A Candidate of a Psi-Epistemic Theory

Abstract

In deBroglie-Bohm theory the quantum state plays the role of a guiding agent. In this seminar we will explore whether this is a universal feature shared by all hidden variable theories, or merely a peculiarity of the deBroglie-Bohm theory. We present the bare bones of a theory in which the quantum state represents a probability distribution and does not act as a guiding agent. The theory is also psi-epistemic according to Spekken\'s and Harrigan\'s definition. For simplicity we develop the model for a 1D discrete lattice but the generalization to higher dimensions is straightforward. The ontic state consists of a definite particle position and in addition possible non-local links between spatially separated lattice points. These non-local links comes in two types: directed links and non-directed links. Quantum superposition manifests itself through these links. Interestingly, this ontology seems to be the simplest possible and immediately suggested by the structure of quantum theory itself. For N lattice points there are N*3^(N(N-1)) ontic states growing exponentially with the Hilbert space dimension N as expected. We further require that the evolution of the probability distribution on the ontic state space is dictated by a master equation with non-negative transition rates. It is then easy to show that one can reproduce the Schroedinger equation if an only if there are positive solutions to a gigantic system of linear equations. This is a highly non-trivial problem and whether there exists such positive solutions or not is not clear at the moment. We end by speculating how one might incorporate gravity into this theory by requiring permutation invariance of the dynamical evolution law.