that when someone tells you "use fewer slides!", you do it by shrinking the fonts until no one can read them from the front of the room, let alone from the back. I should note some exceptions: Most of your flow diagrams, such as Figure 2, are actually quite good. Figure 3 on bivectors and trivectors is also pretty good, since it translates the definitions into nicely understandable figures.

I've scanned about half your papers at viXra.org -- please take that as a genuine complement -- and in one case you have a "one slide is best" presentation that is, um... 57 pages long? With one slide marked as the "one slide"? Even that one slide used small fonts packed densely, since you tried to get some kind of reference to all of your ideas into it that were then explained on all the other pages.

You are not getting it.

A good one-slider is visually simple, with a small number of lines, not much text, and an absolute minimum of novel words, preferably none at all. The one and only thing that should be novel about it is the collectively the content of that one slide should clearly capture some completely novel concept that will make your audience go "say what??" and "I never thought of it that way!" Both your impedance idea and your geometry idea are examples of concepts that might work very well for such slides, and I do think you tried to do just that. But in what you have, there is just too much noise, by which I mean too many math or and visual terms that are not really needed to make your point.

A gorgeous example of what not to do is Figure 4, with the only quickly comprehensible bit of text in the entire figure being the word "proton" in a box in the middle... and of course even that is baffling, because most readers (like me) came to the figure kind expecting it to be about fundamental fermions, which of course the three-quark proton is not. You do not even define that the zoo of letters and subscripts means! Your explanation under the figure instead seems to toss in every concept you can think of, including the unexpected remark that the top row is the electron and the left column is the positron... which was not the kind of orthogonal geometry one would immediately expect for a particle and its antiparticle, unless I am missing something obvious about a flip on the main diagonal? Since this is... sort of?... a matrix? Argh!

Tossing that kind of confusion into a figure that is supposed to explain some critical concept is even more risky for you that for most paper writers, because you are explicitly attempting to introduce ideas for which most readers will not have any prior familiarity.

Do you understand why that is risky?

As an editor, one of the biggest warning signs to me of an accidentally (or intentionally) bogus paper is that it always introduces a huge amount of impressive-looking noise--misuses or undefined terms and equations-- that ultimately don't fit together at all, but do leave most readers so exhausted that they give up.

If the author is famous and the review gets too exhausting from trying to look up and make sense of all of the noise terms, most reviewers abandon giving it a careful review and just rubber-stamp "OK!" on the paper... which they should not do, by the way!

If the author is not famous, they conversely automatically stamp "FAILED!" on the paper and toss it into file 13, mostly because they have no reason to trust the author and no desire to get called out later for passing what could be total nonsense. But at least this is what they should do in such cases, since if the authors have made the paper too difficult to comprehend, that's on them, not the reviewer.

Now, since you tend to write dense papers full of undefined terms, you have to ask yourself: Which of those two I-give-up review categories to you think most or all of your papers will fall into? (Bummer about your name being so similar to a famous mathematician, Peter. That just makes matters worse, ouch.)

And that brings us to my assessment.

Peter, Michaele, even though I think your ideas and papers are some of the best developed and most conceptually intriguing ideas I've seen, and even though I am very familiar with some parts of your turf where my own research and idea overlap, I can't tell based on your figures whether your really know what you are saying, or you are just blowing a lot of smoke our to make what you have look more impressive than it is. Figure 4 is a good example. That may be the most brilliant chart ever devised for explaining the Standard Model... but if it is, wow, you fulled me. I can't even figure out how it relates to standard particles, even to the only comprehensible label, which is the word "proton" in the middle.

So I find myself in the ironic position that while I really do like the descriptions you give of some of your ideas, such as in particular the impedance idea, your papers and this essay give me no easily defensible reason for thinking that you have worked those ideas out in detail. And I just don't have the time or inclination to spend hours or days trying to figure out the answer to that question on my own.

So, good luck in any case. I likely will come back for some more reading of your papers, if nothing else just to see if me initially positive impression was justified or a case of me fooling myself into believing there was more there than there really is.

And by the way, a secondary issue, one that is shared by I dunno, maybe over half of the essays this year?, is that you didn't really answer this year's FQXi question, which was how to tell if something is fundamental.

