Every so often, a scientist is born who is
so brilliant and so charming that they become
a cultural icon.
Now, I know you thought I was talking about
myself, well, because… I get that a lot-
but I was actually talking about Richard P.
Feynman, who is definitely one of the coolest
scientists of the 20th century.
While stories abound of his interest in picking
locks and his fondness for having a good time,
it is in the realm of understanding the quantum
nature of matter and energy that he made his
real impact.
I tell the story of quantum electrodynamics
in another video. In this video, I want to
talk specifically about his contribution to
how modern physicists calculate how particles
scatter.
Now Feynman can’t take all the credit. He
shared his Nobel Prize with Julian Schwinger
and Sin-Itiro Tomonaga, but those two guys
were all about really intense equations. Feynman’s
real genius was the way in which he made the
whole process intuitive. He made it so that
anyone who can doodle can at least start the
process of calculating what happens inside
a high energy particle collision.
Feynman diagrams are easy to write and easy
to understand, at least at the most basic
level. For example, let’s talk about the
simplest particle collision imaginable, when
two electrons bounce off one another.
Classically, we’d calculate this process
using the electric field and considerations
like conservation of energy or just a smidge
of calculus.
However, in the quantum world, we need to
remember that not only do electrons come in
discrete chunks, but so do photons. In fact,
a form of photons make up the electric field.
So maybe when two electrons scatter, they
do so by two electrons approaching one another
and then one of them emits a photon which
then hits the other electron. Both electrons
recoil using the standard energy and momentum
physics you might have encountered in school.
So we can draw the Feynman diagram that does
precisely that. Two electrons exchanging a
photon. Easy, right?
We’re going to focus on this particular
Feynman diagram, but you should know that
there are others. For instance, another way
in which two electrons can scatter might be
that one of the electrons might also emit
an additional photon, either before the “big
scatter” or after.
There are other options. For instance, maybe
one of the electrons could emit a second photon
that is absorbed by the other electron. Or
maybe an electron could emit a photon that
it then reabsorbs. Or maybe as the photon
moves from one electron to another, it might
temporarily turn into an electron/positron
pair before it recoalesces into a photon to
complete the scatter.
Or, we could imagine something even crazier
still, with multiple photons being exchanged,
with some of them creating other particles
and the photons interacting with the temporary
particles. There are tons of possible combinations
of particles and the result is the same basic
outcome, which is that two electrons scatter.
While all things could happen, it turns out
that each time a photon interacts with a charged
particle, the chance that this happens is
less and less likely. And that’s a big effect.
A single extra photon emission drops the probability
to 1%, while two emitted photons drops the
probability to 1% of 1%. So really only the
one simplest Feynman diagram is truly important.
And this is a crucial point. The single photon
exchange is the dominant contribution and
only for very precise calculations do you
need to take into account the other diagrams.
So let’s return to the case of a single
photon exchange. So what does that picture
tell us? Well, I’m gonna say something that
might just blow your mind. The picture is
really… an equation! Now, to understand
that, I’m going to guide you through the
pieces, staring with the vocabulary. Each
symbol in the picture corresponds to a piece
of an equation.
For instance, the incoming electron corresponds
to the letter I, while the outgoing electron
corresponds to the letter O. The photon corresponds
to a fraction, specifically –i g-sub-mu-nu
over p-squared. The i is the square root of
negative 1, while the g-sub-mu-nu is used
to handle adding up all the relevant subatomic
spin for the photon. The p is just the energy
carried by the photon.
A vertex has its own corresponding mathematical
term, which is an i e gamma, where the superscript
mu or nu doesn’t mean a power like square
or cubed. Instead, it has some implied information
on how to add everything up and is related
to the subscripts in the g from the photon.
So now we’re ready to stitch things together.
We can draw the simple Feynman diagrams and
immediately write down a corresponding equation.
Check it out.
See how each piece fits in. I’ve color coded
the symbols and the figures so you can see
how they come together.
Now actually solving that equation is pretty
hard and you shouldn’t expect to get very
far with that math. It’s not until your
second year of graduate school as a physics
major where you learn to do that and it takes
even longer still for it to get easy.
But the real message and the real genius of
Feynman diagrams is that each drawing has
a corresponding equation. So you first have
to imagine all the possible pictures, and
then the equations come more or less for free.
When you get right down to it, the whole idea
is pretty amazing. Who ever knew that doodling
was such an important skill for being a physicist?
