Magnetism is literally everywhere around you.
The Earth is magnetic, even your blood is magnetic, and you use magnets to stick your
favourite photos to the fridge.
But in fact, magnetism is a purely quantum mechanical phenomenon and the extent to which
it's purely quantum mechanical has only been understood about a hundred years ago, in what
has been called by some people one of the most deflationary theorems in modern science.
And the reason why this was such a surprise is that in fact, the relation between magnetism
and electricity has been known for a very long time.
It's called electromagnetism, classical electromagnetism.
For example, people knew for a long time that if you take electrical wire and you run a
current through the wire, this current produces a magnetic field that circulates around this
wireless called the magnetic field B. So this current along the wire produces these lines
of magnetic field.
And you can easily imagine that if you shape the wire, instead of being straight, into
a circular coil and you have a current circulating through the coil, then these circles of magnetic
field around the coil collectively take the shape of what you've probably seen many times
as being the magnetic field lines produced by something like planet Earth.
So you have these lines of magnetic field that come from this magnetic dipole so if
this was the field produced magnet, planet Earth, this would be the north pole and the
south pole and so on.
And it was also known for a long time and this is where things get complicated that
there are materials that without any electrical current, produce a magnetic field out of themselves.
These are called ferromagnets.
And these are the objects that you use to attach photos to the fridge.
So these ferromagnets produce the same type of magnetic field lines that are produced
by a coil carrying current.
And so here is where it becomes complicated.
What is the reason why certain materials produce the same magnetic field as a coil that carries
a current?
So people thought they could find an explanation to this by imagining that in these materials
there are microscopic currents like atomic currents, that circulate in the material and
therefore produce the same magnetic field patterns.
Now of course, you cannot see these atomic currents and so to convince yourself that
they exist, the best thing to do is to see how the material responds to a magnetic field
that you produce from the outside.
This is best done with materials that are called paramagnets so they are not intrinsically
magnetic, but they become magnetic when you apply a field from the outside.
And to understand what you expect should happen, you need to know about something that's called
the Lorentz force.
The Lorentz force is the same kind of force that's used for example in particle accelerator
like the Large Hadron Collider in Geneva, to keep the particles within the accelerating
loop.
The way it works is this.
Let's say you have a charged particle like an electron with charge minus E, it has a
certain velocity for example an electron moving upwards.
If you then apply a magnetic field perpendicular to the velocity of the electron, there will
be a force resulting on the electron that's called a Lorentz force and the force is always
perpendicular to both the magnetic field and the direction of motion of the electron.
So in the presence of this magnetic field, now this force makes the electron bend its
trajectory.
So the trajectory instead of being straight, will be a bent line so it goes around in a
circle in fact.
The important property of this Lorentz force is that in itself, it does not change the
energy of the particle because it's always perpendicular to the velocity.
So it can bend the trajectory but it cannot make the velocity increase.
So the total kinetic energy of the particle remains the same.
So now lets think of this example of a material that normally doesn't have any magnetism of
itself, but may become magnetic when you apply a magnetic field from the outside.
So you can imagine, in zero magnetic field, inside of this material, there might be some
electrons that move randomly, some move up, some move down, some move fast, some move
slow, and if you look at the magnetic field produced by each one of these electrons and
you take the sum, the average of all of them, the total magnetic field you'll see from the
outside is going to be zero.
But if you now apply a magnetic field from the outside, the Lorentz force will make all
the electron trajectories bend in the same direction.
So now you will have these little loops of current effectively.
Some will be big, some will be slow, some will be small, but they all bend in the same
direction, and so you will think, okay, this gives me a net magnetic field produced by
these internal currents.
There's a problem with this, this is wrong.
The reason it's wrong is that physics always tells you that the preferred configuration
that nature chooses for our physical system, is the one with the lowest energy.
But we just said that the Lorentz force does not change the energy of the particles so
the energy of the electrons in this situation and in this situation is the same.
Before, there is no reason why this configuration in which the magnetic field is produced by
the material, should be preferred over the other one.
So this wipes out in one stroke, the classical concept of electromagnetism that magnetic
materials could be magnetic because of some internal currents.
So what's the solution to that?
Well, actually, that's where quantum mechanics comes in.
The solution to this is to realise that these internal atomic currents actually do exist
but they pre-exist the external magnetic field and they come in quantise values.
So to understand why certain materials are magnetic or become magnetic under a magnetic
field, you need to realise that the electrons, being quantum mechanical particles, do not
just have any random velocity and any random energy, but they can only take orbits that
are quantised.
And once these orbits, these quantised orbits pre-exist, then they respond to a magnetic
field in the way that you observe in the experiments.
The other ways in which materials are magnetic and is in fact the most common way, is for
particles to have already an intrinsic, purely quantum mechanical, magnetic dipole of their
own which is called the spin.
So electrons, as well as protons, as well as neutrons, have intrinsically a magnetic
moment so they themselves produce this magnetic field.
But this does not arise from any motion of the particle.
It's an intrinsic quantum mechanical property of the system.
So with this short story, I just wanted to tell you one of the most incredible historical
realisations that told us, only a hundred years ago, that actually, magnetism only exists
thanks to quantum mechanics.