P-adic Integers and Quantum Reality: Towards a realistic locally causal theory of fundamental physics.

Abstract

Almost the first thing we learn as human beings is a sense of spatial awareness: the smaller the Euclidean distance between two objects, the closer they are. As adults, we apply this deeply held intuition to state space. In particular, as philosopher David Lewis made explicit in his seminal 1973 paper on Causation, we presume that one counterfactual world is closer to reality than another if this world resembles reality more than does the other. This intuition has guided the development of physical theory over the years. However, I will argue that our intuition is letting us down very badly. Motivated by results from nonlinear dynamical systems theory, I will argue that the so-called p-adic metric provides a much more physically meaningful measure of state-space distance than does the Euclidean metric, and moreover that the set of p-adic integers, for large p, provides the basis for constructing a realistic, locally causal description of quantum physics which is neither fine tuned nor violates experimenter free will, the Bell theorem notwithstanding. Indeed, using the p-adic metric  in state space, I assert that experimenters (from Aspect onwards) are not actually testing the Bell inequalities at all - not even approximately! A description of cosmological state space based on the set of p-adic integers suggests a new geometric route to the unification of quantum and gravitational physics, consistent with general relativity.