# Why do we think Spin is angular momentum as opposed to some other quantity? [duplicate]

What leads us to the conclusion that spin is angular momentum? Could it not be some other quantity? Sorry if this is a rookie level question.

• Because it behaves like angular momentum: (1) it follows the angular momentum algebra, (2) it interacts with magnetic fields in the normal way, (3) it adds to other angular momenta to make total angular momentum, etc., and all of this matches experiments. Feb 16, 2016 at 5:06
• Feb 16, 2016 at 7:34

By treating spin as angular momentum a lot of phenomenon could be explained.

• Conservation of angular momentum makes sense only if you include spin with the orbital angular momentum. Spin-orbit coupling will mix these quantities even if the system is isolated.

• The algebra of the spin operators (which can be represented by the Pauli matrices) is analogous to the angular momentum algebra.

• Charged systems that have an angular momentum will have a magnetic moment. They act like little magnets. The magnetic moment of electrons can be measured using Stern-Gerlach-like experiments. These experiments also elucidate the quantum nature of spin.

The idea that electrons may have an intrinsic angular momentum was theoretically proposed to explain the anomalies in the spectrum of hydrogen. It is necessary to explain the behavior of the spectrum when the atom is subjected to magnetic fields.

• Neutrons are uncharched particles but also have a spin and a magnetic dipole moment. Feb 16, 2016 at 6:36
• @HolgerFiedler as their internal constituents are quarks which are charged and therefore contribute to the magnetic dipole moment of the neutron... Feb 16, 2016 at 6:43
• @Bruce Lee This does not contradict the phenomenon that the measurement of the neutrons magnetic moment gives a result, does it? Feb 16, 2016 at 6:51
• @HolgerFiedler to the contrary, it explains your observation made in your first comment.. Feb 16, 2016 at 6:53
• @HolgerFiedler A better question would be ask if a neutrino (which is point-like, neutral, spin 1/2 particle) has a magnetic moment? I don't know the definitive answer, but the consensus seems to be that it is very very small. Feb 16, 2016 at 6:57
1. The generators for spin follows the same commutation relation as that of angular momentum. i.e $$[S_{x}, S_{y}] = iS_{z}$$ obeys the similar commutation rule for angular momentum

$$[J_{x}, J_{y}] = iJ_{z}$$

The similarity in algebra is an indication why spin should be considered to be angular momentum, although it is not the complete reason.

1. It has been observed experimentally that spin couples to orbital angular momenta as in systems obeying $L-S$ coupling. It follows similar rules of angular momenta addition as resulting from the addition of two angular momenta. The observed spectrum in such a coupling observed matches theoretical predictions accurately if spin is considered to be angular momentum. This completes the reason why spin should be considered as angular momentum.

2. It gives rise to a dipole moment in case of charged objects, similar to what angular momenta does.