Deriving Einstein's General Relativity from the Axioms of the Panvitalistic Theory (PVT)

Author: Pohl, M.U.E.
DOI: https://doi.org/10.5281/zenodo.19901212
Published: 2026-04-30
Cite as: Pohl, M. U. E. (2026). Deriving Einstein's General Relativity from the Axioms of the Panvitalistic Theory (PVT) (Part I). Zenodo. https://doi.org/10.5281/zenodo.19901212
Abstract: The Panvitalistic Theory (PVT) replaces the external time parameter and the irrational number $\pi$ of standard physics with internal angular curvature $\pi \equiv T/L$ and a single rational length scale. Physical reality is described by continuous 6-dimensional volumes, while all measurements are strictly rational comparisons $V_A = x V_B$ ($x \in \mathbb{Q}$). Dynamics are governed solely by the volume-invariance constraint $\delta V = 0$. In this work we derive Einstein's field equations directly from these axioms. We introduce the complete set of 12 volume operators together with their geometric commutator algebra, project the timeless constraint $\delta V = 0$ onto 4D spacetime, and obtain the Einstein equations as an effective description in the limit of maximal orthogonality. We explicitly verify that both the Newtonian limit and the Schwarzschild geometry emerge consistently, with singularities resolved into finite angular boundaries. The derivation eliminates the problem of time and the quantum-gravity incompatibility at the axiomatic level while reproducing all classical predictions of general relativity.

Deriving Einstein's General Relativity from the Axioms of the Panvitalistic Theory (PVT) - (Part I)