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A new type of symmetry breaking unlocking the scalar field's creative potential
Goal: The study of a new type of synchronous scalar field selfinteraction, through which the free field produces a potential well in which massive fermions and their interactions emerge, shaping for example an entire hydrogen atom.
Methods: 3D Modeling, ComputerAssisted Numerical Analysis
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In QFT, nonlinear or selfinteraction, or also enharmonic interaction represents a creative mode, unlike linear interaction or interference, as new wave numbers (k) are added. Each two parent waves create 2 child waves, which are the resp. sum and difference of the parents. A rudimentary example is, if Φ = sin (θ), then Φ^{2} = ½ + ½ sin (2θ). In other words, the child waves are 2θ and 0 (the stationary offset). The general case, in the exponential notation is: f(ξ) = ∫ Φ (x, t) e^{2πixξ}. I.e the resulting set is a Fourier transform of the original interaction, constituting the set of child waves ξ in the linear regime.
Alternatively, the transform can be represented as a binary or bifurcation tree, accounting for all sums and differences as per the terms {(0,0,0), (0,0,1), ..., (1,1,1)}.
In Bell's theorem, all possible combinations (resp. permutations), of passes and fails are represented by a binary tree, from which useful equalities and inequalities can be derived. To make plausible that Bell's theorem equally represents a Fourier transform, Bell's test is viewed as a labbench implementation of what is actually a natural gauge field or symmetry for spin states. The polarizer angles could, for the sake of argument, be imagined as continuously rotating, however considering a continuum of all possible orientations should be sufficient to imply or represent phase waves. Indeed the nonlinear interaction of the latter is correctly represented as a probabilistic correlation of event counts, as a function of the polarizer settings. Moreover, the spacelike component, that is the "wavelength" or wavenumber, could be arbitrary or wellchosen, whereas there is a single common phase rotation for all waves. This way all relative settings, and thus also all pass / fail combinations / permutations can conveniently be encoded.
Of special interest is the case where F(Φ{...}) contains a k=0 term, that is, an infinite phase wave, as it would directly represent the violation curve or integral. E.g. as per the earlier, rudimentary example, with implemented phase term : Φ(x,t) = e^{2πi(0  αt)}. For more than 2 waves / channels, such as in Bell's original design, there are various k=0 scenarios. If along with a k=0 term, an additional scenario of scaleinvariance is considered, the system is adequately defined as follows (omitting the negative terms):
φ^{2} + φ^{1} + φ^{0} = 2φ^{2}
φ^{2} + φ^{1}  φ^{0} = 2φ
φ^{2}  φ^{1} + φ^{0} = 2
φ^{2}  φ^{1}  φ^{0} = 0
...
with lower case φ indicating not the field but the scaling factor (Golden Ratio = 1.618...). This represents a comprehensive underlying invariance which is not derived, and which is superior to its effects and inferred by them. The recurring factor 2 is highly significant for the dimensionalization and discussed elsewhere. It is proposed that this state correctly represents entanglement without spooky interaction, and an interpretation of Bell's result in terms of nonlocal realism.
If the k=0 term in the present scenario is viewed as a Goldstone mode in a geometrized QFT, entanglement could be characterized as a special case of symmetry breaking, in the vein of "nonuniqueness of the groundstate" (Goldstone), in this case not facilitating a local mass term, but sustaining correlation by not localizing but also not dispersing energy, that is, the conserved quantity. Equivalently, the proposed scaleinvariant selfinteraction could be viewed as a special mode with a zero net group effect, therefore not transporting or dispersing energy in any capacity. In this geometrical approach, the scaling factor φ breaks the symmetry (there is no quartic term added to the free field).
Of course this raises the question whether Bell was in fact correct presenting his inequality as the local realist limit. If indeed the experiment can be viewed as an physical manifestation of a natural gauge field or symmetry, then it appears that the presumed nonlocality, that is, the entanglement itself, is contained within the inequality, and that the so called violation is nothing but the local gauge condition. Indeed the inequality is entirely theoretical or inferred, whereas the violation appears upon detection.
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The violation of Bell / CHSH inequality in and of itself doesn't provide a presently known groundwork for its interpretation in terms of nonlocal realism.
However, if we consider that the polarization interaction is not merely a handy way of doing the measurements, and even it is not merely the ONLY way, but in reality it is an inalienable part and parcel of the entire phenomenon under scrutiny, then at least in principle the Bell / CHSH test could provide a useful context.
If we also consider that the phrase "violation of the inequality" is rather ill chosen, and is replaced by something like "confirmation of the integrity of the underlying action", then we could view the Bell / CHSH test as in fact a benchtop (emulation of a) natural gauge field or symmetry for spin states, indeed confirming a nonlocal underlying action, through correlation. In a more abstract sense, the whole concept of pair production and correlation might even be cancelled out.
Moreover, in Bell's original concept there are 3 channel correlations, resulting in a binary tree of 23 = 8 measurement combinations resp. permutations, as a whole representing the integral action, and from which also useful inequalities can be derived. Thus seen, the so called "violation of the inequality" does not strictly signify the trespassing of an entirely theoretical, classical, local realist limit by quantum mischief, rather it signifies the gauge condition or state of what in the ungauged or unconditional state is a pure, integral action. Sure is that gauge symmetries are local, so in that sense it is not quantum mischief "violating" innocent local realism, it is virtually the way around  local mischief "violating" a pristine quantum state.
Again, Bell's inequality is entirely theoretical, and could very well rather indicate a real, but unconditional state, than a local realist state that as a matter of fact doesn't exist at all.
In summary, in this view, the so called "violation" is not a quantum but a local gauge effect, and that which is "violated" is a pure, inferred quantum state or nonlocal action, and not a theoretical, local realist state that de facto is nonexistent.
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The classical resp. local realist case is a theoretical scenario, the same as illustrated by Bell himself, where the individual pair  analyzer interactions each somehow have a certain level or amplitude (essentially representing the Malus Law just like in a macroscopic beam of light), which are then detected against a given calibration level, typically around 50%.
It is easily believed that such type of interactions, which after all are cosines resp. cosines squared themselves, will therefore naturally also lead to a sinusoidal correlation curve, but that is not the case. The correlation in this case is simply on a yes/no basis, i.e. independent from the (theorized) levels. The correlation curve over all AB angles is instead triangular, and this is indeed the Bell inequality. It is can also be shown that  within extremes  the inequality is largely independent of the primary interaction curves or functions, so in that sense it is very robust.
In the QM probabilistic case, where individual events are not like a miniature Malus Law, the "levels" actually indicate count rates, or more precisely, count or event numbers for a given setting and interval. The correlation in this case is proportional to those event numbers. The integral correlation curve over all AB angles then is apprx. sinusoidal, depending on the threshold. This the violation of Bell's inequality.
