Oct 27, 2026 · 16 min · 12 segments
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Matt O'DowdHost
To give you an idea of how messy quantum field theory can be, let's look at what should be a simple phenomenon, electron scattering, when two electrons repel each other.

In old-fashioned classical electrodynamics, we think of each electron as producing an electromagnetic field.

At least in the simplest cases, the Coulomb equation governing this subatomic billiard shot is really easy to solve.

But in quantum field theory, specifically quantum electrodynamics, or QED, the story is very different.

We think of the electromagnetic field as existing everywhere in space, whether or not there's an electron present.

One electron excites a photon, and that photon delivers a bit of the first electron's momentum to the second electron.

In fact, we call it a virtual photon, and it only exists long enough to communicate this force.

There are other types of virtual particle whose existence is similarly ambiguous.

The brilliant Richard Feynman developed these pictorial tools to organize the painful mathematics of quantum field theory.

Here we see two electrons entering in the beginning and moving towards each other.

To give you an idea of how messy quantum field theory can be, let's look at what should be a simple phenomenon, electron scattering, when two electrons repel each other.

In old-fashioned classical electrodynamics, we think of each electron as producing an electromagnetic field.

At least in the simplest cases, the Coulomb equation governing this subatomic billiard shot is really easy to solve.

But in quantum field theory, specifically quantum electrodynamics, or QED, the story is very different.

We think of the electromagnetic field as existing everywhere in space, whether or not there's an electron present.

One electron excites a photon, and that photon delivers a bit of the first electron's momentum to the second electron.

In fact, we call it a virtual photon, and it only exists long enough to communicate this force.

There are other types of virtual particle whose existence is similarly ambiguous.

The brilliant Richard Feynman developed these pictorial tools to organize the painful mathematics of quantum field theory.

Here we see two electrons entering in the beginning and moving towards each other.
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