Particles and Spacetime Diagrams

Abstract

This chapter begins the process of making a 3D interpretation of the plaid model. The idea is to group together certain of the light points and think of them as instances of 1-dimensional worldlines rather than as a succession of points. It fixes an even rational parameter p/q and uses the notation from Section 1.2, i.e., ω‎ = p + q. Section 4.2 explains a different notion of adjacency for the ω‎ × ω‎ blocks, dividing up the plaid model. Section 4.3 says what it means for two horizontal light points in remotely adjacent blocks to be different instances of the same particle. Section 4.4 does the same for the vertical particles. Section 4.5 shows a few pictures of spacetime diagrams and discuss their symmetries. Section 4.6 proves a technical lemma, the Bad Tile Lemma, which is very similar in spirit to Theorem 1.4.