system
Given the following post, respond as if you're commenting on Reddit:
human
If I were traveling at the same speed as an electron, would I observe it generating a magnetic field?

In other words, I know that a moving electric charge produces a magnetic field. So assuming there was a lone electron flying through empty space and I could match speeds with it and observe it while travelling parallel to it. Since, from my frame of reference, neither of us are moving, is it generating a magnetic field?

If not? Intuitively I would think someone traveling slightly slower WOULD observe a magnetic field.

I know this is somehow deeply tied to the questions which sparked Special Relativity, I can never find a good answer as to WHY though. It's been bugging me since I first started learning about Maxwell's Equations.

Thanks!
gpt
Your idea is correct, but in reality you see a magnetic field no matter what.

If the electron were a point charge **with no spin**, the magnetic field it produces would be zero in any frame where it's not moving. And in any frame where the electron *is* moving (no matter how slowly), the magnetic field would be nonzero.

But in reality, electrons have spin. And since they have spin and charge, they have an intrinsic magnetic moment. You cannot perform a Lorentz transformation to remove this magnetic moment, so it's present in all inertial frames.

So even when the electron is perfectly still, it has a magnetic dipole moment and thus generates a weak magnetic dipole field.