Philosophy of Quantum Mechanics 1

This paper examines the axioms of algebraic quantum field theory (AQFT) that aim to characterize the theory as one that implements relativistic causation. I suggest that the spectrum condition (SC), microcausality (MC), and primitive causality axioms (PC), taken individually, fail to fulfill this goal, against what some philosophers have claimed. Instead, I will show that the "local primitive causality" (LPC) condition captures each axiom's advantages. This claim will follow immediately from a construction that makes explicit that SC, MC, and PC, taken together, imply LPC.

To understand how problems of self-interaction are to be addressed in quantum electrodynamics, we can start by analyzing a classical theory of the Dirac and electromagnetic fields. In such a classical field theory, the electron has a spread-out distribution of charge that avoids some problems of self-interaction facing point charge models. However, there remains the problem that the electron will experience self-repulsion. This self-repulsion cannot be eliminated within classical field theory, but it can be eliminated from quantum electrodynamics in the Coulomb gauge by fully normal-ordering the Coulomb term in the Hamiltonian.

Reconstructions of quantum theory are a novel research program in theoretical physics aiming to uncover the unique physical features of quantum theory via axiomatization. I argue that reconstructions represent a modern usage of the axiomatic method as successors to von Neumann’s axiomatizations in quantum mechanics. The key difference between von Neumann’s applications and Hardy’s “Quantum Theory from five reasonable axioms” (Hardy 2001) is that von Neumann did not have an established mathematical formalism to base his axiomatization on, whereas Hardy uses an established formalism as a constraint, which is a unique feature of the axiomatic method in the reconstruction programme.

Why are quantum probabilities encoded in measures corresponding to wave functions, rather than by a more general (or more specific) class of measures? Whereas orthodox quantum mechanics has a compelling answer to this question, Bohmian mechanics might not.