Live from the Whirlwind: Things I will never believe I understand: "Where wast thou when I laid the foundations of the earth? Declare, if thou hast understanding: Who hath laid the measures thereof, if thou knowest? Or who hath stretched the line upon it? Whereupon are the foundations thereof fastened? or who laid the corner stone thereof; when the morning stars sang together, and all the sons of God shouted for joy?"
Sean Carroll (2008): [Sean Carroll][]: "The important distinction... is...
...the “pile on top of each other”/”take up space” distinction. The fact that these sets of features come hand-in-hand is the content of the spin-statistics theorem: particles that pile on have integer spins, particles that take up space have half-integer spins. Which is a deep and beautiful result that relies on the fact that nature is fundamentally quantum rather than classical, and on the topology of the group of rotations in three (or more) spatial dimensions, and on the features of relativistic field theory. None of which I’m going to explain right here, but John Baez has a fun “proof” of the theorem using ribbons which is worth checking out.... If the fermions comprising a turkey didn’t take up space, it would hardly constitute a filling meal; and if the gravitons from the Earth didn’t pile up to form a classical field, the traditional football game really wouldn’t work at all. So for the spin-statistics theorem, we should all be thankful...
