There are lots of questions one could ask
about particle physics, from why there exists
quarks to why would anyone care about particle
physics at all.
Luckily, the answer to that last one is easy.
We study particle physics because it’s totally
bleeping awesome. I mean, come on- who would
even ask such a silly question?
However, there are questions that even reasonable
people might ask. For instance, one question
might be why the various subatomic forces
have different strengths. At a distance scale
about the size of a proton, the strong nuclear
force is the strongest. Electromagnetism is
about one percent as strong as the strong
force. And the weak nuclear force is only
about 0.001 percent as strong as the strong
force.
Just why these forces have the strength they
do is an interesting one and the answer differs,
depending on the force. So, I thought I’d
tell you why the weak force is so much weaker
than the electromagnetic force when they have
so much in common. They’ve even been unified
into a single force that we call the electroweak
force, but that particular story I’ll leave
for another day.
To understand what’s going on, you need
to remember a few things. The first thing
is that the photon is the particle that mediates
the electromagnetic force. It is massless
and has no electrical charge. For the weak
force, there are two particles that mediate
the interaction. They are the W and Z bosons.
Both of these particles are very massive.
The W boson has an electric charge and the
Z boson is neutral.
The points I’ll be making are universal,
but let’s just compare the photon and the
Z boson for purposes of illustration. And,
to do that, I’ll describe a specific example.
Let’s talk about when a quark and antimatter
quark come together and annihilate into a
force carrying particle, which then decays
into an electron and antimatter electron.
There’s nothing particularly special about
this particular process. It just helps me
make my point.
So we see here two Feynman diagrams that show
what’s going on. On the left hand side,
we see that quark and antiquark coming together,
making a photon, and then decaying into the
electron and antimatter electron. On the right
hand side, we see the same thing, but with
a Z boson. They’re obviously very similar.
I made another video about Feynman diagrams
that’s relevant. It might be worth your
time to watch it. While Feynman diagrams are
little drawings that help visualize what is
going on, they are also equations in disguise.
In this case, each diagram contains seven
elements. There are the two incoming particles
and the two outgoing particles. That’s four.
Then there are the two vertices where the
interactions occur. That brings us to six.
And finally, we have the force carrying particle.
That’s seven, and we see that both the electromagnetic
and the weak force Feynman diagrams have the
same number of components.
We could therefore write an equation that
kind of brings that all together. For instance,
we could say that the EM interaction is equal
to incoming particle 1 times incoming particle
2 times outgoing particle 1 times outgoing
particle 2 times the creation vertex times
the decay vertex times the created particle.
And, for the weak force, we can say the same
thing.
So, since this equation structure governs
both interactions and the diagrams are so
similar, what exactly is the difference that
makes the weak force so much weaker than electromagnetism?
Well, we see that the incoming and outgoing
particles are the same in both cases, so they
can’t be the source of the difference. So
let’s just gray them out. That means that
we’re left with the two vertices and the
force carrying particle.
The vertex terms contain within them the charge
of the interaction and it seems pretty reasonable
that the difference might occur there. After
all, we know that in electromagnetism that
some particles have a lot of charge and others
don’t. However, if we actually calculate
the weak force charge and the electromagnetic
charge, we find that they turn out to be pretty
similar in magnitude. They’re not the same,
so don’t think that. But they’re not so
different. So that isn’t the cause either.
So let’s gray them out too.
And that leaves us with the force carrying
term. Now the trick is to explain how the
force carrying term causes the weak force
to be so weak.
To take this next step, we need to talk about
the Heisenberg Uncertainty Principle. This
is one of the principles of quantum mechanics.
It’s often said that it means that you can’t
simultaneously measure a particle’s momentum
and position and that’s true.
But there’s another expression of the Uncertainty
Principle that says that if you look at a
particle for a shorter and shorter time duration,
you will have a less and less precise measurement
of the particle’s energy. And, since energy
and mass are connected via Einstein’s equation
E equals M C squared, that means a particle’s
mass can also differ from what’s expected.
So that’s a lot to get your head around,
so let’s just take a step back. Basically
what this is saying is that while a photon
has zero mass, if the photon participates
in an interaction that takes a very short
time, for that split second, the photon might
have a mass. Similarly, the Z boson has a
nominal mass of 91 billion electron volts
of energy, but its actual mass might differ
in interactions that are very brief.
This, of course, means that the mass of the
Z boson can vary from interaction to interaction.
That’s a pretty mind blowing concept, but
it’s true.
In fact, we have studied the Z boson to death
and while we know that its most probable mass
is 91 billion electron volts, it really has
a range and we can easily find it to be anywhere
between 89.5 and 94.5 billion electron volts.
Now that’s just the normal range. The mass
of any particular Z boson could be anywhere
between 0 electron volts and infinity. It’s
just very rare to find it outside that normal
range.
And we can quantify how likely it is for the
Z boson to have any particular mass. If the
most likely mass is 91 billion electron volts,
you can find it with a mass of 88.5 billion
electron volts about twenty percent as often.
Finding it with a mass of 76 billion electron
volts is only about one percent as likely
and finding it smaller than that is even more
unlikely.
So now we’re ready to answer the question
of why the weak force is so weak. It boils
down to energy. So let me hang some numbers
on that.
The type of radioactive decay using the weak
force is called beta decay. It’s when a
neutron decays into a proton and emits an
electron and a neutrino. An example of this
kind of decay is the carbon 14 decay that
is used to date how old some objects are.
If you look at it more deeply, what you see
is essentially that the neutron emits a W
particle, which then decays into an electron
and a neutrino. And you can figure out the
mass that this particular W particle must
have. It turns out that it must have a mass
of 156,000 electron volts or, in round numbers,
0.0002 billion electron volts.
Now the W particle has a natural mass, which
is 80 billion electron volts and its natural
range is between 78 and 82 billion electron
volts. That means that’s incredibly, stupidly,
ridiculously rare for a W particle to have
a mass of 0.0002 billion electron volts. It
just almost never happens.
And because it almost never happens, then
it is exceedingly unlikely that, for example,
a carbon 14 nucleus will emit a W particle
and decay. That means interactions that proceed
by the weak force are very rare and THAT is
why we call the weak force weak. It’s a
matter of energy and the probability of making
such a very light W particle.
Now I wouldn’t be telling you the complete
story if I didn’t tell you about how top
quarks decay. Top quarks decay by emitting
a W boson and turning into a bottom quark.
And they do this decay so fast that it happens
before the top quark can interact via either
the electromagnetic force or the strong force.
In fact, in top quark interactions, the weak
force actually happens first, which suggests
that this is the strongest of the forces in
that situation.
Don’t feel bad if you feel a bit confused.
I’ve been telling you that the weak force
is weak and I just told you that in one case
it was super strong. And again, the reason
is energy. A top quark has a mass of 172 billion
electron volts, so it has enough energy to
decay into a W particle with only 80 billion
electron volts of energy. And, if it can decay,
it will.
But in the world of nuclear physics, which
is much lower energy than the world of the
top quark, the decay involves only something
like 0.0002 billion electron volts of energy,
which means that it won’t happen until a
W particle is created with an outrageously
unlikely mass. When that happens, then that
form of nuclear decay can proceed.
So that’s the basic idea. The weak force
is weak in radioactive decay because it can’t
happen until a very rare W particle happens.
But in interactions with enough energy, it’s
easy to make W particles and, in those circumstances,
the weak force isn’t weak at all.
In fact, this is an excellent example of just
how complicated particle physics can be- indeed
any advanced science. The simplest lessons
are right, but incomplete. And as you dig
deeper and deeper into the subject, your mind
can get blown again and again.