This relatively clumsy (compared with Bell's simple and elegant math) simulation shows that there are no localrealist loopholes. That is, any hypothetical construct involving particles and / or equipment that should demonstrate violation based on classical causality, in reality only reproduces the inequality. Unless the system is so completely changed that it is not a Bell test anymore. This illustrates why journals such as Am. Phys. Soc. have an a priori "nointerest" policy re. loophole hunting claims:
"… With regard to local realism, our current policy is summarized succinctly, albeit a bit bluntly, by the following statement from one of our Board members:
“In 1964, John Bell proved that local realistic theories led to an upper bound on correlations between distant events (Bell’s inequality) and that quantum mechanics had predictions that violated that inequality. Ten years later, experimenters started to test in the laboratory the violation of Bell’s inequality (or similar predictions of local realism). No experiment is perfect, and various authors invented ‘loopholes’ such that the experiments were still compatible with local realism. Of course nobody proposed a local realistic theory that would reproduce quantitative predictions of quantum theory (energy levels, transition rates, etc.). This loophole hunting has no interest whatsoever in physics."
(Btw. said paper by Thompson imo makes exactly the mistake discussed above.)
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(in reply to Nancy Wanatabe posting a painting showing a lot of "action")
As interesting, welcome and oftentimes elucidating cultural outings are, the action principle in physics has an utterly prosaic definition, in it's simplest form:
S = ∫ E•dt or S = ∫ p•ds (p = momentum, s = distance)
and in it's simplest incarnations, e.g.:
E = h•f, or ΔpΔx >= h/4π resp. ΔEΔt >=h/4π.
These are the PlanckEinstein relation (as in the photoelectric effect), and Heisenberg uncertainty. Obviously the two are very closely related. Here h is the Planck constant, the quantum of action (so quantum physics concerns the discretization or counting of action). From the PE relation we learn that light has a particle aspect when the energy is measured, however light / energy itself is continuous.
If you have difficulty to understand or intuit what the action in physics is about, you're not alone. Books have been written about it*. An interactive demo of the history of the action principle I made myself: http://www.trigunamedia.com/slimconference/timeline/index.htm(move mouse over items).
As for the Battle of Chancellorsville  indeed it shows a lot of "action", but this is energy at work in the ever polarized, belligerent world of timeplaceperson (causality)  indeed every battle is a battle for space, for time, and for status quo. What you see is never the action principle of physics. In physics, energy is said to be conserved, but actually "energy" is the somewhat visceral term for something entirely abstract that is conserved, maintaining a "conflicted equilibrium". Likewise, the action principle maintains equilibrium, but this is hidden, and it is not a conservational but stationary principle. So:
Energy = Abstract = Conservational, Belligerent, relates to the manifest
Action = Abstract = Stationary, Harmonious, relates to the unmanifest
So although these two principles are abstract, they are superior to their effects and inferred by them (Ed Darnell got this completely wrong, but hey, what to expect from incomplete logic).
To realize the action principle of physics and mathematics in the Battle (!) of Chancellorsville, one has to look at its function at large  indeed, an integrative viewpoint. You could think of competition as serving the greater purpose of evolution. Without so many battles of the past, we would not have the civilization of today. Without Adolf no Kofi. But battle alone is not enough, there must be a greater attractor or drive  and that same in physics is the action principle. It is effectively a "peacemonger", but not after also first having given the incentive.
Back to (quantum) physics  if you remember there's always an interplay between kinetic and potential energies, typically in a vibratory / undulatory style (the "battle"), all under the direction of the action (excitatory ánd evolutionary drive), the formula's become easier to understand.
To discern not only the excitatory, but also "evolutionary" aspect of the action principle in quantum physics, could help solve a number of issues caused, indeed, by conservatist bias.
To close with the De Broglie: "Nevertheless, action is a very abstract notion, and as a consequence of much reflection on light quanta and the photoelectric effect, we have returned to statements on energy as fundamental, and ceased to question why action plays a large role in so many issues”
* Jennifer Coopersmith: The Lazy Universe, An Introduction in the principle of least Action.
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The laws that are well established in the natural sciences are final laws. However the transition from the noumenal the phenomenal is not arbitrary either, and is not yet very firmly established in physics. Also, the noumenal is though itself complete and unqualified, not arbitrary either  its creative action is bound by its native operative principles.
If indeed the intellect functions in and off the domain of the incomplete, the noumenal must be beyond intellectual comprehension. It's important not to see that as a dogma or cop out  it is a direct consequence of the intrinsic, and rather well established incompleteness of the knowing faculty (not to speak of inconsistency and undecidedness). Logic could apply, but not in any proprietary sense  the noumenal, though inferred by its effects, is superior to them, and thus the logic of the noumenal is always subordinate to the noumenal.
That which can logically be comprehended belongs to the phenomenal. This has been solved by accepting the existence of (latent) operative / creative strata in the noumenal, but being indistinguishable. In distinguishable form the strata comprise the noumenal or formal state, the transition or mutative state, and the final, phenomenal state. This is referred to as the characteristic bearing of the noumenal. Patient and careful analysis shows why this is a nonproprietary logic or synthesis.
It's interesting in this connection that Gödel as well as Turing turned to selfreference to prove their point, that is incompleteness and inconsistency, resp. undecidedness. In all this, the selfreference itself is the constant factor, and this selfreference is the characteristic bearing of the noumenal.
The challenge in physics is therefore, to relate invariance to selfreference.
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The difficulty is, if we view an emitted photon as a nondirectional, expanding wave front, the notorious perpendicular electric / magnetic fields are hard to imagine. Here the Poincaré "sphere" could be (somewhat) useful, in ways probably not anticipated. Namely, not as a mere nifty polarization diagram, but as a representation of the 2DF wave dynamics itself. That is, topologically, a Gaussian 2sphere (or similar 2form), with an invariance as per Gauss' Theorema Egregium.
The E+M components would then likely be modeled analogous to the spin theorem (noting that the 2sphere and the torus are diffeomorphic if I'm correct). This could be useful for a deterministic model of entanglement, obviously nonlocal.
A local realist view is pursued by D. Graft (based on calibration bias, dismissing quantum correlation, lacking a mechanism). A (semi?) local realist by Peter Jackson based on a spherical interaction theorem / mechanism causing quantumlike correlation.
My view is nonlocal / deterministic (requiring one additional mode), but PJ's model could possibly be a realistic local take on geometrical aspects of latter.
