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.
