Ben (narrator/author of the LessWrong post)

In 1909 Minkowski proposed that actually, the momentum of the same energy worth of light in a material is increased by a factor of n relative to vacuum.

This gives a single photon momentum of, here's a formula, which was right.

It's still not settled.

Not really.

A lot of papers will tell you that the Labraham-Minkowski controversy is now resolved, but they won't all agree on how it has been resolved.

At least three mutually incompatible resolutions have been published.

New papers claiming a resolution, or else knocking holes in the old resolutions, are still coming out.

In the rest of this post I'm going to sketch out why this is a complicated problem and how some of the proposed solutions work.

An analogy.

The runner.

Why is the momentum of light in glass complicated?

Consider a runner running, as is usual, on land, with some speed.

Here's a formula.

On their route the runner encounters a region of knee-high water.

while traveling through the water our runner travels at a reduced speed of.

Here's a formula.

Now, we ask, what is the momentum of the runner while they are moving through the water?

There's an image here.

Description.

If we take the mass of everything inside the runner's skin and multiply it by their velocity then clearly this has fallen by a factor of, here's a formula, relative to their momentum outside the water.