Well hello, Jess.

Nice to see some serious work presented on introduction. Ignore the inevitable nay sayers, they come out from under their bridges when scientific method is demonstrated in studious efforts. You have opened a new door for me, I'll have to read up some on Pascal. But it sounds to me that you have researched quite well, the questions that arise in theoretical representations of atomic structure and molecular arrangement.

Tetrahedra have interesting orientations when representing polarity. I personally like Octahedral representational schemes, passing a plane midway and parallel to any two opposites faces results in a Hexagon as most commonly found in molecular arrangements. Also constructing radii as additional axii through midpoints of the eight sides gives 14 potential dimensional orientations, which might be satisfying to String Theorists.

I thought it important that you can state that total shell energy is conserved over deformation in the simple harmonic oscillation model, as this would relate well with topological modeling of any unitary field definition of particulate matter. Too much emphasis is often given to the methodical difference between Quantum and Classical paradigms, when both are commonly incorporated in most areas if real research. And both seem to be embraced by your studies of mathematical patterning. Good Luck in finding kindred spirits, some do come here. I have been shying away for some time as there seems to be an army of irrelevant posters spewing blueline links of questionable origin and potential viral pedigree ever since Google implemented system wide reCAPTCHA protocols that over-rode the previous FQXi sub-routine. best jrc

I'm including part of a post I sent to an email list I participate in, which is devoted to alternative periodic table description:

Given how successful (and exact) my recent findings about shell energy changes over deformation in the harmonic oscillator model were, I thought to look at the actual energies themselves.

If we multiply the shell energies by the shell occupancies, we end up with the following (all energies in terms of h-bar omega-bar):

1.5 x 2= 3 (1s)

2.5 x 6= 15 (1p)

3.5 x 12= 42 (1d2s)

4.5 x 20= 90 (1f2p)

5.5 x 30=165 (1g2d3s)

6,5 x 42= 273 (1h2f3p)

7.5 x 56=420 (1i2g3d4s)

8.5 x 72=612 (1j2h3f4p)

The shell energies are all 3x the following 1,5,14,30,55,91,140,204...

And differences between the latter are 4,9,16,25,36,49,64.... (and starting with 1 if we use 0 as initial shell energy).

The discerning reader (if there are any readers...) may notice that there is some relation to quantum number l of the highest spin orbital in these shells.

I wonder whether the fact that the sizes of harmonic oscillator period analogues are all doubled triangular numbers, and that the slopes of linear component rays are all multiples of 1/3 h-bar omega-bar per delta deformation, the multiplication by 3 is any accident here. I kinda doubt it.

The email I sent to the circulation list concerning the shell energy conservation:

Hi folks. On page 20 of https :// application .wiley -vch.de/

books/info/0-471-35633-6/toi99/www/struct/struct.pdf 'Appendix Nuclear Structure', which I generally use to analyze shell model data graphically, is the harmonic oscillator plot of energy levels versus deformation.

As some of you may remember, all the spherical magic numbers in this simple model are exactly (and only) doubled tetrahedral numbers from a term-doubled Pascal Triangle. The doubling comes apparently because in fact we are counting spin-opposed PAIRS of nucleons.

The intervals between these counts are from period analogues, with orbitals of all the same parity (alternating positive and negative). The sizes of such period analogues are always here doubled triangular numbers in size, thus:

1s=2

1p=6

1d2s=12

1f2p=20

1g2d3s=30

1h2f3p=42

1i2g3d4s=56

1j2h3f4p=72

The energy levels in the harmonic oscillator plot at the site above are all straight line 'component rays' (I'm not sure how generally that term is used, but I've seen it in several papers and books). As such they have fixed slopes.

The orbitals are still split here, but in the sphere NOT differentiated by energy value (unlike in the spin-orbit model).

Slopes are (in terms of h-bar, omega-bar (energy) versus delta (deformation parameter, as defined in the paper):

1s1/2 0/3; *1s-1/2 -3/3 (hypothesized empty level to keep math consistent)

1p3/2 1/3; 1p1/2 -2/3

1d5,2 2/3; 1d3/2 -1/3; 2s1/2 -4/3; 2s-1/2 -7/3

1f,7/2 3/3; 1f5/2 0/0; 2p3/2 -3/3; 2p1/2 -6/3

1g9/2 4/3; 1g7/2 1/3; 2d5/2 -2/3; 2d3/2 -5/3; 3s1/2 -8/3; 3s-1/2 -11/3

1h11/2 5/3; 1h9/2 2/3; 2f7/2 -1/3; 2f5/2 -4/3; 3p3/2 -7/3; 3p1/2 -10/3

1i13/2 6/3; 1i11/2 3/3; 2g9/2 0/3; 2g7/2 -3/3; 3d5/2 -6/3; 3d3/2 -9/3; 4s1/2 -12/3; 4s-1/2 -15/3

1j15/2 7/3; 1j13/2 4/3; 2h11/2 1/3; 2h9/2 -2/3; 3f7/2 -5/3; 3f5/2 -8/3, 4p3/2 -11/3; 4p1/2 -14/3

You can see from the above that each move to the right, within any period analogue and between contiguous suborbitals within the all-harmonic-oscillator model, is a change of -3/3 slope. And all moves downward between the highest slopes are all +1/3.