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Gödel incompleteness and dimensional issues in physics, especially QFT, imo are closely related. There are strong topological arguments such as brought forward by Farhad Ghaboussi (discussed on this thread). Perhaps from a somewhat physics inclined viewpoint, dimensionality (in the broadest sense) is at the same time universal and controversial. That's of course curious, and noone can be "blamed" for that. If, at least momentarily, we can adopt the viewpoint that nature doesn't need, and doesn't function in terms of spacetime at all, it seems that the latter represents an alternative form of selfconsistency, one that is experiential in nature  and this is the point  the ONLY one. There's no choice of metrics to pick from (or it be trivial ones), and the whole concept of a metric itself is unique. Also, it is an alternative state that is not obligatory. Mathematically, a dimensional form or manifestation constitutes a unitary transition, or isomorphism of the noumenal state. Perhaps it is very much a human condition. Reza Sanaye referred to it as "the psychotopological order", which makes sense. For physics, in order to be able to deal with this, it needs to descend from its edifice and question it's very foundation of timespacecausality, its experimental paradigm, and its perpetual search for selfconsistency, in, and in terms of the latter. Or it must, in the vein of Bohr, only claim that physics is concerned with what we know about nature, not with how nature is. This seems often overlooked by the league of pigheaded Standard Model dissenters, dwelling in unfulfilled childhood nostalgia where physics opens the gates to nature's innermost reality. But that's metaphysics. The more rational approach seems to be Bohr, or in perhaps a broader sense De Broglie (much ref.'ed), whereby (e.g.) Farhad shows in great detail what's controversial about the dimensional paradigm, but unlike Farhad, one can also accept the factual state of human experience and interaction as a science in and of itself.
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"Spin" is the rudimentary principle that has the same dimension before and after detection: kg•m2/s or J•s. I'm particularly interested in the former, as it can be viewed as a spherical dynamic which not only allows to geometrize the action, but also in that capacity functions as a nonlocal hidden variable, which is NOT excluded by Bell's result.
Although @Peter Jackson proposes a classical, causal measurement sequence, I do agree with the general idea that (Bell's) spin "statistics" have a distinct (probably geometrical) origin. It could be the "nonspooky" explanation for the violation of classical statistics which Bell was sure to be out there, but failed to ascertain.
I propose that the geometrization of the action functions as a nonlocal hidden variable (in the Bell experiment) and that by the almost tautological nature of "spin", this nonlocal functionality transitions into the world of timespacecausality.
Also attn. R. R. Poznansky who arduously seeks to define and employ that dimension of "nonlocal functionality", with the additional note that spinlike phenomena may be the morphogenetic drive behind biomolecules: biochemistry as spinmimicry with the ulterior result of biomolecular helicity aka DNA.
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"An exception [Ehrenfest's theorem implying that the quantum mechanical expectation values obey Newton’s classical equations of motion] occurs in case when the classical equations of motion are linear, that is, when V is quadratic and V' is linear. In that special case, V'(<x>) and <V'(x)> do agree. Thus, for the case of a quantum harmonic oscillator, the expected position and expected momentum do exactly follow the classical trajectories."  https://en.wikipedia.org/wiki/Ehrenfest_theorem
This could be one way to interpret my modest modification of QFT, in the sense that I propose a scalar quantum harmonic oscillator, replacing, or being a discrete subset of the continuous quartic mode in the standard theorem (~Higgs mechanism) which has some persistent disadvantages.
Ehrenfest's theorem might thus help model a case where a (rather) classical oscillation (atomic, molecular) is resonant with, and thus in a sense driven by the underlying scalar field selfinteraction.
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Consider E = h•f. or h = E / f. If the measurement concerns the frequency resp. corresponding wavelength, in a sense that the energy doesn't really matter, you see a wave in space, e.g. in the double slit experiment. If the measurement primarily concerns the energy, and the frequency doesn't actually matter, you get a particle, as in Einstein's photovoltaic effect.
The perceived controversy is because one mistakenly takes space as preeminent and absolute. The action h is what reconciles both, in the sense that its unit being (proportional to) m2 / s, can equally be a 2DF or a 3D (not: 3DF) action.
Topologically, the boundary between the two is 2sphere, that is, the 2DF action is embedded in 3D space. Physically, the "boundary" or rather transition between the 2 is spin, which, if quantified, still has the unit of action. As Farhad Ghaboussi correctly pointed out, it must not be embedded.
For example, the photovoltaic effect in the core is not a 3D experiment. The double slit experiment by its very premisse is explicitly 3D. So the waveparticle effect is only perplexing to those who view space as preeminent and absolute.
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Not literal references that I readily know of, I've never looked further into Bohmian mechanics.
But the reasoning is simple: the particle being "guided" is massive, mass being the resistance felt when a particle is classically accelerated.
Q functions "as if" there is such a classical (i.e. local) mechanism, but there isn't.
Therefore we identify the quantum potential "Q" as the resistance felt as if a particle would classically be accelerated.
To say then that mass and Q are one and the same thing is inaccurate. Because, Q can only be factored out if the particle (mass) follows a certain trajectory, a "geodesic" as it were, which of course is the whole point of Bohmian mechanics.
In other words, the "guiding wave" and the "quantum potential" are 2 wings of the same bird  without the quantum wave in some form, which is really the Schrödinger picture, there is no Q.
Does this mean that if the mass, i.e. the nonlocal "resistance mechanism" is meaningfully related to the Schrödinger wave, "Q" becomes redundant? I think the answer is affirmative, Q is indicatory but not explanatory.
Note "meaningful" here  it is only so a truly nonclassical system or subsystem. In other words, if the massmechanism / vibration system is such that a quantum potential could be factored out, the latter is a measure of intrinsic nonlocality, perhaps also in larger than quantum systems, and thus of "nonlocal functionality". Q itself however does not explain it, and the nontrivial case cannot be accredited to Q.
As for the "massmechanism" itself, this is well understood (the "99%"), but needs modestly be tweaked to match a "Q" i.e. nontrivial case.
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As a result of the conservational bias (such as remarked by Louis de Broglie back in 1924), including 4D exaggeration, infinitisimal calculation and probabilistic orthodoxy, we are lacking the incentive, veracity and precision to correctly evaluate the "spinstatistics" / violation of Bell inequality, creating an illusion of "spooky action at a distance".
In reality, spinstatistics are not statistics at all, but the result of the spherical nature and discrete spectrum of both the Hamiltonian and the action, whereby the latter constitutes the preeminent, noncausal, simultaneous state. Therefore it is not the action that is "spooky", but the perceived classical distance.
What the "spin statistics" show is the discrete spectrum of spooky distance at an action.
The role of the spinor, that is the principal, unquantified spin, is exactly to moderate in between those invariant and conservational states. Mathematically, this transition involves straightforward integrability i.e. a unitary Fourier transform, allowing the geometrization of the 2D wave in time and space. In other words, spin itself IS the Fourier "mechanism" / integration.
Physically, and somewhat proverbially, hereby the "2θ" of the spinor transitions into the "θ" of the Hamiltonion / wave / orbital, and this is what creates the "violation" of classical correlation. It does not refute the scope and sovereignty of the action.
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Mathematically and principally, the (Mandelbrot) fractal consist of a number space, in this case complex numbers, on which for each number an iterative operation is performed. That's all. If we place the result in a 2D plane, we suddenly see all sorts of structures, such as spirals. The latter is a gauge effect. Moreover, if we zoom in, the spirals appear to be rotating, i.e. in the dimension of time.
