How Special Relativity Makes Magnets Work

Only a few elements can be permanent magnets - iron is one. Copper is not. But if you pass an electric current through any metal, it becomes a magnet - an electromagnet. But how does this work? Well, strangely enough, it's a consequence of special relativity.

Special relativity is the fact that in our universe, length and time aren't absolute; they're perceived differently by observers moving relative to each other (hence, "relativity"). For example, if you measure carefully enough, you'll find that time passes slower for observers moving relative to you.

Hey Derek, when did you last shave?

Derek1: Six hours ago.

MovingDerek: Actually, it was five hours, 59 minutes and 59.99999999999 seconds.

And moving objects are also contracted in their direction of motion. You're looking slim.

Derek1: Only in your frame of reference.

So when an object is moving relative to you, it actually takes up less space than when it's not moving. And even though this effect is obviously way tinier than we've shown, length contraction IS what makes an electromagnet work.

Picture a copper wire - it consists of positive metal ions swimming in a sea of free negative electrons. Now the number of protons is equal to the number of negative electrons so overall the wire is neutral. So if there were a positive charged, err... positively charged cat nearby, it would experience no force from the wire on it at all.

And even if there were a current in the wire, the electrons would just be drifting in one direction, but the density of positive and negative charges would still be the same, and so the wire would be neutral, so no force on the kitty. But what if the cat starts moving? Imagine for simplicity that the cat is moving in the same direction as the electrons with the same velocity.

Well now in my frame of reference, the wire is still neutral and so there should be no force on the cat, but consider the same situation in her frame of reference. In the cat's frame of reference, the positive charges in the wire are moving, so according to special relativity their separation will be ever-so-slightly contracted.

Also, from this perspective, the electrons aren't moving so they'll be more spread out than before - remember, objects take up more space when they're not moving than when they are. These two changes together mean there's a higher density of positive charges in the wire, so it's no longer neutral - it's positively charged!

Which means that the positively charged cat will feel a repulsive electric force from the wire. But in my frame of reference, this seems mysterious: there's no force on a stationary charged cat, but a moving cat is somehow repelled from this neutral wire. How do you account for this force?

Well, we say it is the magnetic force, and that's mainly because a wire with current in it deflects nearby magnets. So really, what this experiment shows is that a magnetic field is just an electric field viewed from a different frame of reference.

In the cat's frame of reference, it is repelled from the wire due to the electric field created by the excess positive charges produced by the effects of length contraction. In MY frame of reference, the cat is repelled from a neutral wire due to the magnetic field generated by current flowing in the wire.

So whether you see it as an electric or a magnetic field just depends on your frame of reference, but in either case, the results are the same. So an electromagnet is an everyday example of special relativity in action.

Now that might seem crazy since electrons drift through wires at about .0000000001% the speed of light - so how can special relativity have anything to do with it? Well, the truth is there are enough electrons in a wire, and the electric interaction is so amazingly strong that even the minuscule effects of length contraction can produce significant charge imbalances that produce a noticeable force.

So special relativity explains electromagnets - but what about permanent magnets? Yeah! I mean there can't be electrical currents flowing around inside lumps of rock, can there? Click here to go to MinutePhysics where we'll explore magnetite, compasses and all the wizardry of permanent magnets.