Angular momentum is a conserved thing (I think?). So... what happens when an electron (spin 0.5) absorbs a photon (spin 1)? Does the electron now have a spin of 1.5? Does it spin faster? What if the electron has a spin of -0.5? I'm referring to a free electron by the way.
Also I'm sorry for asking so many questions... I've taken a liking to physics recently and it seems for every thing I learn a dozen more questions arise.
If a free electron can't absorb a photon what happens to the angular momentum of each when a photon bounces off an electron? Is it left untouched?
Spin in quantum mechanics does not mean "spin" like you would normally think of it for a real object. Although the mathematics do behave similarly, it is not correct to say that something in a spin state of 1 is spinning "faster" than a spin state of 1/2. This quantity does not have a good macroscopic analogue--the choice of the word "spin" is mostly historical--because nothing, as far as we can tell, as actually spinning.
You have to be a bit careful when adding spins. When we say an electron has spin of 1/2, it can take values of +1/2 or -1/2. A spin 1 photon can take values of +1, 0, or -1. All other values simply cannot exist. So if an electron with +1/2 spin were to scatter off a photon with 0 spin, then either the electron would remain at +1/2 and the photon would remain at 0, or the electron would switch to -1/2 and the photon would switch to +1.