Sean Carroll

emerge the world from this bare-bones description of a vector traveling through Hilbert space.

And the root is something that we have called quantum myriology.

This is the title of a paper that I wrote with Ashmeet Singh again.

And myriology is borrowed from the philosophers who used that word to refer to the relationship between a whole thing and its parts into which you divide it up into.

The relationship between parts and wholes.

You may have heard the famous idea that philosophy is about carving nature at its joints.

This goes back to Plato.

In Plato's dialogue, The Phaedrus, he talked about how you understand the world better.

If you carve it as a butcher would do when you carve up a piece of meat, you should do it by cutting in between the bones, that is to say at the joints, rather than artificially carving it somewhere else.

So we're basically asking, how do you carve Hilbert space at the joints?

That's what we're trying to do.

That's what you don't have given to you by the theory.

That's what we're trying to figure out.

So said in slightly more technical terms, what we're looking for is a definition of subsystems in Hilbert space.

Again, this is very backward from how the game is usually played.

If you learn quantum mechanics as an undergraduate or you pick up a textbook or whatever, usually what you're told is the following.

You have an electron.

You have a way of describing the electron.

It has a wave function, etc.

Oh, what if you have two electrons?