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Abstract
The Panvitalistic Theory (PVT) replaces the external time parameter of conventional quantum mechanics with internal angular curvature π ≡ T /L. The dynamics of any physical system are governed solely by the volume-invariance constraint δV = 0 in a discrete, rational
12-dimensional spacetime. In this work we derive the complete set of twelve volume operators and their geometric commutator algebra directly from the discrete comparison chain of the intrinsic variation principle. Each link of the chain corresponds to a rational comparison pair Vn = xnVn+1 with xn ∈ Q. By a natural basis change to center-of-mass and difference coordinates followed by a discrete Legendre transform, canonical momenta emerge on the link space. The volume constraint δV = 0 is implemented as a Dirac constraint; its gauge fixing is identified with the measurement postulate. We show that the time-dependent Schr¨odinger equation is an artefact of an ontologically inconsistent external-time postulate and re-derive the Bohr model of the hydrogen atom—including radii rn, energy levels En ∝ −1/n2 , and the fine-structure constant α—directly from the unified canonical structure. A macroscopic Earth-satellite analogue confirms the geometric origin of quantization. The framework eliminates the measurement problem, the problem of time, and the QT–GRT incompatibility at the axiomatic level while reproducing all spectroscopic successes of standard quantum theory.
12-dimensional spacetime. In this work we derive the complete set of twelve volume operators and their geometric commutator algebra directly from the discrete comparison chain of the intrinsic variation principle. Each link of the chain corresponds to a rational comparison pair Vn = xnVn+1 with xn ∈ Q. By a natural basis change to center-of-mass and difference coordinates followed by a discrete Legendre transform, canonical momenta emerge on the link space. The volume constraint δV = 0 is implemented as a Dirac constraint; its gauge fixing is identified with the measurement postulate. We show that the time-dependent Schr¨odinger equation is an artefact of an ontologically inconsistent external-time postulate and re-derive the Bohr model of the hydrogen atom—including radii rn, energy levels En ∝ −1/n2 , and the fine-structure constant α—directly from the unified canonical structure. A macroscopic Earth-satellite analogue confirms the geometric origin of quantization. The framework eliminates the measurement problem, the problem of time, and the QT–GRT incompatibility at the axiomatic level while reproducing all spectroscopic successes of standard quantum theory.