QM CN derived from 4D-Spacetime & CAP dual 4D-Momentumenergy Gravity!

Complete Non-Reducible "mathematical" derived from a required adapted Comprehensive Action Principle, i.e. including the always required only elementary Symmetrical Spin 2 Graviton. Einstein solved required dual degrees-of-freedom of the spin 2 Graviton CN representing the invisible Gravitational-Field in a higher-dimensional so-called Riemannian-manifold, however he just couldn't understand QM spin just like everyone else!

Conserved Spin is conserved Angular-Momentum in the Direction-of-Motion and must be described math. Explicitly! Conserved Spin is the result of Symmetry of the describing wave-function (with spin s) of an object under Rotation of this Wave-function around its Axis-of-Motion (SR-worldline). The average extensiveness in the inertial-frame moving with origin at the average position of the oscillating Object is given by: 2<>
At Universities QM models use an analyzed not even (necessary always required) Complete Non-Reducible set-of easy linear, i.e. "mathematical", Point-Particles analyses. As a direct result these models have to use math. non-logical so-called "intrinsic" properties related to the analyzed 26 different stable “Quantum Particles” in our 3 Fermi-Families universe!
All stable (elem. or compound) "quantized" Particles always possess Energy ÷ "linear-proportional" to a Frequency f, E = h · f:
Always required Energies > 0 of Quantum Particles already implies NOT Point-like Spacetime-like extensiveness with required Ideal Harmonic Oscillating Properties!
All elementary particles also have Conserved (experimental-proven) Non-Zero Angular-Momentum in the Direction-of-Motion (Helicity of the CAP - dual 2 orthogonal zero rest-mass bosons {Graviton & Photon} & Chirality in all other “massive”-cases) related to their "oscillating" energies called Spin, which in QM is incorrectly assumed to be an intrinsic property of stable analyzable QM pointlike objects!
In line with Albert Einstein's theory of General Relativity any valid math. model of reality must comply to the Comprehensive Action Principle, i.e. always include the dependent, so required, (orthogonal ónly elem. symmetrical spin 2) Gravitational-field!
NB Albert Einstein never realized these "difficult" QM requirements of his developed CAP himself, because he didn't like the non-logical behavior of these in his "math." linear logical-eyes really misunderstood “Stupid Statistical” Quantum Mechanical analyses of reality!
Einstein's 1st Nobel-prize of the Photo-Electric effect proofs that the EM-field is CN represented by Photons, but he disliked the used simple Point-Particles analyses of QM, even though all particles have Energy proportional to a Frequency.
Therefore, to analyze “Quantum Mechanics” CN (math.) Logical Consistently compliant to the CAP, stable elementary and CAP - dual otherwise stable compound “Particles” must be described CN as math. dual (orthogonal in 2 different ways*) ideal oscillating identities:

Ideal Harmonic Oscillating math. Point-Waves in the 2D-Plane* Perpendicular to the Direction-of-Motion (SR worldline) with CAP - dual Open- or Closed- Boundary Conditions. (1)

As a direct result elementary particles must have Energy proportional to a Frequency & Conserved non-zero Angular-Momentum in the direction-of-motion (Helicity of the CAP-dual 2 perpendicular zero rest-mass bosons {Graviton & orthogonal Photon} & Chirality in all other “massive”-cases). The last-property is usually called spin (in the direction-of-motion) as an incorrectly assumed so-called “intrinsic” property of elementary always analyzed math. Point-Particles in the still not-understood so-called QM  A CAP-dual logical (math.) CN theory where all possible particles with all their required extended properties are explicitly described & explained CN according to (1) to math. logically explain QM spin math. necessary solved in the resulting Complex Hilbert-Space of QM.
CAP dual, force-fields are either elementary spin 2 Symmetrical described by the orthogonal, so invisible, masses > 0 - related Graviton or analyzable spin 1 Anti-Symmetrical non-zero charge-density related force-fields, described by so-called Gauge-Symmetries. The CN Gauge-Symmetry of 4D-Spacetime & CAP- dual 4D-Momentumenergy analyses are just the always used Gauge-Symmetries of the Standard-Model: U(1) x SU(2) x SU(3): U(1) x SU(2) describe the U(1) – EM-field CN describing the Photon with it's (spin) 1 x (anti-symmetrical) 6 = 6 degrees-of-freedom and the 3 SU(2) – Gauge-Symmetry both charged (non-zero charge-densities) and massive (rest-masses > zero) weak nuclear force bosons {W±, Z} mixed by the Weinberg-angle. The last possible Gauge-Symmetry, SU(3) describes the 3 Fermi-Families with only different rest-masses resulting into CAP - dual 2 x 3 = 6 different spin 1½ so-called Quarks {(up, down), (strange, charm), (top, bottom)}, which in the also not-understood so-called Quantum Chromo-Dynamics of QM are incorrectly assumed to be (stable) spin ½ fermions with as a direct result of that also required so-called (also dual spin ±½) Isospin ½!

