Non-relativistic quantum mechanics

Abstract

This chapter is an introduction to some of the most important philosophical and foundational issues that arise from or concern non-relativistic quantum theory. The chapter introduces the theory, including some of the important mathematical results required to formulate and address many of the philosophical and foundational issues. The formalism of quantum mechanics is normally understood in terms of the theory of Hilbert spaces. The chapter explains how to represent observables and how to calculate expectation values (and probabilities). It discusses transformations––both of the states of physical systems and of the observables associated with those systems. While some might find non-locality to be contrary to intuition, the real problem that it poses is an apparent incompatibility with the theory of relativity. Supposing that the non-locality of quantum theory is completely and unambiguously compatible with the theory of relativity, it is difficult to see how there could be serious objections to it. The chapter concludes by discussing the mathematical appendix, reviewing essential definitions and results, ––mostly from the theory of Hilbert spaces and groups