We always hear that electron spin is merely analagous to angular momentum in classical mechanics, but it never seems to be followed up by what is actually going on based on first principles (not even once did I hear a professor try to explain it throughout my entire undergrad in mechanical engineering at a pretty reputable university).
Only years after college I ran into a video (which I can't seem to find sadly) that described the polarization of light split up in x and y directions, leading to a circular, or sinusoidal rotation (see this https://www.google.com/search?q=rotating+polarity+of+light&tbm=isch&tbo=u&source=univ&sa=X&ei=Lbm8VJSGGoHfgwSMsoLoAw&ved=0CFEQsAQ&biw=1349&bih=758) . This was a step closer to what was "actually" going on with spin of particles )including the electron), since particles at the quantum scale are probabilities of existence, rendering the classical notion of a body spinning to be not applicable to fundamental particles.
Is this rotation of polarization of light as close as the description gets (i.e. is this what is fundamentally going on for an electron also), or is there another more accurate explanation of electron spin?
If it is as close as it gets, can someone explain how/why an electron would get polarized like a photon does? Is it just a feature of all fundamental particles, or just some?
If not, can you provide a more accurate description of what electron spin is?
A photon seems to travel, and can be polarized, correct? In such geometry, the rotation of polarization occurs in the plane perpendicular to the direction of the photon's direction of motion. But what would it mean for the polarization when for photons that have been slowed to a stop, as I believe scientists have managed to do? Or more applicably, what would it mean for the "spin" or "polarization" (if they are indeed closely related) for an electron that is bound by a positive charge, not having any real direction of motion as a photon does (or does it?)?