The emergence of classical worlds from a quantum universe

Abstract

How does a classical world emerge from a quantum world? Can this emergence occur without invoking non-unitary processes such as measurements? Recently, an approach that makes use of just a Hilbert space and the associated Hamiltonian to explain the emergence of a classical world has been proposed. To understand this approach, we will require a clear understanding of the nature of measurements in quantum theory and the different interpretations of it. We then progress onto discussions regarding quantum Darwinism and related _elds of knowledge and how they bypass" the problem of measurement in quantum theory. Then, we discuss how, using the appropriate choice of factorization of a Hilbert space into a system and an environment and using an acceptable basis observable, we can obtain a quasi-classical state of a system. This approach has previously been applied to study one limit (when interactions dominate the Hamiltonian), but we generalize by applying it to the opposite limit (when interactions are minimal) and suggest a method for the general case (when interactions are neither minimal nor dominant). We then look at Hilbert space fundamentalism, which is the idea that a vector in Hilbert space is the fundamental nature of reality. Hilbert space fundamentalism is a generalized application that takes the idea of the emergence of a classical world from a quantum one and applies it to the Universe as a whole. This leads to the question: could Hilbert space fundamentalism be a candidate for the fundamental theory? Before we evaluate Hilbert space fundamentalism as a candidate fundamental theory, we analyze the theory and inquire as to what makes something a fundamental theory. To understand Hilbert space fundamentalism, we see what a model of the world it predicts looks like. This is done by proposing a mapping from a fundamental Hilbert space to emergent space times utilizing entanglement and the aforementioned recently proposed approach that makes use of Hilbert spaces and Hamiltonians to explain the emergence of classical worlds. To determine if Hilbert space fundamentalism could be a fundamental theory, a set of criteria (completeness in all domains, self-contained, and that speci_c theories emerge from it) is noted. We find that Hilbert space fundamentalism, when viewed through these criteria, cannot be the fundamental theory.