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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?

  1. 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?

  2. 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?)?

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The spin of the photon is intrinsic in its description as an elementary particle, +/-1 when measured. There is no zero component because the photon has mass=0., so the spin is always either parallel or antiparallel to the direction of motion of the photon.

This wiki article describes the relation between light polarization and photon spin.

I find this image useful:

polspin

Left and right handed circular polarization, and their associate angular momenta.

The polarization of the classical electromagnetic wave is the direction of the electric field (by convention), seen here as the red arrows giving the circular polarization of the beam , in this example.The purple arrow shows an individual photon in the em wave which is circularly polarized , left hand top, right hand bottom.

The classical beam is built up (emerges) from an enormous number of photons, each of which will have its spin either parallel or antiparallel to the direction of motion of the electromagnetic wave (ensemble of photons).

This orientation (+/-1) reflects, like a right hand ( left hand) rule the direction of propagation of the rotation, that is the connection of photon spin to electromagnetic wave polarization. Each individual photon wavefunction is also described by a value connected with the vector potential of the electromagnetic field ( not shown in the image) and that is what contributes to the build up of the red vectors (electric [and magnetic] field[s]).

So the polarization of classical electromagnetic waves is not a good analogue for the polarization of an electron beam, for example, where the experimenter tries to orient the spins of the electrons in one direction. The electron spin is also an intrinsic phenomenon and it is what is measured in describing its polarization.

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Well you can get Weyl spinors, it's exactly the same description of electron in terms of light helicity - 'left' and 'right'-handed. But if you will go deeper you have to remember, that in Standard Model left-handed electrons are paired with neutrinos, but right-handed electrons are single (there is no right-handed neutrino for couple).

Ah, one more information - when you describe photon spin, it is always $\pm\hbar$. Spin (or intrinsic angular momentum) for electron is half of $\hbar$ (plus or minus).

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  • $\begingroup$ I'm not quite grasping everything you're saying, due to my lack of knowledge, but I get it at a partial level, and it certainly give me areas to investigate, and keeps me excited about physics! The universe is a grand, beautiful puzzle, where the only sad thing is we won't live to understand it all. The critical leap is eternally sustainable biological regeneration, or consciousness transferring technology. $\endgroup$ – ahnbizcad Jan 19 '15 at 10:10
  • $\begingroup$ The asymmetry. Very peculiar. Unrelated: Physics sure is a great field for people with OCD or Asperger's =] $\endgroup$ – ahnbizcad Jan 19 '15 at 10:12
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    $\begingroup$ If you want we can exchange few mails about field of theoretical physics. I know standard model and quantum field theory a little, but my field of work are quantum computations (in c++). I think i have somewhere in my profile my email adress... :) $\endgroup$ – Cheshire Cat Jan 19 '15 at 21:23
  • $\begingroup$ I appreciate that a lot. but that's OK. If you do have concise, easy to absorb material that would be most helpful, and I'm sure for others =] $\endgroup$ – ahnbizcad Jan 19 '15 at 23:41

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