On a hunch, yesterday I worked out that when level occupancy is factored in (that is, how many particles are actually in each level), then something very interesting happens.

Multiplying the slope by its occupancy to give a product, and then adding all the slopes within any shell to give a sum, yields result of ZERO. Within the harmonic oscillator model there appear to be no exceptions to this new rule.

Thus the TOTAL ENERGY of any level is conserved despite the deformation, even though INDIVIDUALLY each component ray varies linearly, but they all do so in a coordinated manner. This reminds me strongly of J, the total spin, in spin-orbit systems. And I wonder whether it relates at all to conjugate variables.

My bisected skew rhombi models, where 4 successive periods cover a tetrahedron surface (2 same length smaller, 2 same length larger), seem to share a bit in common with Penrose tilings. They cannot be said to be periodically organized (from a tiling perspective), and they scale up (where tiles for 2p3s, 3p4s have the same outline as 3d4p5s, 4d5p6s, 4f5d6p7s and 5f6p7d8s, and so on. Only the 1s and 2s look different, if only because they only present two spheres each. I can't say if there is any quasicrystalline quality to this mapping. Perhaps one day a mathematician will tell me.

Jess Tauber

    Crystal like, for sure. And I may be able to explain why I consider this to be a fact if you would like to know.

    Hi Sherman. Yes, I'd like to hear more about this.

    BTW, are we allowed to post pictures here on the forum? I have a graphics of tetrahedral periodic table arrangements so people can see what I'm referring to.

    You can "add file attachments" 1MB file size limit. I am not sure of restrictions as to file type. Also you can see "link help page" for instructions on linking to other web sites.

    a year later

    Please see the attached file.

    A model, built on orthodox Wave Mechanics with no changes, is validated against a list of experiments. John Bell: "so long as the wave packet reduction is an essential component, and so long as we do not know exactly when and how it takes over from the Schrodinger equation, we do not have an exact and unambiguous formulation of our most fundamental physical theory." The model answers this. It solves the measurement problem, the wave function collapse problem, and the micro verses macro problem. The model shows that the EPR experiment and EPR like experiments do not require any communication between detection points. It shows that in Quantum Teleportation, the teleportation distance is not a factor. It shows that some dreams for functionality from entanglement are too optimistic, ... and more.

    Yet Quantum Mechanics Model is just a model. There was never any claim that this is the true material, structure and mechanism that runs the universe. It IS claimed that the Static Universe Model and Quantum Mechanics Model are much more useful than Copenhagen or any of the other interpretations of Quantum Mechanics. The author submits that it is a certainty that none of these is the true material, structure and mechanism that runs the universe.

    It is my conjecture that, for those seeking the true material, structure and mechanism that runs the universe, Quantum Mechanics Model with the Static Universe Model is a much better starting point than Copenhagen or any of the other interpretations.Attachment #1: QuantumMechanicsModel.pdf

      4 months later

      Please see The file QuantumMechanicsModel.pdf attached to the parent to which this is a reply. Please see the file UnifiedModel.pdf attached to this reply.

      The main objective of Quantum Mechanics Model was to get a more sensible model of basic Quantum Mechanics. The secondary objective of Quantum Mechanics Model was to get a model of basic Quantum Mechanics that is fundamentally, right from the start, friendly to General Relativity.

      UnifiedModel.pdf suggests an approach to get a Unified Quantum Mechanics and General Relativity Model, using the more friendly Quantum Mechanics Model. It is only a suggested approach. This is a call for Theoretical Research by others to either build such a unified model or convincingly show that this approach cannot lead to such a model.Attachment #1: UnifiedModel.pdf

