Chapter 1 Expository Articles 1.1. Quantum mechanics and Tomb Raider Quantum mechanics has a number of weird consequences, but in this article I will focus on three (inter-related) ones: • Objects can behave both like particles (with definite position and a continuum of states) and waves (with indefinite position and (in confined situations) quantised states). • The equations that govern quantum mechanics are deterministic, but the standard interpretation of the solutions (the Copenhagen interpretation) of these equations is probabilistic. • If instead one applies the laws of quantum mechanics literally at the macroscopic scale (via the relative state interpretation, more pop- ularly known as the many worlds intepretation), then the universe itself must split into the superposition of many distinct “worlds”. What I will attempt to do here is to use the familiar concept of a com- puter game as a classical conceptual model with which to capture these non-classical phenomena. The exact choice of game is not terribly impor- tant, but let us pick Tomb Raider—a popular game from about ten years ago, in which the heroine, Lara Croft, explores various tombs and dungeons, solving puzzles and dodging traps, in order to achieve some objective. It is quite common for Lara to die in the game, for instance by failing to evade one of the traps. (I should warn that this analogy will be rather violent on certain computer-generated characters.) The thing about such games is that there is an “internal universe”, in which Lara interacts with other game elements, and occasionally is killed 1 http://dx.doi.org/10.1090/mbk/059/01

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2008 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.