# symmetry-pool-table.mp4

Chapter section: Symmetry

Caption (verbatim):

Symmetry transforms don't change how pool balls behave

Image description (verbatim):

The same pool-ball collision under position and time translations, rotation, and a velocity boost

## Before the animation

Chapter lines 2–2:

Strike a pool ball with a cue, and the balls move in an expected way. Move the table over a few feet, and the balls move in recognizably the same way. Wait a few minutes, and the balls move in the same way. Turn the pool table a few degrees, and the balls still move the same way. Put the pool table on a train at constant velocity, and, again, the balls move in the same way. These are the manifest "symmetries" of the world we live in -- position and time translation, rotation, and velocity "boosts."

## After the animation

Chapter lines 10–10:

Our pool game illustrates what we mean by symmetries of physical behavior, but why should we start our story here? We will argue that symmetry constrains both the laws that govern physical evolution and the classification of the objects that undergo that evolution. The term "symmetry" in this context may not at first glance seem like the same concept as, say, a triangle's symmetry, but it precisely is, as we will see.

Chapter lines 12–12:

We will start with the familiar world of these discrete symmetries and build up the definitions we need from there. Then we will turn to “continuous symmetries,” specifically rotations and translations, where we will encounter a new branch of math, Lie algebra, that joins symmetry ideas with calculus. We will discover that waves arise naturally when we represent translational symmetry, and this will lead us to a discussion of Fourier analysis. Finally, we will situate these ideas in the context of quantum mechanics.