Pixellation and Curve Turning

Abstract

This chapter revisits the idea of pixelated spacetime diagrams considered in Chapter 5. It proves a technical result, the Curve Turning Theorem, which gives a way to understand the spacetime diagrams in terms of patterns of oriented lines. Section 6.2 assigns directions to all the particle lines. This is done using a key feature of the oriented plaid model which has already been established: the directions of all instances of a particle are the same. The Curve Turning Theorem is also stated at the end of this section. Section 6.3 proves a technical result about the spacing of the particle lines in spacetime diagrams. This result will help with the proof of the Curve Turning Theorem. Section 6.4 and 6.5 prove the Curve Turning Theorem, respectively, in the vertical and the horizontal case. Section 6.6 gives two applications of the Curve Turning Theorem.