# Quantum Ontology

thesis

posted on 21.10.2015, 00:00 by Joshua D. NortonIn this dissertation, I discuss the ontological and metaphysical implications of two quantum theories: quantum mechanics and loop quantum gravity. Central to this dissertation is the role that our interpretation of the mathematics of these theories plays in motivating particular, philosophical positions on the ontology of spacetime and identical particles. In the case of quantum mechanics, the interpretive question is how the singlet state $|\uparrow\rangle|\downarrow\rangle-|\downarrow\rangle|\uparrow\rangle$, represents the world and whether or not it represents two things. In the case of loop quantum gravity, the interpretive question is whether or not spacetime and spin networks are represented in the model $\langle\mathcal{M},\Psi[A]\rangle$ or, perhaps, by the states $\Psi[A]$ of the theory. Both of these interpretive questions have repercussions on how we understand fundamental ontology.
Regarding quantum mechanics, the ontological issues at stake are the nature of identical particles and the status of Leibniz's principle of the identity of indiscernibles. It is standardly thought that identical particles demonstrate that the principle is false. While Muller and Saunders attempt to save the principle by showing that identical particles are ``weakly discerned," I argue that their account fails since it utilizes mathematical structures which are foreign to quantum theory, and that we have little reason for interpreting the singlet state as representing two particles.
Regarding loop quantum gravity, the ontological issues at stake include the status of spacetime, the nature and reality of spin-networks, and the relationship of time to dynamics and to the Hamiltonian constraint. I argue that, while spacetime seems to disappear, the spirit of substantival spacetime lives on in loop quantum gravity. Moreover, in order for there to be physical spin-networks (and not merely ``quantum space time"), I argue that we must interpret the theory as including a substantival background manifold. Finally, contrary to standard presentations, I demonstrate that time does not disappear in LQG because of dynamical considerations stemming from the Hamiltonian constraint, but because of our interpretation of spacetime and its relationship to $\langle\mathcal{M},\Psi[A]\rangle$.