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.