      Hello Mr Sager,

      Thanks for sharing your ideas about this unification of our quantum theory and general relativity. It's not easy to unify even G,c and h, that does not converge actually,we have a problem about the quantization of our quantum gravitation. We have several models trying to explain it but it lacks Something.The twistors of penrose,the loops,the E8 exceptional Lie group and geometrical algebras,the non commutativity of Connes.....But we cannot quantize it. I read a paper of Penrose,Fuentes,Howl published 3 monts ago on arxiv,it was an interesting approach with the Bose einstein condensate.Penrose is so relevant. I try to find the correct road correlated with my theory.But the formalisation is difficult mathematically speaking.I consider spherical volumes and sphères like foundamental mathematical and physical objects.Not points or strings,but I can recognise several relevances about these branes and properties.The mathematical strings have many relevant works considering the waves ,fields.... We can converge with the oscillating rotating spherical volumes,spheres. At the difference of strings, I Don't consider a 1D main field philosophically speaking, but a gravitational coded aether from the central cosmological sphere.These main informations probably are series finite of sphères playing with cold and heat between this zero absolute and the planck temperature,after all the combinations appear in function of codes.That implies our geometries,topologies,properties of matters.Imagine the combinations with these oscillations,densities,informtions,encodings,volumes,surfaces(relevant about the pixels at these surfaces for the informations with superimposing,sorting,synchronizationthe densities become relevant and the emergent proportions),the Density seems interesting to analyse. About the Planck scale,so I Don't consider strings like you can see but these spherical volumes,spheres.All this to tell too that we can consider that-this-Dark matter can be superimposed at our standard model.If this matter exists at our cosmological scale so it is too encoded in nuclei.This matter balances the systems at all scales in logic,that becomes relevant to consider so this cold. This cold seems more than we can imagine it seems to me humbly. The Bose Einstein condensate has probably many properties that we Don't know.All this is interesting generally because we can unify G,c and h and explain this matter dark. Gravitons,darkphotons,axions.....are beautiful approachs,that said we have probably an other logic.Regards

      a year later

      Please see the file Quantum Mechanics Model Addendum.pdf after the parent Quantum Mechanics Model.

      A non-local model solves problems. Facing Reality. A few of Wigner's Friends. A fun Popper's Diffraction Experiment. Frauchiger - Renner Paradox: No paradox, but, in Copenhagen, we need some serious thinking here. No Physical Virtual Particles. Force Carrying Bosons. The Casimir Effect. The Lamb Shift. Saving the universe (fixing The Cosmological Constant).

      System has refused the file upload. Try one more time to upload.

      If this doesn't work, you can get the file at https://www.researchgate.net/publication/346650113_Quantum_Mechanics_Model_Addendum

      3 months later

      I'd like to say something about Schrodinger's cat. Attribution of a state or value for a property can be relative,, Velocity, momentum, kinetic energy, orientation, direction of rotation are all examples of that. Some characteristics are absolute. I.e, "viewed or existing independently and not in relation to other things; not relative or comparative." definition from Oxford Languages. Un-decayed and-decayed (atom), unbroken and broken (flask) and alive and dead (cat) are all examples of absolute not relative differences. Herrin lies the problem with the thought experiment.

        Heads and tails of a coin are relative differences. As which is called depends on the relation to the observer or measuring device. Milled edge or smooth edge of the coin is an absolute difference. It can only be milled in all observation scenarios for smooth in all scenarios. The relation to the observer or measuring device does not affect the state outcome. From this argument: Some states are in actualized 'superposition'. Both states being potentially observable for that reason. Some so called superpositions are not actualized superpositions of relative states. Instead they are different variants of an unknown absolute state. These are different situations. Superposition of relative states applies to something real. Whereas superposition of absolute states is unreal.

        Position of a fermion particle, atom, ion or object such as a buckyball is absolute not relative. Such a particle can not pass through two slits of the double slit experiment at the same time nor be on two separate paths of an apparatus. What could be happening is the concentrated existence known as the particle passes through one slit or path with some environmental disturbance caused by its motion, and just environmental disturbance associated with the particle passes through/along the other. This allows interference of the particle associated disturbances to interfere when they meet; guiding the onward path of the particle in the double slit experiment.

        What about photons? They are different from particles and objects that have mass. It makes sense that they are a disturbance of base existence, rather than just having some disturbance associated with them. The disturbance is cohesive and non dissipating. Which is likely due to the properties of the medium of base existence. Just because only whole photons are produced by electron energy level transition, and only whole photons can be detected, does not mean they are never divisible. If under particular circumstances they are divisible parts of the photon disturbance can take different paths. It would not be correct to say the photon takes both paths, as the parts are not photons. Also if the whole photon took both paths that would be double the energy. The last two posts are arguing against the oft repeated saying that- quantum particles can be in two places at once.

        The Hafele-Keating experiment and the double slit experiment are consistent with the hypothesis that there is base existence. In the former experiment it having an effect upon matter with mass. More so with greater absolute motion. In the latter case the motion of matter with mass having an effect upon it.

        Clarification; 'base', as in the base of a soup

        One whole photon taking two paths is two photons, twice the energy. Energy is not created, so that is not happening.

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