Topos Theoretic Quantum Realism. (13th April 2016) - Eva, Benjamin
ABSTRACT: Topos quantum theory (TQT) is standardly portrayed as a kind of 'neo-realist' reformulation of quantum mechanics. 1 In this article, I study the extent to which TQT can really be characterized as a realist formulation of the theory, and examine the question of whether the kind of realism that is provided by TQT satisfies the philosophical motivations that are usually associated with the search for a realist reformulation of quantum theory. Specifically, I show that the notion of the quantum state is problematic for those who view TQT as a realist reformulation of quantum theory. 1 Introduction 2 Topos Quantum Theory 2.1 Phase space 2.2 Hilbert space 2.3 Beyond Hilbert space 2.4 Defining realism 2.5 The spectral presheaf 2.6 The logic of topos quantum theory 3 Interpreting States in Topos Quantum Theory 4 Interpreting Truth Values and Clopen Subobjects in Topos Quantum Theory 4.1 Interpreting the truth values 4.2 Interpreting S u b c l ( Σ ̲ ) 5 Neo-realism 5.1 The covariant approach 6 Conclusion