The Logic of Existence: Relational Meta-Hamiltonian Geometry Unifying Photon–Graviton Dynamics within the Cantor–Minkowski Continuum

The Logic of Existence: Relational Meta-Hamiltonian Geometry Unifying Photon–Graviton Dynamics within the Cantor–Minkowski Continuum

Author: Krzysztof Sawa

Date: 8 November 2025

Abstract:

This paper extends the Logic of Existence (LoE) formalism into a unified geometric framework that links photons and gravitons as local and global resonant modes of one relational field. By embedding Minkowski spacetime into a transfinite Cantor hierarchy, LoE defines a Meta-Hamiltonian of Hamiltonians—a recursive structure in which each relational layer gives rise to a higher-order manifold of existence.

Photons correspond to countable relational interactions (ℵ₁) and embody local informational exchange, whereas gravitons arise at the uncountable layer (ℵ₂), shaping global curvature. Their coupling occurs through the LoE relational cone, where curvature marks the transition between local coherence and cosmic geometry.

In this view, energy, geometry, and meaning are conjugate aspects of one continuum.

The work proposes that classical spacetime is a limiting case of the LoE metric

ds^2_{LoE}=c^2dΦ_{relation}^2 - dΦ_{order}^2 - dΦ_{chaos}^2 + ε\,dH_{meta}^2,

Key Concepts:

Relational Physics · Photon–Graviton Coupling · Cantorian Meta-Geometry · Meta-Hamiltonian · Minkowski Continuum · Logic of Existence