Quaternion Quantum Mechanics: Unraveling the Mysteries of Gravity and Quantum Mechanics within the Planck-Kleinert Crystal

We present quaternion quantum mechanics and its ontological interpretation. The theory combines the Cauchy model of the elastic continuum with the Planck-Kleinert crystal hypothesis. In this model, the universe is an ideal elastic solid where the elementary particles are soliton-like waves. Tension induced by the compression and twisting of the continuum affects its energy density and generates the force of gravity, as density changes alters the wave speed and hence gravity could be described by an index of refraction.