By comparison, the "gauge" in this case does NOT "prechoose" the 2D or 2+1D plane, it chooses the (rotating) spirals (or: there is no precognized ordinal metric). Again by comparison, the instrument of choice is conservation laws and it's method is essentially Noether's theorem. Space and time as a metric then emerge from that choice. It is in fact a cognitive principle, but it is universal, i.e. not arbitrary. Once more by comparison, the "Higgs mechanism" is the spiral (mediating principle), the final dimensions are the same, and the formal scalar field selfinteraction is the iterative procedure.
From this analogy we can learn that the Higgs mechanism is NOT a gauge theory, but it has a gauge aspect, represented by the EW bosons, which are gauge bosons. The Higgs mechanism couples the scalar field (Goldstone modes) to the EW bosons, and that's what gives them mass. The Higgs boson is NOT a gauge boson, it has no spin  that's precisely what's brought in by the EW's, that alone shows that the Higgs mechanism is not a gauge theory.
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To appreciate what CERN, and high energy colliders in general are doing, you first have to appreciate that the cosmic epochs not only (and perhaps not at all), represent a literal historical sequence, but also (or actually) mass resp. energy levels or concentrations.
I'm perfectly alright with considering the Big Bang a metaphor for principal deconfinement, and nothing else. The nature of the subsequent phases of the sequence is characterized by "infinite mass / zero lifetime" to "zero mass / infinite lifetime", and the resp. particles / assumed gauge symmetries representing those phases. It's very good that you highlight the artificiality of collider experiments, but the philosophy here is that there's simply nothing that could distinguish between what's natural or not. High energy = high energy.
Instead of worrying whether CERN is good or bad, better is to think whether or not gauge theory / the Yang Mills framework holds up at those scales, because THAT is not certain. For what it's worth, I think it doesn't, and even I think it doesn't really already at the electroweak scale. Just to be clear, CERN does not claim anything in that regard, it only shows the signature of an extremely short lived high mass event, and that's it.
The surprise is, at first from the theoretical background, that the latter is in some sense a residual effect, in standard terms meaning that the Higgs boson is not a particle that takes part in the fabric of nature, at least not in any way we're familiar with. I do feel that the latter is reciprocally related to the artificiality of the experiment, and thus indeed the Higgs boson may not be exorbitantly representative for how nature is, but it is utterly unsophisticated to depict that as wrongdoing, either by the theoreticians or the experiment. It's simply the result of doing physics by physics' standards  CERN is not concerned with the second coming of Jezus.
Those who fancy a Higgsfree theorem, instead of pointing their wrath at CERN, should work on YangMills free solutions (and not forget to send it to ClayMath).
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How does bifurcation relate to trifarious action? That is, how does counting Planck constants relate nontrivially to the triple aspects of the thermodynamic process.
One is fairly trivial in fact, that is the common energyaction relation. Entropy and negentropy exist inside atoms only in prototype form. When the bifurcation ratio equals the bifurcation principle, the bifurcative action figure consists of 2^{3} = 8 eigenstates in principal or simultaneous form (= negentropic) and 8 distinct energy levels in sequential form (=entropic). Note here Louis de Broglie's later "hidden thermodynamics" principle action / h ∝ entropy.
The bifurcation has a 3D volumetric expansion isomorphism, that is radius : surface : volume = 21 : 2^{2} : 2^{3}. One could argue that this characterizes a Hydrogen atom, but rather it is the way around: the Hydrogen atom identifies the quantum field's bifurcation at the most rudimentary level.
The unitary principle that underlies even the bifurcation is Golden Ratio: ϕ^{0} ± ϕ^{1} ± ϕ^{2} = 2 × (ϕ^{0} or ϕ^{1} or ϕ^{2}). This is highly nontrivial in QFT as it correctly defines the self (i.e. nonlinear) interaction bifurcating the field.
Moreover, the bifurcative selfinteraction generates the k=0 (zero wave number, infinite wave length) crucial in symmetry breaking (k = ± (ϕ^{0} + ϕ^{1}  ϕ^{2}) ). The accurate proton2electrons mass factorization (including a resonant coupling = electroweak theory) is (6ϕ)^{3} ≈ 914.99 units, which corrected for the spin gfactor matches the empirical value within 0.011%.
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The idea is that if e.g. two objective, local molecules have a certain distance between them, the latter can be measured relative to the size of the molecules.
If intrinsic spins would be modeled by a log spiral, such a measurement is not possible. That is, there is no absolute metric or reference for the distance between the centers.
This represents imo the proper understanding of "nonlocal"  it is not "spread over the universe" per sé, rather the idea of space itself is meaningless.
A 3D variation (of the log spiral) is hypothesized to model (at the very least metaphorically) entanglement and the closely related Pauli exclusion.
In other words, not only nonlocality of spin is modeled, but also why not 2 identical spins can coexist (have the same quantum number) as they would simply overlap and be one. The combined effect is that of a nonlocal, hidden "variable".
This is worked out in a somewhat dated (not scholarly) article: http://science.trigunamedia.com/subspacevorticity/
The functional 3D spiral is now referred to as the "bifurcation vortex", preliminary demo: https://www.youtube.com/watch?v=BWGJr2Cq6t8&t=2s
The physical meaning of the log spiral is the path integral of a momentum over angular distance, that is, the action, in an inverse square law scalar force field.
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The free field is quantitative and detectable. The bifurcative action implied by the selfinteraction is qualitative and hidden, but can become articulated if predicated not solely by a mass term but by an integrative approach or model.
This leads to the rudimentary phenomenal state comprised of 2^{3} = 8 detectable eigenstates.
Vice versa, based on the latter, a highly nontrivial, hidden, qualitative action can be inferred.
However if the approach is overgeneralized by assuming a prefixed mass or momentum, real, underlying actional discipline is indiscernible, and the physics remains business as usual.
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Main stream physicists, typically lacking the creativity to think constructively about paradigm shifting concepts and theories, are also typically the first to play the evidence card when such theories surface.
Ironically, that same main stream physics established that ultimately evidence breaks down. We're not talking about probability, as famously illustrated by Schrödinger's cat, which is still controversial, but about Heisenberg uncertainty. There's nothing controversial about the latter  it can be demonstrated with household equipment (done by myself: https://www.youtube.com/watch?v=PQJmU16Jg).
Heisenberg showed that at fundamental scales, the principles that constitute objective reality break down. It's formulation is utterly simple: ∆ x ∆ p = ћ / 2. In other words, there exists no such thing as a particle at a specific point in time and space.
What's however remarkable about uncertainty, is that the Action Principle (as in the Principle of Least Action) remains unaffected. In other words, at scales where everyday reality breaks down, the action prevails.
