Understanding Electron Spin: The Mystery Behind a Fundamental Property

[Orodruin]

The underlying reason why particles have intrinsic spin is the classification of particles in terms of irreducible representations of the Poincaré group. This is something that arises from relativistic quantum mechanics.

 

[Orodruin]

Several comments more resembling namecalling than an actual physics discussion have been deleted. Please keep on topic and keep the discussion civil.

 

[my2cts]

The underlying reason why particles have intrinsic spin is the classification of particles in terms of irreducible representations of the Poincaré group. This is something that arises from relativistic quantum mechanics.

This states that particles _can_ have intrinsic angular momentum, corresponding to half integer or integer multiples of h.
It does not pertain to a physical explanation of spin in terms of actual rotation.

 

[HomogenousCow]

This states that particles _can_ have intrinsic angular momentum, corresponding to half integer or integer multiples of h.
It does not pertain to a physical explanation of spin in terms of actual rotation.

Because there is no "actual rotation". If you take a free dirac field and compute the noether current resulting from lorentz symmetry and then take the current to the non-relativistic limit, you will clearly see that in addition to the usual angular momentum, there is an extra piece resulting from lorentz boosts which can be quantized into a spin operator for the fermions. This noether current arises from internal component mixing due to (a representation of) lorentz boosts. I don't see how one could interperet this as a physical rotation.

 

[Vanderpol4]

That still does not undermine my2cts point, in fact all intuitive reasoning does still apply, electron magnetic moments precess around an external B-field precisely as if they were generated by infinitesimal current loops with an intrinsic angular momentum, ( hence the term gyro-magnetic ratio), and classical vector analysis can get you to the correct answer for the larmor frequency, the gyromagnetic ratio, etc, etc.

Extremely curious but seemingly true. In fact the transition from classical to quantum Pauli spin operators was seamless, quite enlightening
Check out Prof. Wolgang Ketterle's 8421 course running now:
https://courses.edx.org/courses/cou...Classical_Magnetic_Moment_in_a_Uniform_Field/

So far it is a brilliant course, and free. The fundamental difference comes when you interrogate the two level system and determine the spin state, then you measure either spin up or spin down. The other key point is a classical system has a ground state so S=1, somehow the the ground state is "entangled" in the two level S=1/2 true quantum state nature of the electron, he also notes you have to be a careful with the quantitative aspects of a free electron...

 

[HomogenousCow]

That still does not undermine my2cts point

Yes it does. Spin angular momentum is not related to physical rotations in space, it corresponds to internal component mixing of the underlying multi-component field (four vector or some spinor).

 

[mfb]

That still does not undermine my2cts point, in fact all intuitive reasoning does still apply, electron magnetic moments precess around an external B-field precisely as if they were generated by infinitesimal current loops with an intrinsic angular momentum, ( hence the term gyro-magnetic ratio), and classical vector analysis can get you to the correct answer for the larmor frequency, the gyromagnetic ratio, etc, etc.

How do you get g=2.00231930436 with a classical analysis?
Actually, starting with g=2 would be interesting on its own, but I really wonder how you would add the QFT corrections to that with classical mechanics.

 

[Vanderpol4]

Not sure he said it was true nature of the local physicality, I understand his comments as being in the same vein of reasoning as Wolfgang's, a classical interpretation which allows, under the specific condition that you can approximate the system as a two level resonant state, to allow a grounding on intuition, e.g. as Wolfgang presents it to paraphrase, "you have my permission to to see precessing vectors in your head when thinking about magnetic moments", nothing more. In my view it is still a field interpretation of a resonant phenomena, certainly for me it really helps with understanding the phase component in the quantized matrix formulation of the electron dynamics.

To be honest I am not sure exactly what you mean by, "internal component mixing of the underlying multi component field (four vector) " to point there is no "ground state" so not sure "mixing" is the verb I would have chosen, for example in my mind a superposition of the two quantized states in which the expectation value of the magnetic moment operator evolves in time under the Heisenberg commutation or state exchange rules implies stationary, not evolving "underlying" field states. It seems to me it is all a matter of probabilistic interpretation of a resonant energy modal condition where there is a specific spatially varying phase between two states, say the ground state and the first excited state of the electron, and that is what leads to the gyromagnetic moments observed.

 

[Vanderpol4]

How do you get g=2.00231930436 with a classical analysis?
Actually, starting with g=2 would be interesting on its own, but I really wonder how you would add the QFT corrections to that with classical mechanics.

That is great question, I am really not to deep in this subject, I am more of a optical physics not AMO guy, just trying expand my intellectual horizons. Maybe it could be stated as, is there a pertabative outer product formulation which allows corrections in sort of a Ptolemaic system for quantum electrodynamics? No idea, not even sure my question is correctly stated, but I will look into it.

 

[mfb]

Precessing vectors are fine as analogy, but not coming from a classical current loop.