Modal logic approach to preferred bases in the quantum universe

Abstract

We present a modal logic based approach to the so-called endophysical quantum universe. In particular, we treat the problem of preferred bases and that of state reduction by employing an eclectic collection of methods including Baltag's analytic non-wellfounded set theory, a modal logic interpretation of Dempster-Shafer theory, and results from the theory of isometric embeddings of discrete metrics. Two basic principles, the bisimulation principle and the principle of imperfection, are derived that permit us to conduct an inductive proof showing that a preferred basis emerges at each evolutionary stage of the quantum universe. These principles are understood as theoretical realizations of the paradigm according to which the physical universe is a simulation on a quantum computer and a second paradigm saying that physical degrees of freedom are a model of Poincare's physical continuum. Several comments are given related to communication theory, to evolutionary biology, and to quantum gravity.