So therefore it makes a lot of sense that a more complete theory of physical reality should be fundamentally based on action, and not on time, space and causality, that is, the jurisdiction of energy.
Cynically, as correctly remarked by mainstream scientist Wolfgang Konle, "most people cannot include the rather abstract concept of action in their terminology". In other words, it is very difficult to convince nonphysicists, let alone the general audience, that the fundamental limitation of physics lies not in physics per sé, but in the prevailing paradigm, giving the mainstream an unfair advantage.
This situation has been practically the status quo since the days of the Copenhagen Interpretation (1920's), which by convention established that quantum physics is probabilistic, and that there is no underlying, deterministic reality.
Because of this, and its sheeplike temple servants, we're stuck with an unsatisfactory and ultimately unsuccessful paradigm, "describing things that are real, in terms of things that are not real" (G. 't Hooft  https://www.youtube.com/watch?v=r0tMVN_9x4&t=5s).
As one can surmise from merely the formulation of Heisenberg uncertainty, but also from the consistent recurrence of the action, that is, it's unit the Planck Constant, in all the early, noncontroversial principles of Quantum Physics (e.g. p = h / λ ; E = h.f ) progress can only be made through an actioncentric approach. This was noted already by de Broglie in his Nobel winning 1924 paper: “Nevertheless, action is a very abstract notion, and as a consequence of much reflection on light quanta and the photoelectric effect, we have returned to statements on energy as fundamental, and ceased to question why action plays a large role in so many issues”.
A more contemporary proponent of the action principle in physics and other sciences was the Indian philosopher P.R. Sarkar, who, in the somewhat didactic form of "microvita theory", in an auspicious series of 40 discourses, outlined in great detail a vastly broader application of the Action Principle, especially to include life.
Therefore, a mathematical model of consciousness, as well as it's physics implications, cannot else but be based on a much more central role and broadest application of the Action Principle. This alone has the potential to push physics, and all of science, beyond the Copenhagen dogma that has dominated thinking about reality for just about a century.
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Standard QM:
 Red: de Broglie phase wave p = h / λ
 Violet: particle phenomenon E = hf
Selfinteraction:
 Blue: "sync wave"  "k=0" zero wave number, infinite wavelength issued by the quantum field's (Golden Ratio) synchronized bifurcative selfinteraction; represents the noumenal or ground state.
Rudimentary perception:
 The external mode is selfevidently cognitive, as it is associated with free photons, i.e. the EM gauge (Noether)
 The internal mode is associated with raw feeling / protopropensities as it represents the noumenal or ground state.
Evolved perception:
 The external mode is associated with complex, integrative sensomotoric interaction
 Submolecular, subcellular, cellular, organic etc.. structure evolves in such a way that the noumenal state is integrally preserved  this is a tautology
 Experience or experientiality is therefore the reflection of the unchanging, noumenal state, in the ever changing material world (different from holistic causation).
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The "most irrational number" and "Divine Proportion" Golden Ratio has a certain (subliminal?) appeal that makes it attractive for pseudo science  from Sacred Geometry to it's so called use in classical art and architecture. As for the latter, Dutch Albert van der Schoot in his 1998 PhD thesis "discovered that it was the Romantics who first placed it on a pedestal."  http://www.letterenfonds.nl/nl/boek/44/deontstellingvanpythagoras (English)
In nature, Golden Ratio is actually, albeit not accurately, implied in Fibonacci scaled patterning. Examples abound, from pineapples to cauliflowers.
On the other thread, Wolfgang Konle remarked: "If you really know a meaningful example in nature, where rational or irrational matters, this would be a sensation "
Obviously this calls for a nontrivial, exact case. As the Golden Ratio, the exact application is shown to synchronize the quantum field's bifurcative selfinteraction, so that the symmetry is broken e.g. according to Jeffrey Goldstone's principle that "The groundstate is not unique". The latter ultimately led to the QFT formulation particle mass, and of course the Higgs boson.
The Standard Model case however suffers from certain, well known, inconsistencies (as addressed e.g. in great detail by Farhad Ghaboussi), and could in short be thought of as a bulkapproach to mass generation. The Golden Ratio case is very similar in principle, but is instead synchronized, which not only produces mass but also structure. This is demonstrated using the simplest occurrence in nature, the Hydrogen atom.
Spectacular or not, considering the scientifically speaking somewhat troubled reputation of the Golden Ratio, which might easily put off less attentive and / or biased readers, it might be good to clear up for once and for all that Golden Ratio in said theory is unrelated to aesthetics as well as to whatever is meant by Sacred Geometry. Golden Ratio steers the nontrivial synchronization of the quantum field's selfinteraction, so that the field can create stable structures.
Summarizing, a general occurrence of Golden Ratio in nature is found in Fibonacci patterning, whereas an exact application, and therefore the nontrivial application of an irrational number, is proposed for quantumrealistic Hydrogen stability.
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The quantum field's (by definition nonlinear) selfinteraction leads to mass of particles which would in Yang Mills theory alone be massless (Goldstone, Anderson, Higgs, and many more...). This is called symmetry breaking, based on the groundbreaking, easily overlooked notion of Goldstone: "the groundstate is not unique".
The standard model solution is an unspecific bulk effect, having a number of well known and generally accepted issues.
A slightly different form of symmetry breaking is proposed, not based on a bulk, but on a synchronized selfinteraction, which not only leads to mass but also predicts structural integrity.
The easy explanation is that also the standard selfinteraction is bifurcative, but this is concealed in chaos. The harmonically synchronized selfinteraction brings out the bifurcation more explicitly, and this functions as the fundamental matrix of Hydrogen stability.
So, "Hydrogen" is somewhat of a didactical placeholder for the more fundamental principle of nontrivial, creative selfinteraction of the quantum field. The message however is, that what we call a (Hydrogen)"atom" is itself nothing but the latter.
The synchronized bifurcative selfinteraction can be highly nontrivially represented purely geometrically. QFT and geometry here are flip sides of one another. The geometry then not only functions for the dimensionalization, but also it constitutes a highly axiomatic foundation of (quantum) physics without any physical units and dimensions.
It's all ratio. This is presented as the noumenal state of quantum realism.
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Radin's experiment, although we assume that technically it is performed correctly, and also he makes no actual claims re. any magical "mechanism" at work, still suffers from a number of interpretational biases. Some are related to the so called "observer effect" as discussed.
But also the nature of the nonclassical state, i.e. the probabilistic wave function is but an interpretation, albeit a stubborn one, presented by Radin as a fait accompli. Fact is that selfinterference, irrespective of the double slits, can only happen if there is directional ambiguity, due to the photon source, perhaps due to Heisenberg uncertainty. At the same time, the impact on the photo screen is nevertheless classical.
