Magnets can seem pretty mysterious. Their
behavior is explained by Maxwell’s equations. However, it’s easy to convince yourself that
Maxwell’s equations prove that magnets don’t work. That’s the hook – if you’re not careful,
you can easily convince yourself that magnet theory is wrong. However, obviously, magnets do
work, so what’s going on? And how does Einstein save the day? Let’s dig into it.
(intro music) As you know, magnets are typically little chunks
of metal that can pick up certain other metals. The details of how the magnets that hold
children’s art to the refrigerator work can be kind of complicated, but luckily we
can also make magnets using electricity, and the theory describing those magnets is much
easier to work with. We call magnets made this way electromagnets and they prove a weird and
completely non-intuitive prediction of Einstein’s theory of special relativity.
Electricity and magnetism are related
phenomena, but different. Electric force can be made by taking two electrically charged
objects and bringing them near one another. Depending on the charges, the
objects will either be attracted or repelled.
Magnets are different. Magnetic forces are
only felt between moving electric charges. If the charges are stationary, nothing happens.
However, if one charge is moving and generates a magnetic force, a second moving charge will feel
it. But that’s the key point – for magnetism, both charges need to be moving.
This effect can be seen most simply when we
put two parallel wires near one another. If we run an electric current through the bottom
one, it sets up a magnetic field around it. If we also run a current through the top wire
in the same direction, it feels a force that pulls the wires together. If, instead, we run the
current in the top wire in the opposite direction, the two wires are repelled.
Now, I don’t want to describe magnetism the way
you might have learned in physics class. That’s all very cool stuff, and you might have sprained
your wrist doing all that right-hand rule jazz, with this right-hand rule or this one or this
one. But that’s not the point of this video.
If you never took physics, or you’ve forgotten all of it, I put links to some other videos on how
magnetism in wires works in the description below. Mind you, I didn’t make those videos.
But some of you might welcome a refresher.
On the other hand, you don’t need to know all the math and whatnot. What you need to
know is that moving charges are needed to make a magnetic force and that if the motion is the same
in the same direction, they attract. If they are in the opposite direction, they repel.
Now, it turns out that if I were to
try to explain the problem using wires, it gets super complicated very fast and highly
mathematical, so let’s use a simplified example that tells you what's going on. And, in the
end, I’ll tell you all about where to find a more detailed explanation.
So, okay, instead of two parallel wires, let’s
have one wire that is carrying a current and a single positive charge moving either in the
direction of the current or against it. If the wire has no current, but the charge
is moving, there's no magnetic force. If the wire has a current, and the charge isn’t moving,
there is no magnetic force. However, if there is a current and a moving charge, there is a magnetic
force and it's the same basic idea as wires – same direction, attract, opposite direction, repel.
Everything I just told you is right, and I’ve
taught it dozens of times in introductory physics classes.
However, now let’s think like Einstein. I mean,
sure, we can say that the charge is moving, but from the charge’s point of view, it’s not moving.
It’s stationary and the world is moving. Since we need a moving charge to feel a magnetic force,
this means that the charge should feel no magnetic force – at least in its own reference frame.
So that makes absolutely no sense at all. We, in
our frame, think the charge should feel a force, but the charge, in its frame, thinks it
shouldn’t. And that, as they say, is a paradox. Relativity does weird things, but two observers
should agree if the charge moves toward or away from the wire.
So that’s how you can convince yourself that
magnet theory is wrong. Yet smart people believe in magnet theory. So how is it saved?
Well, to do that, we need to think about what’s
really going on in the wire. In the wire, there are positive and negative charges.
The wire itself is electrically neutral, but in standard electricity theory, we say that
the positive charges are moving and the negative ones are stationary. Yes, there are issues with
that, I’ll get back to that. But let’s stick with the traditional ideas.
So, an outside observer will see stationary
negative charges and moving positive ones in the wire, and a moving charge above
the wire. For illustration purposes, we’ll say they're moving to the right. The
positive ones set up the magnetic field and there we are.
If we ask what the positive charge on the top sees
in the reference frame in which it's stationary, the negative charges are moving to the left.
The positive charges are probably still moving to the right, but slower than they appear to
someone who is stationary compared to the wire.
And this is where relativity comes in and the magic happens. Remember that special
relativity says that not only do moving observers have clocks tick more slowly, it’s also true that
moving objects get shorter. This is called length contraction, and I made a video about that, which
you can watch. The link is in the description.
Thus, according to the charge outside the wire, it sees the negative charges in the wire
moving fast, and the positive ones moving slower. Because the negative charges in the wire are
moving faster according to the outside charge, the spacing between the negative charges is
contracted more than the positive ones. I’ll even stop the animation so you can see the effect.
This means that the negative charges
are more concentrated than the positive ones. And that means that the wire now
has a net negative electric charge. Since we know that opposites attract, what
happens is that while the now-stationary top charge doesn’t feel a magnetic force downward,
it feels an electric force downward. What once was magnetism is now electricity,
but either way, the force is downward.
What happens if we look at the case where the charge outside the wire is
moving in the direction opposite the current – at least from our point of view? Well, we do the
same thing. Since we see the negative charges in the wire to be stationary and the positive
ones to be moving, in the frame of the charge outside the wire, it sees the positive charges in
the wire moving faster than the negative ones. This means that the charge outside the wire sees
more concentrated positive charge than negative. Since the top charge is positive and same sign
electric charges repel, the charge outside the wire feels a repulsive force and is pushed away
from the wire. Again, the outside observer and the charge outside the wire disagree on magnetism
and electricity, but they both agree that the charge is pushed away from the wire.
So let’s recap. Moving charges make and feel
magnetic forces. If charges aren’t moving, they neither make, nor feel, magnetic forces.
And, depending on the reference frame, the charges could be either moving or not. Luckily, special
relativity saves the day and converts magnetism into electricity and vice versa.
Okay, so this is all very cool, what about
the caveats? Well, to begin with, this is all very hand-wavy. If you want to see how it’s done
with math and equations and whatnot, it was first written down in a book by Edward Purcell back in
the 1960s. The book was revised and re-released back in 2013 and the reference is in the
description, plus there are some online resources that go through the argument more simply.
Some of you will also note that we
know in a real wire that it’s the negative electrons that are moving, not the
imaginary positive ones. Yep. That’s true, but it doesn’t really change anything. If
you think it through, you get the same result.
The absolutely key point here is that the experiment I have described here absolutely proves
that Einstein’s length contraction is a real phenomenon. Magnets wouldn’t work otherwise.
And, another thing is amazing – in the wire, the electrons are moving much less than a millimeter
per second. While most relativistic effects need you to be moving at a substantial fraction of
the speed of light, for magnetism, the speeds are tiny, and yet relativity theory really matters.
This is some really weird stuff, but it’s
true. Magnetism proves Einstein’s theory of relativity and the crazy-sounding idea of Lorentz
contraction. And now you know something you didn’t know this morning. You’re welcome.
(phasing sound) Okay, like I said- this is a crazy thing, but it’s
absolutely true, even if it’s a bit mind-blowing. If you like getting your mind blown, I sure
hope you’ll like and subscribe and share. And I hope you’ll return for future videos
where we’ll visit other physics topics and, when you watch those topics, I hope you’ll agree
with me that physics – especially the mind-blowing stuff – is everything.
(outro music)
