Abstract

In recent years there has been a resurgence of interest in quasi-cyclic cosmologies. With this is mind, consider the universe U as a deterministic dynamical system and ask what is the geometry traced out by trajectories of U in U’s state space. WIth positive cosmological constant and with Planck-scale information loss at black hole singularities, there are good grounds to postulate that, asymptotically, this causal geometry is a measure-zero fractal. With this as motivation, a fractal I_U is constructed from which the statistics of multi-qubit quantum theory are emergent. I_U is a causal but atemporal invariant set for the deterministic dynamics of U and forms the basis for the development of a causal realistic geometric theory of quantum physics where Bell’s Theorem is nullified without conspiratorial fine tuning. The complex Hilbert Space of standard quantum theory arises as the singular limit of geometric properties of I_U. Invariant set theory provides a potential explanation for why zero point vacuum fluctuations do not contribute to the value of the cosmological constant, and, above all, suggests that attempts to quantise gravity (in the traditional field theoretic sense) are physically misguided. (Ref: Proc Roy Soc A: 465, 3165-3185).