QED: The Strange Theory of Light and Matter

I expected this to be a gentle tour. It is gentle, but it is not a tour: Feynman actually teaches you how to calculate, using nothing more than little arrows drawn on paper. The book is based on four public lectures, and you can still hear the speaking voice in it.

The arrows

The whole book rests on one device. Every way an event can happen gets an arrow. You can picture each arrow as the hand of a tiny stopwatch that turns while the photon travels. To find the probability of the event, you add up all the arrows head to tail and square the length of the result.

That is it. No complex numbers by name, no wave equation, and yet it is not a simplification in the misleading sense. The arrows are the complex amplitudes, just drawn instead of written.

Partial reflection

The first worked example is the one that convinced me. Shine light on a sheet of glass and a few percent bounces back. Make the glass thicker and the amount reflected goes up and down periodically, between almost nothing and roughly sixteen percent. A photon cannot “know” how thick the glass is before it reaches the back surface, so how does the front surface decide?

In the arrow picture there is nothing to decide. The reflection from the front and the reflection from the back each give an arrow, the back one turned by an amount that depends on the thickness, and you add them. The puzzle disappears, and in its place is a different kind of strangeness: nature computes over all the ways something could happen.

Mirrors and lenses

The mirror chapter is my favourite. Light from a source to your eye via a mirror could bounce off any point on the mirror, not just the middle. The arrows from the edges point in all directions and cancel; only the paths near the “angle of incidence equals angle of reflection” spot point roughly the same way and survive. Scrape away the right strips of the mirror and the edges stop cancelling, and you have made a diffraction grating. A rule from school optics turns out to be an emergent pattern.

The three actions

The later lectures add electrons. Everything in quantum electrodynamics, Feynman says, reduces to three basic actions: a photon goes from place to place, an electron goes from place to place, and an electron emits or absorbs a photon. Each has its own arrow rule, and complicated events are built by combining them. This is the clearest explanation of what a Feynman diagram is that I have read.

What I am still chewing on

He is honest about the weak spots. He calls the procedure for removing infinities, renormalization, a kind of trick that works without anyone fully understanding why. I appreciated that he did not hide it.

The other thing that stays with me is his attitude: you are not supposed to find this reasonable. The theory is accepted because its predictions agree with experiment to an absurd number of decimal places, not because it makes sense. That is a strange thing to be comforted by, but I was.

A short book, about 150 pages. I would read it before any longer quantum book, not after.