Projection Principle for Quantum Orbitals: Angular Momentum, Spin, and the Pauli Exclusion Rule as Elastic Torsion in the MMU Tetrahedral Model
Wollbold, Jurgen
This work extends the Methane Metauniverse (MMU) framework by introducing a projection principle that connects the internal elastic geometry of the dual-tetrahedral MMU cell to the observable quantum numbers of atomic physics. The MMU model describes spacetime using three internal modes: an electric stretching mode 𝑤2, a torsional mode 𝑤3, and a volumetric mode 𝑤4. In this paper, these internal modes are shown to project deterministically onto the radial, angular, and spin degrees of freedom of the Schrödinger equation. A central result of this study is that the three coupled torsional motions of the tetrahedral faces naturally generate the familiar angular-momentum spectrum 𝐿2=𝑙(𝑙+1)ℏ. This spectrum emerges mechanically from the geometry rather than from group-theoretic postulates. By equating torsional kinetic and elastic energies, the MMU further yields a new identity 𝐿2=𝑚𝑐𝑎, linking angular momentum to the internal scale of the tetrahedral cell. The dual nature of the torsional mode provides a geometric origin for spin-½ and enforces the Pauli exclusion principle as an intrinsic occupancy rule. Summing all angular sublevels reproduces the shell capacities 2,8,18,32,… , showing that orbital structure follows from internal symmetry rather than quantum statistics. This projection principle offers a unified geometric explanation for quantum orbitals, spin, and Pauli exclusion within the elastic architecture of the MMU spacetime model.
•Jan 1, 2025•0 citations