Re:Evidence for Anyons, a Third Kingdom of Particles
by knzhou on Thursday May 14, 2020 @08:44PM
(#23187580)
Okay, now I see what you mean. They were going in the right direction, but they did mess up. Everywhere they talk about moving a particle in a loop around the other, they really should have talked about moving two particles to exchange them. An exchange is of course topologically distinct from doing nothing. A loop is two exchanges in a row -- which is, as you say, topologically trivial in 3D (so the loop phase must be 1, and the exchange phase is +1 or -1, allowing for bosons and fermions).
> To understand the quantum kingdoms, think of a drawing of loops. Imagine two indistinguishable particles, like electrons. Take one, then loop it around the other so that it ends up back where it started. Nothing seems to have changed. And indeed, in the mathematical language of quantum mechanics, the two wave functions describing the initial and final states must be either equal or off by a factor of −1. ... If the wave functions are identical, your quantum particles are bosons. If they’re off by a factor of −1, you have fermions.
This is nonsense. In 3D, you can't even define what it means to loop one particle around another, and there is nothing at all that says that fermions behave in a particular way when you loop them around some other particle.