What the nonclassical case or phase really shows, is that the directional discrepancy is truly a superposition of all possible directions (at least in that general direction, or even spherically). This of course is captured by the Feynman path integral. Wrt. to Radin's experiment, it means that a hypothesized "observer effect" not necessarily collapses the wave function per sé, but actually solves the path integral.
This is significant, because the process of the latter involves a number of operations (Delta Function normalization, nonlinearity, integration) which are also found in the brain. Popularly hypothesized, the brain is an active, concentrated, explicit "Path Integral Solver".
To ask "what ultimately causes the Path Integral to be solved" is not a good question  it is not "caused", it is merely the flip side of the unconditional state that constitutes the conditional state. The nice thing about a quantum experiment is that we can see an afterglow of the "flipping moment", such as the interference pattern of a double slit experiment.
We can however ask, if there is no cause, then "what universally and invariantly characterizes the potential of the unconditional to become conditional?". This is: acausality, selfreference and selflocalization. This is what occurs explicitly during a tightly controlled quantum experiment, and quite surreptitiously all the time, and this we call the characteristic bearing of, and which is consciousness.
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"Vitalism is the belief that "living organisms are fundamentally different from nonliving entities because they contain some nonphysical element or are governed by different principles than are inanimate things"  https://en.wikipedia.org/wiki/Vitalism
" But after a chemist is acquainted with the theory of microvita, he or she will no longer use this formula. He or she will prefer to use the new formula – say FeSO4 7H20 (Group A MV 20 million). Take another case, say copper sulphate (blue vitriol). The present chemical formula is CUS04 5H20, but after the theory of microvita is well established, a chemist will use the new formula – CUS04 5H20 (Group B MV 20 million). This means the chemical formulae regarding the inner structure of objects is undergoing a tremendous change. Of course, it is true that the size of formulae will be bigger than what they are today. It is also true that the denomination of the object and its internal qualities will not be changed. There will only be a change in the case of chemical formulae. A scientist in the microvita age will refuse to accept the carbon atom as the rudimental factor for the emergence of life. To him or her a carbon atom is nothing but billions of microvita getting solidified. "  P.R. Sarkar  The Theory of Microvita and Its Possible Effects on Society – Section A
In other words, according to microvita theory, ALL objects, inanimate AND animate, are  at least in part  governed by different principles than currently known in physics. This should however not be mystified: " (B) Doing principle or supramundane seed of the actional principle, ready for being sprouted. (Microvita of different characters, either of positive or negative nature, collectively maintaining the balance of the actional universe creating initial forms of carbon atoms that help macro and micropropensities in having their pure physical auxiliary media with mass and wonts.)"  P.R. Sarkar, Microvita and Cosmology.
The action principle is very well known and commonly used in physics. However already Louis de Broglie, in his 1925 paper, expressed the following concerns about the latter: "Nevertheless, action is a very abstract notion, and as a consequence of much reflection on light quanta and the photoelectric effect, we have returned to statements on energy as fundamental, and ceased to question why action plays a large role in so many issues”.
Since then, several authors and one may say, most prominently P.R. Sarkar, have gone through great length to rehabilitate and expand the scope of the action principle, to include life, mind and evolution. In this broader scope, Sarkar proposed the term "microvita" for the smallest instance of action, comparable to the Planck Constant in physics.
Also note that " In principle, negative and positive microvita are the same, but their field of activity is different". In other words, "positive microvita", which are proposed as promind, prolife (whereas "negative microvita" are promatter), do not constitute a fundamentally different element.
Conclusion: microvita theory is not vitalism, because it doesn't fundamentally distinguish between the constituents of the inanimate and the animate.
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My fellow country man and physics Nobelist Gerard 't Hooft said: "Quantum Physics describes things that are real in terms of things that are not real. A theory that describes things as they really are is more likely to be true and successful. We cannot say that Quantum Physics is wrong, but our interpretation is unsatisfactory".
So, how can the wave equation be correct, and our interpretation of it is not?
Louis de Broglie gave a very clear hint in his famous 1924 paper (in short): "due to so much focus on energy effects, we have forgotten about the importance of the action principle". I'm reminding that the Planck Constant h has the unit of action (Js or kg m2 /s), and thus the "ultimate unit or quantum", is the quantum of action.
The wave equation however is a Hamiltonian, and therefore an energy phenomenon. This is problematic because we think of the wave equation as an ontological state, whereas the point of de Broglie is that energy states are not ontological.
Now the point is not that the action principle is ontological all on its own, this is a bit inaccurate ("ontology" / "epistemology" don't entirely apply here), but that the action has a far greater say in things than suggested by the wave equation. We could call this, moving from an energycentric bias in Quantum Physics, toward an actioncentric approach.
The practical consequence is that (over) generalizations are abandoned, which obscure hidden potentialities of the quantum field. For example, in the de Broglie relation we decompose the momentum (which is energycentric), and in QFT we abandon the quartic interaction, which is also energycentric.
This can be done without fundamentally changing QM resp. QFT, but in the latter case it requires quite a bit of rehashing of the field's selfinteraction. Exactly the latter is the basis of the actioncentric Hydrogen model in my recently published paper.
In terms of the Copenhagen Interpretation, it means that an observer state is no longer isolated from the quantum phenomenon's (more or less) ontological state. They keep forming a harmonically resonant unity which among others has qualities that are associated with negentropic process, that is, with life and conscious perception. R. R. Poznansky for example suggests that this harmonic resonance is the nature and essence of teleonomy. It applies to quantum systems as fundamental as the matter wave itself.

The Flaws of Quantum Mechanics  Full Interview  Gerard 't Hooft https://www.youtube.com/watch?v=r0tMVN_9x4&t=5s
The Hydrogen Atom as an Integrative Eigenstate of the Bifurcating Quantum Field pc/laptop: https://www.thegms.co/publications/archives/mobile: http://science.trigunamedia.com/microvitra20080202.pdf
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Wolfgang Konle wrote on Aug. 18, 2020:
Frank, indeed, it is the combination of the key words “golden ratio”, “Fibonacci numbers” and “quantum mechanics” which in my mind rings the scam alert bell. It is also true that after this alert I tend to ignore further information of an according article. But to be honest, after rereading your hydrogen article, I encounter many similar scam alerts triggered by arbitrary accidental coincidences, which became excessively highlighted. In no single case the coincidences have been substantiated or consequences have been articulated. The foundations in that article have the quality of “this must be true because my grandfather had similar experience.”
Reply:
You've obviously become too partial due to past experiences to spontaneously tell consistency from trivial coincidences (apophenia), and therefore your "grandfather told so" quip only shows your lack of discernment. By the same token you could for example also call (other) Fibonacci numbers in nature unsubstantiated.
The real joke however is that the theory / model doesn't hinge on Golden Ratio in the first place, but on the Goldstone argument of QFT. My guess is that your lack of familiarity with the latter caused you yourself to "excessively highlight" the Golden Ratio aspect, whereas it is merely a curious, however well substantiated coincidence.
