Question

Can spin angular momentum be understood as orbital angular momentum in extra dimensions?

Answer 1

Let us start with Spin Classification. One essential parameter for classification of particles is their "spin" or intrinsic angular momentum. Half-integer spin fermions are constrained by the Pauli exclusion principle whereas integer spin bosons are not. The electron is a fermion with electron spin 1/2. Experimental evidence like the hydrogen fine structure and the Stern-Gerlach experimentsuggest that an electron has an intrinsic angular momentum, independent of its orbital angular momentum. These experiments suggest just two possible states for this angular momentum, and following the pattern of quantized angular momentum, this requires an angular momentum quantum number of 1/2

Answer 2

Because you mention spin, I will assume that you mean magnetic dipole moment. In most contexts, if you just say “dipole moment” people will assume you mean electric dipole moment.


Also, because you have Quantum Mechanics as a topic, I will assume you are referring to the intrinsic quantum mechanical spin of a particle. Spin also has a straightforward classical meaning: the angular momentum associated with the spatial rotation of an extended body.


The ultimate goal of a physical theory is to be able to predict the future state of a system, as described by its degrees of freedom . On the macroscopic scale, we have a good intuition for what the degrees of freedom of systems should be. For example, a rigid body like a basketball can go forward or backward, sideways and up or down. That’s three degrees of freedom, which we normally label [math]x[/math],
[math]y[/math] and [math]z[/math]. But, it can also rotate about those three axes. That’s an additional three degrees of freedom, usually described with the Euler angles,
[math]\alpha[/math], [math]\beta[/math] and
[math]\gamma[/math].