In particle physics, there are lots of particle
names, mostly ending with the syllable ‘on.’
Electrons, protons, hadrons, baryons, leptons,
mesons and the list goes, well... on.
But two particles have a special meaning and
those are fermions and bosons.
Unlike all the other particle names, which
are related to particles’ electric charge,
mass or the forces they feel, the factor that
both ties together and distinguishes fermions
and bosons is the idea of subatomic spin.
Since the early part of the twentieth century,
physicists have known that there is a natural
unit of spin.
This unit is represented by a symbol which
is an h with a little slash through the top
of it.
We call in hbar, but it is more properly called
the reduced Planck constant.
It has a value of 1.2 times 10 to the minus
34 joule-seconds.
Now that numerical value isn’t something
you have to remember because we scientists
use it as a unit, just like you might use
pounds or kilograms.
I mean, when you weigh yourself, you probably
don’t always attach the unit.
You don’t say “the scale said 150 pounds,”
you just say “the scale said 150 today.”
In terms of spin, it’s kind of the same
way.
If a subatomic particle has a spin of one
unit of hbar, we just say that the particle
has a spin of 1.
If it has a spin of four units of hbar, we
say that the particle has a spin of 4.
When we talk about fermions and bosons, they
represent different classes of particles and
they are distinguished by their spin.
Bosons all have a spin that is an integer
multiple of hbar.
They have spins of 0, 1, 2, 3, and so on.
In contrast, fermions all have half integers
of spin, specifically 1/2, 3/2, 5/2, etc.
So you might wonder if there are other possible
values of spin, say a third or a quarter or
something like that.
The answer seems to be no.
We have never observed any particles with
any value of spin other than an integer or
half integer.
Now you never say never in exploratory physics
and it may be that we’ll find some new particle
governed by new rules, but we probably won’t.
The reason I say that is that we can tie the
spin to the mathematics that describes the
particles.
The technical term for the mathematics is
called the wave function, but there appears
to be just two possible forms.
In one case, the equation of the particle
seems to be symmetric, which means that if
you flip it around the center, it looks just
like it did before the flip.
In the other case, the equation of the particle
is antisymmetric, which means if you flip
it around the center, it’s the opposite.
This has real consequences when you’re trying
to do calculations, but you’ll have trust
me on that one.
Bosons, the particles with integer spin, are
described by symmetric wave functions, while
fermions, their half integer spin cousins,
have antisymmetric wave functions.
If fermions and bosons are different kinds
of particles, they must have different properties,
right?
So how are they different?
Bosons are the puppies of the subatomic world.
The more, the merrier.
You can have an unlimited number of bosons
in the same place at the same time.
In contrast, fermions can be thought of as
subatomic cats.
They’re stand-offish.
Two identical fermions cannot be in the same
place at the place at the same time.
If you ever took a chemistry class, you probably
encountered the Pauli exclusion principle,
which explained why atomic orbitals are the
way they are.
It boiled down to identical electrons cannot
exist.
And, since electrons are examples of fermions,
it all hangs together.
In the particle physics world, all of the
particles of matter, the quarks and leptons,
are all fermions.
In contrast, the particles of force, the force
carrying bosons are, well, of course, bosons.
Quarks and leptons all have spin of 1/2.
Well, technically, since they can spin clockwise
or counterclockwise, they can have spin of
plus 1/2 or minus 1/2, but that’s a minor
complication in what I’m talking about here.
What’s really important to know is that
there are no fundamental particles of the
standard model with spins of 3/2, 5/2 or anything
like that.
Only 1/2.
On the boson side, there is more diversity.
The Higgs boson has a spin of zero.
The photon of the electromagnetic force, the
gluon of the strong force and the W and Z
bosons of the weak force all have a spin of
1.
And the graviton, which is the hypothetical
and undiscovered carrier of gravity, must
have a spin of 2.
So that’s about it.
You have the gregarious, force carrying bosons
and the stand-offish, matter, fermions.
They are important because they represent
two distinct classes of particles in the Standard
Model.
They also have an interesting significance
in that the fermion and boson roles in the
Standard Model are blurred in some speculative
theories that go beyond the Standard Model.
For instance, in a class of theories that
include a principle called supersymmetry,
all of the known fermions are hypothesized
to have new boson cousins that are identical
in every way except for spin.
Similarly, the known bosons are postulated
to have a new cousin fermion.
I made a couple of videos about supersymmetry
and why the idea is considered interesting
by researchers.
Check them out if you want to learn about
the idea.
In this video my goal was to teach you the
differences between fermions and bosons and
I hope I’ve done that.
Because all these particle physics terms are
enough to make your head spin!
