# What does magnetic moment mean exactly?

1. Oct 1, 2011

### nhmllr

A friend asked me this but I'm not sure of my answer.

On a particle level, I said that the value of the magnetic moment determines how the probability is that the particle absorbs/emits an electron.

Is this right?

Thanks

2. Oct 1, 2011

### strangerep

No. Try http://en.wikipedia.org/wiki/Magnetic_moment

3. Oct 1, 2011

### nhmllr

Right. I know the practical definition. Let me elaborate.

I read QED. My friend is now reading QED. Both of us are thinking with those amplitude arrows and Feynman diagrams. The question is, what does magnetic moment determine? On a macroscopic level I know that it's the strength, but on a subatomic level, what does a particle with a high magnetic moment do differently from one with a low magnetic moment?

4. Oct 1, 2011

### strangerep

Its interaction with a background magnetic field is stronger. Have you seen the
$\mu \cdot B$ term that occurs in the potential energy? (Look at the section titled "Effects of an external magnetic field on a magnetic moment" in the Wiki page I mentioned.)

Basic derivations of the electron magnetic moment in relativistic Dirac theory use a nonrelativistic approximation to get it. More accurate QED derivations involve the electron-photon vertex. Peskin & Schroeder do this in sect 6.2 et. seq.

5. Oct 1, 2011

### nhmllr

Wait a second, what do the symbols mu and B represent? It doesn't say on the Wiki

Also, to clarify, I mean that we're reading QED by Richard Feynman

6. Oct 1, 2011

### strangerep

$\mu$ is the magnetic moment vector of the particle. B is the external magnetic field vector. (Also note that "magnetic moment" is short for "magnetic dipole moment" -- the lowest order term in a multipole expansion of a general magnetic field.)

Wiki uses "m" instead of $\mu$. (I used $\mu$ because that usage is more familiar to me.)

Unfortunately, I don't have that book -- and Amazon doesn't have "look inside" enabled for it so I can't see what you're reading.

Do you have a textbook on ordinary relativistic quantum physics (not full-blown QED) which discusses the Dirac equation and derives the (non-anomalous) magnetic moment of the electron? That might be a better place to start understanding this magnetic moment stuff. The more accurate anomalous magnetic moment derived in QED is just that: a more accurate derivation using a better theory.

7. Oct 1, 2011

### nhmllr

Neither of us have any real experience with quantum mechanics. QED is a book for the layman, very few equations.

The answer I'm looking for is one that just says, qualitatively, how particles with different magnetic moments behave differently with virtual photons.

It is a weird question, I admit.

8. Oct 2, 2011

### strangerep

Oh, you meant "QED: The Strange Theory of Light and Matter"?
I thought you meant this one:

https://www.amazon.com/Quantum-Elec...=sr_1_2?s=books&ie=UTF8&qid=1317533218&sr=1-2

Virtual particles are just mnemonics for certain mathematical terms in a perturbation series. Thus, they are unphysical. But magnetic moment is a physical quantity. It's best not to mix fiction and nonfiction, or severe confusion becomes inevitable.

The closest I can get to a nonmathematical answer is that particles with larger magnetic moments have... well... a stronger magnetic field. Therefore they interact more strongly with another applied magnetic field, among other things.

Try to resist the widespread temptation to think of physical electromagnetic fields as being made up of (unphysical) virtual photons.

Last edited by a moderator: May 5, 2017
9. Oct 2, 2011

### nhmllr

Aww, why you physicists gotta keep bursting my bubble? :P
Thanks, though.

Last edited by a moderator: May 5, 2017