Danielewski, M.; Sapa, L.; Roth, C. Quaternion Quantum Mechanics II: Resolving the Problems of Gravity and Imaginary Numbers. Symmetry2023, 15, 1672.
Danielewski, M.; Sapa, L.; Roth, C. Quaternion Quantum Mechanics II: Resolving the Problems of Gravity and Imaginary Numbers. Symmetry 2023, 15, 1672.
Danielewski, M.; Sapa, L.; Roth, C. Quaternion Quantum Mechanics II: Resolving the Problems of Gravity and Imaginary Numbers. Symmetry2023, 15, 1672.
Danielewski, M.; Sapa, L.; Roth, C. Quaternion Quantum Mechanics II: Resolving the Problems of Gravity and Imaginary Numbers. Symmetry 2023, 15, 1672.
Abstract
The correspondence between classical and quaternion quantum equations, permits considering the universe (vacuum) as an ideal elastic solid. Elementary particles would have to be standing or soliton-like waves. Tension induced by the compression and twisting of the elastic medium would increase the energy density, consequently generate a gravity forcing and affect the wave speed. Consequently the gravity could be described by an index of refraction.
Theory was created by combining the Cauchy model of the elastic continuum with the Planck-Kleinert crystal hypothesis. The quaternion-imaginary Lagrange’an, the quaternion motion equation and the quaternionic oscillator allowed deriving:
- The Schrödinger equation from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian.
- The 2nd order wave equation system describing both the bosons and the gravity in terms of quaternionic Poisson equation.
- The first order quaternionic wave equation system.
- The family of the second order wave equation systems describing both the particles and the generated quaternionic force-fields (four-potentials).
- The fundamental Planck and gravity constants.
- The quaternionic continuity equation in an ideal elastic solid.
Copyright:
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