SHADOW DARK MATTER AS A MANIFESTATION OF i ↔ -i SYMMETRY IN PRE-QUANTUM TRACE DYNAMICS

We propose an alternate version of the "shadow world" hypothesis for the origin of dark matter. Instead of postulating that the shadow world is a "mirror" world under parity or charge-parity reflection, we suggest that the existence of a shadow world arises from the fact that i or –i can be the imaginary unit in complex quantum mechanics. This mechanism is a natural consequence of "trace dynamics" pre-quantum theory, from which quantum mechanics over the complex number field emerges as a statistical mechanical approximation. Because the pre-quantum dynamics does not pick out a preferred imaginary unit, the emergent quantum dynamics contains two sectors, one based on i and the other on –i, with both sectors coupled to gravity.