Hawking Boxes and Invariant Sets  A New Look at the Foundations of Quantum Theory and the Associated Role of Gravity Speaker(s): Tim Palmer
Abstract: We start by studying the noncomputational geometry of fractionallydimensioned measurezero dynamicallyinvariant subsets of phase space, associated with certain deterministic nonlinear dissipative dynamical systems. Then, by studying the asymptotic states of the Hawking Box, the existence of such invariant subsets is conjectured for gravitationallybound systems. The argument hinges around the phasespace properties of black holes. Like Penrose, it is assumed that phasespace volumes shrink when the contents of the Hawking Box contain black holes. However, unlike Penrose, we do not argue for any corresponding phasespace divergence when the Box does not contain black holes. We now make the hypothesis that these invariant phasespace subsets play a primitive role in fundamental physics; specifically that the state of the universe (“reality”) lies on such an invariant subset (now and hence forever). Attention is focussed on the implications of this hypothesis for the foundations of quantum theory. For example, what are referred to as “measurements” of the quantum state, are defined in terms of symbolic dynamics on the invariant set, relative to some partition of the invariant set. This immediately leads to the notion that any theory which treats these invariant sets as primitive, must be contextual (since counterfactual perturbations almost certainly take states off the measurezero invariant set and hence to “unreal” regions of phase space where the symbolic partition is undefined). This in turn leads to a new perspective, both on the foundations of quantum theory and on the role of gravity in formulating these foundations. In particular, a measurementfree NeoCopenhagen Interpretation of quantum theory, based on the Invariant Set Hypothesis will be presented.
Date: 21/10/2008  4:00 pm
Series: Quantum Foundations