I realize by now (this is my first year, and despite many good interactions I am still ambivalent about having submitted my work here) that there exists at FQXi a lively history of the same people participating year after year just to share the latest iterations of their personal physics theories (or anti-theories in some case) via the FQXi community. So each year they (many of you who are reading this!) largely ignore the real question. They (you) instead write up a snippet of intro text that "explains" why the next iteration of their (your) idea falls under the new question, whether it dos or not. It's a tradition, sure... but it also is not really what FQXi is asking for, either.

Cheers,

Terry

Fundamental as Fewer Bits by Terry Bollinger (Essay 3099)

Essayist's Rating Pledge by Terry Bollinger

Dear Terry,

Pretty cool to start the day with comments such as yours. Thanks for screwing up my schedule.

you nailed it with the frustration thing. Quick summary

- arxiv won't let us post

- can't get past the editors at most journals

- those editors who do send papers out can't find referees

- in seven years since foundation of present work synthesized itself, we've not been successful in securing even one opportunity to speak, to present our ideas in a logical coherent sequence.

so yes we are frustrated. and this drives the attempts to present enough information to make each paper a coherent whole, the information overload. Aware of it and hate it, Michaele and I have been arguing about it. She wants me to make the next little note two pages long, and I put my foot down at one. Posted on vixra now, perhaps you've seen it. We've focused on what is probably single largest problem with SM, the infinities and renormalization.

please, if you would, give us a critique? How can we improve it? Identify the tripping/tipping points? else?

taking a risk here, as a non-expert presuming to summarize a Buddhist perspective on the arising of consciousness, a five step model proposes:

0. form - internal or external, presents itself to

1. emotional tone - where it excites some pre-existing balance between sympathetic (fight or flight) and parasympathetic (relaxation) branches of autonomic nervous system

2. perception - preconscious perspective integrates and encounters

3. volitional formations - the residue of previous iterations of this feedback loop/network, most often deeply entrenched, which filters all but that which reaches

4. consciousness

Michaele and I have gone again and again thru this, where/why/how the tripping point emerge and the tipping points get lost.

obvious is that bringing those two lost threads of geometric wavefunction and impedance quantization to the surface gives a new perspective that appears to be well-integrated, and of course it is not the answer any of the searching communities are invested in. Those in privileged positions of comfort and esteem really don't want to see the Higgs as an incredibly short-lived magnetic resonance,...

lol re the 57 page 'one slide'. funny, i remember it as being longer, eighty something. Wonder what's missing from the one you see. gotta fix that.

re figure 4, well, yeah, i know. Point well taken. If i ever have to regurgitate this stuff again, now see a way to fix that. thank you for the attention to it.

again re fig 4, conceptually you seem to be following it pretty well. phases rotate in opposite directions for electron and positron shown at top and left. Or one could have them rotate in same direction if wanting to model that. For vacuum wavefunction i think they should rotate opposite.

presuming one knows how to do so, when one excites that vacuum wavefunction first things that appear are lightest rest mass particles, pair production. In approach we present, as a consequence of the dynamics that emerge if one increases excitation energy, higher order resonances appear. Muon is first, according to MacGregor is 'platform state' for all the rest. That seems to work for the proton spin structure paper we presented to SPIN16.

and that paper was based on the modes highlighted in green in fig 4. It seems to be all of one piece, surprisingly so, everywhere we look. So yes it is a matrix, apparently the long-sought particle physicist's S-matrix.

lol, scrolling down thru your comments to the only comprehensible word, 'proton' in the middle. indeed we are blowing a lot of smoke here, with great delight.

agree re we are all selling our schtick in the present forum. For those of us with no other access it is a precious resource.

    coming back again to fig. 4, your comment

    "I can't even figure out how it relates to standard particles,..."

    caption has the phrase

    "Modes indicated by symbols (triangle, square, dot, diamond) have their impedances plotted in figure 8, opening new windows on the unstable particle spectrum."

    Conclusion from figure 8 could be that production and decay of the remainder of massive particle spectrum is governed by the impedance structure of the most easily excited massive particle, by the excitation of the full eight-component geometric electromagnetic Pauli wavefunction of the particle we call the electron.

