# Can we measure the electron spin independently of its magnetic moment?

What experimental evidence do we have for the intrinsic angular momentum of the electron (its spin)? I am specifically interested in whether we have a value for this that is independent of the intrinsic magnetic moment, and hopefully a value for the bare electron alone (i.e. not in some system such as an atom).

• How can we measure the spin without making it interact with something? – Sofia Feb 6 '15 at 16:35
• Good point, hence the "hopefully" ;) Something as simple as possible would be preferable, such as another electron or photon, or charged particle (I realise if you choose a proton you're effectively choosing an atom). – kotozna Feb 6 '15 at 19:11

In quantum mechanics, the magnetic moment operator is related to the spin operator by:

$\vec\mu = -\left(\frac{e}{mc}\right)\vec{S}$

In other words, they are directly proportional up to some known physical constants. This means that measuring the spin of an electron is exactly equivalent to measuring its magnetic moment: if you obtain either quantity, you just multiply or divide by a constant to get the other. In other words, your question is equivalent to "can we measure two times the momentum of an object independently of its momentum?"

An example of an experiment which can measure the spin of electrons outside of atoms is the Stern-Gerlach experiment.

• If quantum mechanics is correct, then obviously you only need to measure one to get the other. I am more concerned with experimental verification that the formula you give is correct, in which case we need to measure $\mu$ and $S$ independently. The Stern-Gerlach experiment uses atoms. – kotozna Feb 6 '15 at 19:07
• In fact, this equation is how S is defined. It's nonsensical to experimentally verify a definition; as I stated in my analogy, it would be like trying to experimentally verify that a quantity you define as twice the momentum is, in fact, two times the momentum. The Stern-Gerlach experiment can be done with any type of charged particle, including atomless electrons. – Izzhov Feb 6 '15 at 19:24
• If that is a definition, then my question does not make sense. Could you provide a reference for it being a definition? According to the wikipedia entry on the Stern-Gerlach experiment, "It must be noted that observation of the Stern-Gerlach effect with free electrons is infeasible" – kotozna Feb 6 '15 at 20:08
• Every experiment that has ever been performed where spin was measured or used as a parameter to measure something else has utilized the equation in my answer. Given that a theory is only as good as its ability to predict experiment, we can conclude that spin amounts to nothing more than a redimensionalized magnetic moment. Apologies for citing Stern-Gerlach; I missed that part of the article. See instead this recent experiment which measures the magnetic moment of a single, free electron: gabrielse.physics.harvard.edu/gabrielse/papers/2006/… – Izzhov Feb 6 '15 at 20:43
• Could you provide a reference to that fact? I'm worried spin might appear independently of magnetic moment in atomic physics/spectroscopy. Are you certain that Dirac's theory does not produce a spin of the electron independent of its magnetic moment? Thanks for the interesting paper. – kotozna Feb 6 '15 at 22:12