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?