    Figure 4 is impedance representation of the scattering matrix. Figure 8 shows how a portion of the resulting network is related to the unstable particle spectrum.

    pdf of early calculations is available on the cloud

    https://drive.google.com/file/d/0B_pzihZZV6IfckpQTVFRQzRtMm8/view?ts=5a182f53

    Dear Michaele and Peter,

    I highly appreciate your well-written essay in an effort to understand «andpresent details of the new perspective»

    It is so close to me. «Of itself the geometry and its algebra are abstractions. It is only with the possibility of excitation by physical fields that the concept of geometric vacuum wavefunction becomes useful».

    I hope that my modest achievements can be information for reflection for you.

    Vladimir Fedorov

    https://fqxi.org/community/forum/topic/3080

    Dear Michaele, Peter

    If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don't rate them at all. Infact I haven't issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to gain.

    Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me and my essay in questioning this circumstance?

    My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. And again, how lucky we are! for if they didn't then gas accumulation wouldn't be halted and the star would again be led to collapse.

    Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?

    For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.

    My essay is attempt of something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up a potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond formation activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemistry processes arose.

    By identifying atomic forces as having their origin in space, we have identified how they perpetually act, and deliver work products. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might explain for intricate structure and complexity within universal physical systems.

    To steal a phrase from my essay "A world product of evolved optimization".

    Best of luck for the conclusion of the contest

    Kind regards

    Steven Andresen

    Darwinian Universal Fundamental Origin

    Peter,

    Thanks for the link, yes, confirms my thesis. Backward causality is just backward thinking.

    I'm afraid I have no access to sophisticated hardware. I can do simple bench top experiments, but consistent with that. Also as in my paper, the controversial 'novel' non singlet state momenta I now find already existing on a 'Poincare sphere'!

    Declan just shows the classical mechanistic sequence using that start point produces CLASSICAL QM! But hard to follow without some expertise in Quantum optics etc.

    We seem both to have exposed aspects of the same fundamental issues with current theory. Our essays are very close (and mine has just been hit with some 1's!) so I hope, as it seems, we equally agree the high value and fundamentality of each others work and score accordingly. Do comment on my string. I'll be applying scores shortly. Well done for yours.

    Very best.

    Peter

    Peter & Michaele,

    You have mentioned bi-vectors and tri-vectors. Can you elaborate on this please. If a bi-vector is the product of two vectors, how is that different from a vector that is perpendicular to both? If a tri-vector is the product of three vectors, how is that different from a scalar?

    Thanks,

    Gary Simpson

      Gary,

      i'm no expert, but my understanding is that bivector is 'dual' of the conventional orthogonal vector of the Gibbs vector cross product. Thing with geometric algebra is that the product changes dimensionality in such a way that scalar/vector/bivector/... formalism works in any dimension, but dual Gibbs representation works only in 3D space and 4D flat Minkowski spacetime. This seems to me to be a rather profound sort of 'symmetry breaking', wondering how it might be related to the topological symmetry breaking that results from great strength of magnetic charge. Brings to mind Veneziano's dual resonance model, as shown in fig. 7 of our essay. It was one of the big steps on the way to string theory.

      in 3D Pauli algebra

      scalar is scalar - one singularity, electric charge

      vector is vector - two singularities, edm and magnetic flux quantum

      bivector is pseudovector - Bohr magneton and electric flux quantum

      trivector is pseudoscalar - no singularity, magnetic charge

      a caution there is a topological inversion buried in that little list, due to strength of magnetic charge. Position of Bohr magneton and magnetic flux quantum are swapped relative to what one might intuitively expect.

      figure 4 of the essay shows that in a little more detail for electron and positron wavefunctions at top and left, but one has to go to the references to get the details. We didn't delve into the topological stuff for the essay. Information overload already, we are too different enough.

      if you look at the thread on Terry Bollinger's essay you'll see about 80% way to the end he and i have a subthread. He seems to know quite a bit about this, please if you quiz him do so in that thread so i can learn as well.

      Peter,

      Our essay got hit by a couple ones as well. Doesn't take much to drop one out of the limelight when unknown late entry. All part of the learning curve I guess.