Here it must be noted that compliant to the CAP all possible math. expressions of reality must be described with stable elementary Leptons & CAP- dual compound spin ½ fermions, i.e. Baryons, the primary-sources of all bosons. Fermions are described with Open- Boundary Conditions & Bosons are described with Closed-BC, see (1).
This math. explicitly described (CAP- dual) conserved spin (in the direction-of-motion) at-once makes it evident (that still assumed to be valid) elementary spinless bosons (Higgs mechanism) which just can not carry energy proportional to a frequency must be discarded as a math. incorrect assumption! 

In Short,

Einstein's CAP demands including the (only elementary symmetrical spin 2, i.e. orthogonal) Gravitational Action into all trustworthy Theoretical Models. As a direct result all elementary particles must be described extended in the 2D-Plane Perpendicular to the Direction-of-Motion (SR worldline) with CAP-dual Open- (fermions) or Closed- (bosons) Boundary Conditions. I.e. Elementary Particles just can NOT be analyzed as Simple Point-Objects with Idiotic QM so-called "Intrinsic-Properties"! This required extensiveness 2<rho> = Spin x Golden Ratio x Planck-length explains the QM Spin completely. The elementary spinless (scalar) Higgs boson must be omitted as not-understood fiction due to not taking into account the always required Gravitational Action in any QM analysis! A non-oscillating spin 0 particle just can not possess energy proportional to a frequency, so can only represent so-called vacuum or "nothing" at all.


A simple sketch of an ideal harmonic oscillating elementary particle travelling in the positive z-axis. The chosen coordinates are logically chosen as polar-coordinates. The conserved extended spin is specified with S and the maxima of the polar-coordinate rho are also specified. The period of the oscillation is represented by its spin s and is equal to: 2π/s

Only CAP - dual analyses are allowed in a mathematical linear-logical Complete Non-Reducible manner:

Elementary Particles Must be described with easy imaginable 4D-Spacetime to allow Fermions which require Knots in their energetic oscillating paths (with Open-BC). CAP-dual, Elementary Particles must be Ideal Harmonic Oscillating math. Point-Waves in the 2D-Plane Orthogonal to the traveled Direction-of-Motion (SR-worldline) with CAP-dual Open- or Closed- Boundary Conditions. CAP-dual there are or (massive) Fermions (primary sources) or (resulting) Bosons. Only 2 orthogonal bosons have zero rest-masses: These CAP-dual elementary Bosons have as sources the CAP-dual EM-Charges & Rest-Masses > 0 of all Charged (non-zero charge-densities) Particles (Fermions & Bosons) which must also be massive. The Anti-Symmetrical, i.e. spin 1, U(1) Gauge-Symmetry Photon CN representing the EM-field & the (orthogonal) Symmetrical, i.e. spin 2, Graviton CN representing the invisible Gravitational-Field with its 2 x 10 = 20 degrees-of-freedom. The CN Gauge-Symmetry in the only possible 4D-Spacetime analyses are exactly the Gauge-Symmetries of the Standard Model of QM: U(1) x SU(2) x SU(3). U(1) x SU(2) describe the U(1) Photon CN representing the EM-field with its 6 degrees-of-freedom & the 3 SU(2) Weak Nuclear-Force bosons {W+, W-, Z} mixed by the Weinberg-angle. The last possible Gauge-Symmetry SU(3) describes the CAP-dual 2 x 3 (Fermi-Families) = 6 different {(Up-, Down-), (Charm-, Strange-), (Top-), (Bottom-)} Quarks. The CN only Symmetrical-Action just is the invisible spin 2 Graviton with its 2 x 10 = 20 degrees-of-freedom. This Action is the source of still not understood Quantum Mechanics & logically Orthogonal to this Simple Linear-Model infinite-dimensional complex (i.e. CAP - dual) Hilbert-Space, so just cannot be included into this model itself.

So, CAP - dual 4D-Spacetime the only spacetime that allows (massive-) Fermions only allows 26 different Elementary Particles:

Three, with only different non-zero Rest-Masses and required non-zero charge-densities, Fermi-Families of each 7 different elementary Fermions & Only 5 different Bosons: Invisible (symmetrical) spin 2 Graviton and Orthogonal (anti-symmetrical) Elementary spin 1 Gauge-Bosons U(1)- Photon and SU(2)- Weak-Nuclear Force Bosons. The last Gauge-Symmetry SU(3) represents the 6 spin 3/2 Quarks describing all Hadronic Processes.
NB: Not stable on their own spin 1/2 quarks with invented additional spin 1/2, so-called "isospin" in still misunderstood QCD

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