Quote by Drakkith
Maybe this is a bad question, but are the sidebands actually propagating outwards from the antenna along with the modulated carrier? Or is this just something that happens when you "do the math"?

A sideband of a modulated signal is a feature of the
frequency spectrum of that signal. So, it is something that exists in the frequency domain (also sometimes called "Fourier space") not in the time domain, or real space. Are you familiar with Fourier analysis?