2025/11/19 by Jurgen Wollbold, Wollbold, Jurgen
Physics and Astronomy · #Quantum Electrodynamics and Casimir Effect #Advanced Mathematical Theories and Applications #Noncommutative and Quantum Gravity Theories
paper · doi:10.17605/osf.io/42k9s
This article shows that the complete Planck scale can be derived from the internal geometric–elastic structure of the Methane Metauniverse (MMU). Instead of using dimensional analysis, the MMU produces all Planck quantities—mass, length, time, energy, momentum, force, density, charge, and temperature—from a single geometric condition: the balance between torsional and volumetric stiffness inside a dual tetrahedral spacetime cell. The key result is that the equality of torsional and gravitational elasticity, expressed as G m² = ħ c, arises naturally in the MMU geometry. This identifies the Planck mass as the unique point where internal forces balance, and the corresponding tetrahedral edge length becomes the Planck length. All remaining Planck units follow from the projection dynamics and internal eigenmodes of the MMU cell. The article presents explicit derivations, geometric interpretations, and a unified picture in which the Planck scale is not an arbitrary dimensional choice but a real geometric equilibrium built into the structure of spacetime. This situates the MMU as a candidate framework for connecting quantum behaviour, elastic geometry, and gravitational coupling.