In other words, it could also not have been Golden Ratio, but apparently it is, and it would be virtually a scam in its own right to observe it, and then to ignore it. You may or may not take my word for it, but I knew this in advance, and I choose not to marginalize Golden Ratio just to stay clear of the likes of you.

Reply:
Here's an example of Golden Ratio is a Nature article, in the title and abstract even (also referring to a Science publication).
".. the masses of two different lowenergy quasiparticles in cobalt niobate approach the golden ratio, indicating that E8 might underlie the lowtemperature physics of this system ..."  https://www.nature.com/articles/464362a
So, now don't distort this as an attempt to promote Golden Ratio  it's only to show that top reputed journals don't freak out on research featuring Golden Ratio.
I've posted your comment and this reply on my project page, as a caution for others believing to have a lee way to dismiss a theory purely because it involves Golden Ratio.

Wolfgang Kohle wrote Aug. 19, 2020
The Golden Ratio 1.618...
Nature provides an extremely huge number of ratios. Ratios close to 1.618 therefore are nothing spectacular.
But it is a common human property to find this ratio aesthetic. This is the reason for its important meaning in architecture, painting, and music. The golden ratio also has a basic meaning in geometry (geometric mean) and mathematics (related to the Fibonacci sequence). In informatics it is involved in optimal layout of hash tables.
However, whenever other ratios in nature closely match to 1.618 or to its inverse, it is incidental and associating a deeper meaning to this incident is purely speculative.
Reply:
" Nature provides an extremely huge number of ratios. Ratios close to 1.618 therefore are nothing spectacular. "
That's a bogus argument. Many ratios have unique properties. Ever heard of Pi, 3.14..?
"associating a deeper meaning to this incident is purely speculative "
That's true, and that's why I don't do that. It is YOU YOURSELF who reads "Golden Ratio" and then jumps to the conclusion that the author implies deeper aesthetic or etc. meaning. There's nothing like that whatsoever, it's your own partiality playing tricks on you.
That said, there is a PhD paper from my fellow Dutch country man Albert van der Schoot, titled "Pythagoras' dismay  about the history of the divine proportion", where he shows that the Golden Ratio as an aesthetic principle is an invention of the Romantic Era, and not of ancient times. This is an example of idealistic appropriation. Observing Golden Ratio in a dynamical system is not, on the contrary it is a much studied phenomenon.
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This peer reviewed paper was recently published by open access journal The Gazette of Medical Sciences.
Citing from the paper:
 The present paper proposes an interpretation of quantum mechanics whereby the matter wave and its eigenstates are formed through an underlying, bifurcative selfinteraction of the quantum field.
 Subsequently it will be shown that based on the latter the protontoelectron mass ratio can accurately be calculated.
 The aim of the present work is to introduce an approach to Hydrogen stability with a decisively more central role for the dimension of action.
 Especially the widespread fractal attractor Golden Ratio (closely related to the Fibonacci numbers) turns out to elicit a number of unique and potentially significant features in the bifurcating quantum field
 The protontoelectron mass ratio thus captures and validates the complexity of the bifurcative selfinteraction or wave function in a single quantum mechanical number.
pc/laptop: https://www.thegms.co/publications/archives/
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This is a very rudimentary evaluation / application of the quantum field's bifurcative selfinteraction, showing a potential well and spinorbital states evolving from an apprx. base ϕ phase cycle bifurcation. Not shown are the volumetric expansion, the eigenstates and the actual spinorbital coupling models (spinors).
So what's the deal with "bifurcative selfinteraction" and what does it have to do with a mathematical model of consciousness?
Normally, if you do a spectrum analysis it shows you which frequencies (or wave numbers) added up to form the composite signal. If, however you do a spectrum analysis on a selfinteraction, that is, nonlinearly interacting waves, you don't see the original frequencies. That is a different spectrum, because it is a different medium. Now, if the wave packet is such that it can form nontrivial, that is, stable and thus perpetual volumetric automorphisms, we say it is synchronized. In that case, the (linear and nonlinear) media are implied in the waves or resonance. Also in that case, the (anyway) bifurcative character of the transformation is most visible and highly nontrivial. The Hydrogen atom is proposed to constitute exactly such wave system  it is a stable, perpetual, selfinteractive state or resonance in and of the quantum field, whereby the field does not even change in the absolute sense. This is in agreement with Goldstone’s argument that "the ground state is not unique". In other words, the quantum field generates Hydrogen atoms "at no cost" and "out of nothing". Therefore we say, with respect to physics, that the Hydrogen atom represents the quantum field's characteristics of acausality (unitaryness), selfreference (resonance) and selflocalisation (quantization). As we learn from 2DF physics, it comes itself with finite locality  it is not a manifestation in a preexisting (3+1)D cosmic theatre  the latter is just a cognitive convenience. These same characteristics are also proposed as the characteristic bearing of consciousness  it's the same principle, once in a more psychological, once in a more physical context
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You can take Einstein's relativistic energymomentum equation and substitute wave function operators for the resp. physical terms. Then you get the correct relativistic wave equation, called the KleinGordon equation. Only it contains no spin. Paul Dirac also took Einstein's equation* but rewrote it a bit, somehow hoping to get to a relativistic theory of the (moving) electron, including spin. He started by splitting up the momentum term into 3 different, independent dimensions. This at first gave him 4 terms  3 momentum (x,y,z) and 1 mass. For simple algebraic reasons it needed to be squared, giving not less than 16 (cross) product terms. How to solve this? This was Dirac's brilliant mathematical move: he realized that if each term represents a (2x2) matrix, then all the 12 crossterms would cancel out. Those matrices were actually Pauli matrices, signifying: spin! Thus what seemed a bug turned out to be a feature: it means that spin is an intrinsic requirement of the relativistic theory of the electron. What came out of this is the famous Dirac equation, which accurately predicts Hydrogen states including the elusive fine structure. The problem was, what Dirac in fact has done is demonstrating how you can mathematically distribute spin, which by itself is correctly represented as a Pauli matrix, over 3 (+1) independent physical dimensions. In physics terms this is a wrong kind of thinking. The two degrees of freedom of spin, plus the 2 degrees of freedom of the Einstein equation, together do NOT miraculously add up to produce 3+1 independent physical degrees of freedom. Therefore Dirac's purely mathematical, 3+1 D relativistic electron theory, resp. it's bispinor isomosphism, does not represent a physical reality. A spinor that correctly represents 2 degrees of freedom, and 2 + 2 components, is a dual spinor, not a bispinor. Note that the spinor is a 3D model  the 3rd. axis does not imply an extra independent degree of freedom  it is just a visualization. The dualspinor relativistic electron is mathematically described through a bifurcative transform, which is a purely abstract (geometrical) representation of the quantum field's synchronized (Higgslike) selfinteraction. Therefore the bifurcative selfinteraction of the quantum field is a realistic approach to a relativistic theory of the electron.
