Abstract
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.
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