A Para-Hermitian Geometric Framework for Quantum Mechanics and General Relativity: Time as a Mode of Each Fundamental Dimension

We propose a six-dimensional para-Hermitian manifold in which each spatial dimension carries an intrinsic temporal mode via split-complex coordinates , . The resulting $(3,3)$-signature geometry restricts exactly to Minkowski space on the four-dimensional submanifold defined by synchronized temporal modes. This arena has two dynamical limits: when the three temporal modes are locked in phase, the Kaluza–Klein reduction recovers Einstein gravity; when they fluctuate relative to one another, the non-relativistic limit of the bulk wave equation recovers the Schrödinger equation. The quantum/classical divide is therefore not a foundational mystery but a statement about phase relationships among temporal modes. The Wheeler–DeWitt frozen-time problem is dissolved because dynamics is relational (it is in the phase difference between modes, not in any absolute time).

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-02
DOI
https://doi.org/10.5281/zenodo.21137114
Primary Topic
Quantum Mechanics and Non-Hermitian Physics
Type
preprint
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preprint

A Para-Hermitian Geometric Framework for Quantum Mechanics and General Relativity: Time as a Mode of Each Fundamental Dimension

G. Kletetschka
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Non-Hermitian Physics
preprint

A Para-Hermitian Geometric Framework for Quantum Mechanics and General Relativity: Time as a Mode of Each Fundamental Dimension

G. Kletetschka
preprint en

Abstract

We propose a six-dimensional para-Hermitian manifold in which each spatial dimension carries an intrinsic temporal mode via split-complex coordinates , . The resulting $(3,3)$-signature geometry restricts exactly to Minkowski space on the four-dimensional submanifold defined by synchronized temporal modes. This arena has two dynamical limits: when the three temporal modes are locked in phase, the Kaluza–Klein reduction recovers Einstein gravity; when they fluctuate relative to one another, the non-relativistic limit of the bulk wave equation recovers the Schrödinger equation. The quantum/classical divide is therefore not a foundational mystery but a statement about phase relationships among temporal modes. The Wheeler–DeWitt frozen-time problem is dissolved because dynamics is relational (it is in the phase difference between modes, not in any absolute time).

Zenodo (CERN European Organization for Nuclear Research)
University of Alaska Fairbanks (US)
Quantum Mechanics and Non-Hermitian Physics
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