The particles are in that position. They are in that position because the boundary conditions of the universe are such that them being in that position has a relatively high amplitude.
If it's an energy eigenstate, it still has to work as a universe. It still has to have a past for every future and a future for every past. If it has the big bang, it will still have the people who remember existing that must inextricably follow. It's just that it has them all at once.
So the time-dependent Schroedinger equation is how the world works, but it doesn't do anything, and by some separate miracle the things that exist look like the time-dependent Schroedinger equation? :D
Sounds neat!
Timeless physics is what you end up with if you take MWI, assume the universe is a standing wave, and remove the extraneous variables. From what I understand, for the most part you can take a standing wave and add a time-reversed version, you end up with a standing wave that only uses real numbers. The problem with this is that the universe isn't quite time symmetric.
If I ignore that complex numbers ever were used in quantum physics, it seems unlikely that complex numbers is the correct solution. Is there another one? Should I be reversing charge and parity as well as time when I make the standing real-only wave?