Particle physics is a mind-blowing subject that really does teach you a ton about the
world around you. By smashing two particles together, you can learn about the most fundamental
rules that govern the universe.
While we call our theoretical understanding of the subatomic world the Standard Model
of particle physics, that actually is a little misleading. It’s not a single theory, but
rather several theories that are cobbled together.
And not all of the component theories are of equal precision. But today, I’m going
to talk to you about the most precise theory ever invented by mankind. This is called the
theory of quantum electrodynamics or QED.
So just what is QED? Well, from the first term in the name, we can imagine that it is
related to the quantum realm. And the second term in the name tells us that it is about
the motion and interaction of electromagnetic forces.
They say that success has many mothers and that is true of QED as well- well, fathers,
in this case. The first step forward was made in 1928 by Paul Dirac, when he successfully
wed quantum mechanics and Einstein’s theory of special relativity. Along the way, there
were many other contributors, but the ones who got the explicit credit for the theory
were Richard Feynman, Julian Schwinger and Sin-Itiro Tomonaga. They shared the 1965 Nobel
Prize in physics for their insights.
Now all three of these guys were crucial contributors, but it turns out that Feynman’s formulation
is the easiest to understand. The reason is that he came up with a series of pictures
called Feynman diagrams that stand in for the equations and it makes the whole process
very easy to picture.
Now, before we get into that in a big way, I should let you know that to do a QED calculation
depends on two crucial components.
The first is an idea called perturbation theory. I made a video that talked about that in detail
and it would help you if you watched it. But the basic idea is that if you are confronted
with an equation that is too difficult to solve, you replace it with an approximate
equation that is easier to solve. As long as the correct and approximate equation are
very similar, you’ll get a reasonably correct answer. And if you need a more accurate calculation,
you just use a more accurate approximation.
The second idea is that every Feynman diagram that you see is really just a pictorial depiction
of an equation. I made a yet a different video that goes into that in a deeper way, but for
right now just remember that when you see a diagram like this, it is actually standing
in for an equation. And every diagram has a corresponding equation.
Okay- so with those ideas out of the way, what we can now do is talk about QED.
So suppose you wanted to simply calculate how two electrons scatter when you shoot them
at one another. If you have any classical physics training, you’ll no doubt think
in terms of an electric field pushing the two apart.
However this is, after all, QUANTUM electrodynamics, so we’re governed by quantum effects. And
one of the big things here is that the electric field is now quantized. Rather than a big
and amorphous force field, the electric field is created by a series of individual and discrete
photons.
Thus the right way to think about the scattering between a pair of electrons is that the two
particles exchange one or more photons. As one electron emits a photon, it recoils, as
does the electron that absorbs it. If multiple photons are emitted and absorbed, the outgoing
electron trajectories will reflect the contribution of all emissions.
Since we don’t know in any specific scattering between two electrons what’s going on, we
can sort of draw it like this, with electrons coming towards one another and then leaving
the interaction, with an amorphous blob that indicates our ignorance of exactly what is
going on in the collision.
However, what we can do is employ Feynman diagrams to show that what the blob represents
is actually just the sum of all things that are possible. To orient you, the wiggly lines
here are photons, while the straight ones are electrons. We have the situation of one
photon exchanged. Then there is the situation where two are exchanged. Since we can’t
uniquely identify which outgoing electron corresponded to which incoming, there are
some other diagrams that really should come into play, but we’re ignoring them here.
After the simplest two diagrams, things get more complicated. For instance, the photon
could temporarily turn into an electron and antimatter electron pair, or while the electrons
are exchanging a photon, one of the electrons could exchange a photon with itself. There
are tons of other possibilities.
So is there a way to simplify this? It probably won’t shock you that there is.
Remember that I said that these pictures were stand ins for equations. So I’d like to
draw your attention to the spots where the photons are emitted or absorbed. We scientists
call them vertices and they are key to figuring out which Feynman diagrams matter more than
others.
It turns out that photon emission or absorption is hard; specifically each emission or absorption
reduces the probability by about a hundred fold.
In practical terms, that means we can simply count vertices and get a sense of how much
each diagram contributes. The simplest electron scattering Feynman diagram has two vertices.
There are no pictures with three vertices that have two electrons in and two out, but
if there were, they would happen about one percent as often as the two vertex case. Four
vertices would be 1% of 1% or 0.01%, etc.
Thus we can see that the first and simplest picture really dominates. All the other and
more complicated Feynman diagrams are just far less likely. And that means that doing
a QED calculation is relatively easy. You don’t have to include all possible Feynman
diagrams, the simplest one does most of the job.
Now, there are a couple of complications. For one thing, other details of the Feynman
diagram can change slightly the conclusion you can draw just by counting vertices. Also,
there are several pictures that have four vertices and each of them adds 0.01%.
A final messy thing that must be taken into account is that one needs to be a little careful
about how one handles the Feynman diagrams that have what we call loops, so that means
diagrams like this, or this, or this. They require a subtle mathematical technique called
renormalization, but that’s a complication that only experts need consider. I just mention
it in case you want to do some reading on your own.
So I’ve told you the basics of theoretical quantum electrodynamics- certainly not enough
to actually do a calculation, but enough to understand the core points. In another video,
I will talk about comparing calculations to measurements, but I’ll give you the bottom
line here. QED is, without a doubt, the most accurate theory ever devised, agreeing to
parts per trillion. It truly is a jewel in the crown of physics.