      One could argue that we had it coming in the case of Michaele and I. Being perverse character that i am, decided i would learn about fqxi by starting at the bottom rather than the top of contributor ratings. Can't be honest there, or at least it became obvious that one has to be very careful with people who are looking to enhance some sort of sense of satisfactory selfness. Horrid disease that is. Stumbled a couple times, gave up on that, and searched for Clifford algebra. Pretty cool that fqxi has that search engine, tho indexing doesn't permit searching by contributor name, as you might already know. Think i understand a rationale for that, but sure would like to follow lines of thought/comment of some of the folks here in a more coherent manner.

      i have no problem with someone giving me a one if they tell me why. gotta believe the moderators are clever enough to be looking at stats on this sort of thing. Sociologist's wet dream imo. Guessing the one givers get tagged at some point by the moderators. Newbie mistake, tho with good intent. I like Terry Bollinger's ratings code of conduct, tho don't totally agree with it. To my thinking it is still a little too rigid.

      He also emphasized looking at Trail's essay again, in the context of Gibbs vector formalism working only in 3D space and 4D spacetime, whereas Hestenes/Clifford scalar/vector/bivector/... formalism works in all dimensions. In 3D the one is supposedly the 'dual' of the other. Odd that Gibbs representation is valid only in 3D, what sort of broken symmetry that is,...

      Couldn't get my mind around Trail on first try, going back for another look.

      bivector pseudovector has no singularity, like trivector pseudoscalar.

      Peter,

      You need to follow my essay ontology before analysing Declan's code & plot built from it. I note you haven't commented there yet (Little time left). See also Watson's.

      The 1's continue to annoy. A simple added rule I've proposed would solve it! (no post and the 1 may get put back on theirs!) As, though different, we seem to appreciate each others I'm sure we'll both be gentlemen and rate them appropriately highly? I hope to see your comment on mine. To help I posted the below on my page.;

      AS MOST STRUGGLE WITH THE CLASSICAL SEQUENCE (TO MUCH TO HOLD IN MIND ALL AT ONCE) A QUICK OUTLINE INTRO IS HERE;

      1. Start with Poincare sphere OAM; with 2 orthogonal momenta pairs NOT 'singlets'.

      2. Pairs have antiparalell axis (random shared y,z). (photon wavefront sim.)

      3. Interact with identical (polariser electron) spheres rotatable by A,B.

      4. Momentum exchange as actually proved, by Cos latitude at tan intersection.

      5. Result 'SAME' or 'OPP' dir. Re-emit polarised with amplitude phase dependent.

      6. Photomultiplier electrons give 2nd Cos distribution & 90o phase values.

      7. The non detects are all below a threshold amplitude at either channel angle.

      8. Statisticians then analyse using CORRECT assumptions about what's 'measured!

      The numbers match CHSH>2 and steering inequality >1 As the matching computer code & plot in Declan Traill's short essay. All is Bell compliant as he didn't falsify the trick with reversible green/red socks (the TWO pairs of states).

      After deriving it in last years figs I only discovered the Poincare sphere already existed thanks to Ulla M during this contest. I hope that helps introduce the ontology.

      Peter

        Peter,

        Looked again a couple times at Traill's essay. Perhaps starting to get the connection Terry Bollinger was trying to point out.

        From perspective of the geometric wavefunction interaction (GWI) model Michaele and I are working with two essential points relevant to Declan's essay seem to stand out.

        1. There exist two different varieties of quantized impedances - scale invariant and scale dependent. Forces associated with invariant impedances can do no work, cannot share energy/information. Resulting motion is perpendicular to direction of applied force. These are the conduits of non-locality. They communicate only the quantum phase of entanglement, not a single measurement observable. Here the GWI approach appears to be in harmony with what Declan shows.

        2. What distinguishes quantum from classical is quantum phase. Once one accounts for the fact that phase is not a single measurement observable, from the perspective of our synthesis of geometric wavefunction interactions with quantized impedance networks QM appears 'classical', again in agreement with Declan's conclusion.

        Having arrived at this, now feel ready to take a look at Watson, and then yours again. Tho we're not math folks here, Poincare sphere is only slightly familiar to me from Penrose's road to reality.

        Peter,

        No maths in mine to worry about, just needs a little brain power to follow the ontological construction. Declan's is essentially just the matching code & Plot. Haven't seen a comment yet, (on the above or my essay) hope you get to it. The 2 pairs of momenta are simply linear, max at the equator, and polar curl' which is orthogonal. Both go to zero at 90 degrees, and both change non linearly over 90o by Cos latitude (known in geophysics).

