Title: Invariant Set Theory: Towards a Realistic Locally Causal Gravitational Theory of the Quantum
Speaker: Tim N. Palmer (University of Oxford)
Abstract: It is traditionally assumed that the application of quantum theoretic ansätze to a suitably defined model of gravity will somehow provide the long-sought theory we call “quantum gravity”. The fact that 60 years of increasingly intense research has failed to uncover this theory may indicate that this is simply not the correct approach to synthesising quantum and gravitational physics. Here a more holistic approach to this problem is proposed. In it the universe as a whole is treated as a nonlinear deterministic dynamical system evolving precisely on some measure-zero fractal dynamically invariant set IU in cosmological state space. It is assumed that the laws of physics at their deepest describe the geometry of IU . It is firstly shown that complex Hilbert vectors of quantum theory can represent points of IU under conditions of epistemic uncertainty. This is used to provide a realistic and locally causal account of the Bell Theorem. Incorporating the geometry of IU into a general relativistic framework suggests a novel geometric proposal for the nature of both dark matter and energy. Overall, it is claimed that the synthesis of quantum and gravitational physics will require a more radical modification of quantum theory than of relativistic gravitation theory, and that the resulting unified theory may more accurately be described as a gravitational theory of the quantum, than a quantum theory of gravity. Much of the theoretical development can be based on properties of the set of p-adic integers, this being to fractal geometry what the set of real numbers is to Euclidean geometry. A detailed discussion of Invariant Set Theory and the Bell Theorem from this p-adic perspective is given in https://arxiv.org/abs/1609.08148 <https://arxiv.org/abs/1609.08148> (currently in review in Phys Rev A).
Time: Friday 25th November 2016, 2.00pm.
Place: Seminar Room, School of Theoretical Physics, DIAS, 10 Burlington Road, Dublin 4.