_{* The derivation of the Dirac equation is obviously simplified here}
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The matter wave constitutes the resonant state mixing action and energy. It consists of an intrinsic and an orbital spin component, resonant in a potential well.
In the unitary or prototype Hydrogen picture, used to calculate the sum total mass synthesis, we consider
 2 electrons (spin up and down) = full s subshell, and
 3 (x,y,z) orbitals constituting the full p subshell as a placeholder for the dimensionalization (azimuthal principle).
Each of the 3 (rate 1) spins resonates nonlinearly with the (rate 2) quadratic potential well, analogous to calculating the surface of a torus. It is a physical, rather than a selfinteraction. This creates resp. sum (rate 3) and difference (0) Fourier (or bifurcation) terms.
The rate 3 Fourier term forms the contributing mass factor for that matter wave's spin component. With a total of 3 spin components and 3 orbitals in the full pshell, the sum total mass contribution of the resonance is 3 (3 + 3 + 3) = 3^{3}.
In the unitary model there is no physical nucleus, only a potential or nuclear well. Hence the integral resonance is essentially a 3D isomorphism of the bifurcation itself. In standard QM, the 3^{3} resonant mass factor is effectively attributed to the nucleus.
In that case, the QFT electroweak interaction can be taken into account. The resonance can itself be modeled explicitly as a baseV3 bifurcation, obviously also yielding the rate 3 term. Base V3 bifurcation has been shown to relate closely to the electroweak (W, Z, H) masses and coupling factors.
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The colloquial "quantum number" is actually a set of quantum numbers defining the sum total state of a quantum system. It is best known for its first use to describe the orbiting electron or matter wave. The electron quantum number consists of:
 Principal QN = shell nr. or energy level n = 1.. 8
 Azimuthal QN = subshell n,p,d,f... typically p = x,y, z orientations
 Magnetic QN = "fine structure"  subtle differences in energies
 Spin QN = intrinsic spin up or down
QN(1) is described by the de Broglie relation (trad. matter wave). QN(1..3) by the Schrödinger wave equation, and QN(1..4) by the relativistic Dirac equation. QN (1) and (2) we learn in high school chemistry. This is almost "classical" Quantum Mechanics. Quantum Field Theory generalizes QM with electrodynamics in the Yang Mills symmetry framework, (arguably) culminating in the Higgs mechanism, giving mass to particles.
If one slams all piano keys at once, it could be argued that this also includes many hidden harmonies. This is what the standard Higgs mechanism is like. Likewise it is hypothesized that a (synchronized) bifurcative selfinteraction (i.e. nonlinear) lies hidden in the Higgs mechanism. This not only gives mass to particles, but also facilitates quantum structure. The question what actually brings it out is somewhat like the "Axiom of Choice" in set theory. The "selection mechanism" in this case is symmetry, and the structure created by symmetry is the Hydrogen energy levels or eigenstates, and on a more basic level the matter wave to begin with.
As shown before, it is hypothesized that the protonelectron mass ratio can be predicted based on the proposed bifurcative prototype Hydrogen (sub) structure. The distinction between resp. the Action and Energy (centric) bifurcations, each having a space / geometric and a time / cyclic aspect, yields 4 bifurcation "chambers" which can nontrivially be mapped with the Aristotelian 4 Causes.
Furthermore, pertaining to the current subject, the resp. reduction and synthesis phases among the 4 Causes can be nontrivially mapped with the 4 Quantum Numbers, which turns out to be useful to (further) validate and refine the bifurcative mass theorem:
 Principal QN (1) => Energy Synthesis/bifurcation i.e. 2^{3} = 8 eigenstates = Volumetric (counting shells)
 Azimuthal QN (2) => Energy Reduction = 1 eigenstate (psubshell counting x, y, z)
 Magnetic QN (3) => Action Syntesis/bifurcation = Phi^{3} = primary mass factor (Higgslike)
 Spin QN (4) => Action Reduction = (counting) 2 spins
Whereas the mass factors associated with the synthesis / bifurcation phases are quite straightforward, that is resp. Phi^{3} and 2^{3}, the mass factor associated with the reduction phases, 3^{3}, can be justified as consisting of 1 (particular) eigenstate, with 2 spins, in 3 dimensions.
Mathematically it can be equally viewed as an integral dimensionalization 3^{3}, or as a more distinct additive synthesis of 3 spherical surface expansions: 3^{3} = 3 (3^{2} + 3^{2} + 3^{2}) where each of the bases 3 = additive synthesis of 1 eigenstate + 1 spin + 1 spin, and the main factor 3 = "psubshell" counting x, y, z. The latter viewpoint is preferred. In summary 3^{3} identifies a single, dimensionalized full p=subshell and integral bifurcative reduction of a particular eigenstate. Obviously the reduction phase mixes a generative and a counting principle.
This yields an integral bifurcative mass theorem, with the value Phi^{3} x 2^{3} x 3^{3} = (6Phi)^{3} ~ 915. This involves 2 electrons. For 1 electron the proton / electron mass ratio is 2 x 915 ~ 1830. Compare with literature 1836.15. Refining by substituting 2 with the electron spin gfactor yields ~ 1836.35, apprx. 1 part in 10.000 accurate.
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The proposed (Higgs, Yukawa  like) selfinteractive mass generation and multiplication gives the correct protonelectron mass ratio, which cannot be calculated in quantum mechanics. The model is further evidenced by modeling Pauli Exclusion as well as the 720° Dirac spinor symmetry.
Not shown in this overview are the detailed formation of the dimensional, resonant (proto matter wave) and nuclear levels, out of the complementary action and energy bifurcations.
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BIFURCATIVE SYMMETRY BREAKING is an interpretation of scalar field theory whereby the free field readily implies a nonlinear or selfinteraction. Therefore there is no added (quartic) interaction.
The nonuniqueness of the groundstate is realised in the form of a unitary transformation adjusting the linear and nonlinear components.
When the selfinteraction is synchronized, a quadratic potential well is implied, and the action becomes effectively negentropic. The Fourier series in this case has a zeroterm, projecting an infinite phase wave.
It's spherical or dimensional form is entirely axiomatic, and is associated with the monoptical viewpoint of a biological (or equivalent) observer. The (ulterior) confined and deconfined states are considered only different in theory.
The double potential well in the standard theorem is effectively a (1,2) torus representation of the quadratic potential well in the bifurcation theorem. In the bifurcation theorem the potential well is a (2,1) torus.
In the dimensional form, the potential well as well as the linear components are represented through toruses resp. spinors, constituting the QCD and electromagnetic particles and interactions.
Because of the resonant coupling, the confined state has a default or lower mass bound.
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The study of a new type of synchronous scalar field selfinteraction, through which the free field produces a potential well in which massive fermions and their interactions emerge, shaping for example an entire hydrogen atom.
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