Ben (narrator/author of the LessWrong post)

Also includes the part in the water.

That is one position.

But alternative theories exist.

A similar, competing theory claims claims that Abraham's momentum is the momentum fully in electromagnetic fields, and that's some other expression.

Here's a formula.

The direct average of Minkowski and Abraham gives the total momentum, including that in the material response.

What is momentum anyway?

I first encountered the Abraham-Minkowski controversy when I was trying to answer a question about recoil.

I was considering an idealized thought experiment and to know if it would work I needed to know how recoil worked as light changes medium.

When light goes into or out of some piece of glass, which way does the glass get shoved by the recoil, and by how much?

This is a basic Newtonian problem, but to answer it one needs to know what to use for the momentum of the light when it is in glass.

Another context in which people worry about momentum is the Heisenberg uncertainty principle.

You can't know the location and momentum of a photon at the same time, and the more you know one, the less you can know the other.

The Abraham momentum feels more like it's trying to work with Newton, while Minkowski is Heisenberg's friend.

This is basically the short version of the paper by Stephen Barnett, where it is argued that the Abraham momentum is the answer to the question what do I put in Newton's second law to calculate recoil, and the Minkowski one answers the question I am doing Heisenberg uncertainty for a photon in glass.

What do I use?

While I am not convinced by the argument, I think it is getting one thing importantly right, and that is that it asks people to think about what they want to use the number, or vector, they are calculating for.

A question of the type what is x becomes increasingly difficult to answer as more and more emphasis is put on this.

What is the momentum?

What asterisk is asterisk the momentum?