Hamiltonian Quaternions as the Mathematical Framework for Photon Precession: Bridging Electromagnetism and Quantum Non-Locality

This paper proposes a novel mathematical framework for understanding photon propagation and the nature of quantum entanglement by interpreting the Hamiltonian quaternion multiplication rule ij = k as a physical principle of electromagnetic field interaction. In this model, the unit vector i represents the electric field component, j represents the magnetic field component, and their product k defines the direction of photon propagation. This formulation suggests that the excitation of a magnetic field by an electric field is not merely a consequence of Maxwell’s equations but a manifestation of the non-commutative geometric phase inherent in spacetime. Furthermore, we posit that the speed of light c acts as a critical threshold; upon reaching this velocity, matter effectively transitions into an imaginary (or “virtual”) numerical domain. This transition implies that photons, and by extension any entity travelling at c, exist in a state where local realism is invalid. We argue that this provides a fundamental insight into the mechanism behind the Einstein-Podolsky-Rosen (EPR) paradox and quantum non-locality, suggesting that quantum entanglement is not a “spooky action at a distance” but a natural consequence of connectivity within this imaginary, non-local quaternionic manifold.