The three most important things in physics are chirality, chirality and chirality. Chirality means the difference between left-handed and right-handed spinors, as representations of the Lorentz group. Chirality means the difference between left-handed and right-handed SU(2), as factors of SO(4). Chirality means WTF is going on in radioactivity? Why is the universe 22% left-handed and 78% right-handed?
Let me tell you a story. I once possessed a remarkable corkscrew, which was made entirely of wood, apart from the metal screw that went into the cork itself. It was almost a family heirloom, though not particularly old. It was destroyed one night by a physicist who thought he understood chirality, but didn’t. The magnificent design of the corkscrew included, besides the (right-handed) metal screw to screw into the cork, a left-handed wooden screw so that the corkscrew could lift out the cork. The physicist assumed that pulling out the cork required turning a right-handed screw to the left. The very clever design required turning a left-handed screw to the right.
Result: the physicist broke the mathematics, and claimed the universe was at fault. Reality: the universe and the mathematics were in perfect harmony, only the physicist was living in an alternative reality. Moral: you must distinguish between a left-handed “unscrewing” action and an anti-right-handed “screwing” action. Otherwise, your theory of the universe is broken beyond repair.