        With that starting assumption replacing 'superposed singlet' states the classical derivation becomes possible (with a few similar more careful analyses including of WHAT we actually 'measure!).

        Final reading now & scoring shortly - hope to do most but clearly those who read/understand/like mine obviously get priority!

        Best of luck in the run-in & judging

        Peter

        Dear Peter Cameron,

        In a response I had overlooked on my page you asked about my view of quantum gravity. My view of this topic is here: The Nature of Quantum Gravity.

        You also mention that Hawking suggests that a 'Planck particle' would have a Compton wavelength thousands of times the observable universe. For me, that's a proof of no Planck particles.

        In my quantum gravity theory (post-big bang) events which occasion extreme energy density (such as LHC collisions: Au-Au, Pb-Pb) are "off-center", i.e., "off axis" and hence also occasion high angular momentum in the resulting perfect fluid. The dynamics of turbulent vortices spit out particles along the gravito-magnetic axis (of angular momentum) and these particles have bounded energy. That is, no matter how much energy you bring to a small region, it does not create a Planck particle, but a cascade of real particles. These are the particles (and resonances) of the standard model. Post-big bang there is nothing beyond them! Just as SUSY has never shown up, nothing beyond additional resonances will ever show up. The particle zoo we have is it. We need a theory that calculates the masses and I believe that my quantum gravity can do so. [I am working on it.]

        The effective field theories are 'bookkeeping schema'. They ignore the perfect fluid particle dynamics leading to toroidal particles and jump straight to the end result, "creating" and "annihilating" particles from 'quantum fields' in a way that conserves appropriate aspects of the particle. From this perspective, there is no limit on the particle zoo, hence wavelengths 1000 times longer than the observable universe arise. This does not occur in a more fundamental particle dynamics. Quantum theory is statistics. The particle and the wave properties arise from quantum gravity.

        I very much enjoyed our exchanges, and I'm always excited to see geometric algebra-ists at work.

        Best regards,

        Edwin Eugene Klingman

        Dear Michaele and Peter,

        I've just discovered that a 2-hr blackout has wiped a long enthusiastic WIP response to your essay -- probably via a valid log-out at FQXi -- and I'm not good at rewritings! So this is short-&-sweet as I look forward to many more ongoing discussions!

        Thanking you for a (for me) beautifully presented and breath-taking essay, I regret (just a little; as you'll see) that it follows the mould of Philip Gibbs' lovely essay on "a universe of stories" as against my fondness for "a universe of dialogue" based on stories, poems, observations, dreams, etc. + MATHEMATICS -- such dialogue itself based on a universe of spacetime (a beable), full of beables and interactions -- the more especially when I see our shared fondness for GA, wavefunctions, interactions, observables (7x on p.1), ++++; plus a healthy avoidance of matrices, etc; ps, though I find avoidance of Bell's lovely term "beables" (nb: in spacetime) not good for digestion; neither of food nor ideas; nb: I also like inferables. [Breathing has now forcibly resumed; and with it the truth that much of your essay is currently beyond me.]

        Re wavefunctions [WFs] -- and reminding you that (imho, if you like) math is the best logic -- please see Fröhner (1988:639), hyperlinked at Reference [12] in my essay; or via direct link to the PDF Missing link between probability theory and quantum mechanics: the Riesz-Fejér theorem.

        Fröhner's work is part of my theory [see essay at ¶11]; so re WFs, see particularly in the vicinity of this on his p.639: " ... Historically, the superposition principle had been established first as a puzzling empirical feature of the quantum world, before M. Born recognised that the absolute square of the wave function can be interpreted as a probability density. ..."

        Re this from you: "The resulting geometric wavefunction model permits one to examine the interface between fundamental and emergent." I see that "emergentia" is a favourite theme (at least on p.1): me being here forced -- similar to my distinctive use of "premiss" -- to return to the much more sensible Latin [subject to latin-experts] since the right word here -- emergency -- is misleading in plain English. Though (please NB) maybe it does apply as a primary-concept that we should first sort out: me trusting that we agree with that fundamental and elementary premiss: TLR (true local realism)?

        PS: Regretting, with apologies, many other wiped comments (though they can be reconstructed in ongoing dialogues), I'll drop a copy of this onto my essay-thread; hoping you'll do likewise if/when you respond.

        With my thanks again, and with best regards; Gordon

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