Anonymous asked: What is the basis problem?
So this isn’t entirely accurate, but I think it’ll help you get the big picture:
So in the usual formulation of non-relativistic quantum mechanics, you have an arena, the Hilbert space and an object in the arena, the wavefunction.
Quantum mechanics, the mathematical theory, thinks of the Hilbert space as just a mathematical object, like a plane. And you can put any coordinates you want on that plane (polar coordinates, putting the origin at different places, putting different lengths on the coordinates,etc). The wavefunction will look different in different coordinates, but its the same wavefunction.
But many worlds wants to treat the wavefunction as more than a mathematical object- they want to say the wavefunction is the reality. Further, they point to different blobs of the wavefunction and say that blob represent a world where X happened and this other blob represents a world where Y happened, etc. But the “preferred basis” question just notices that “wait- if I change coordinates to some other basis, then I get a totally different set of blobs! And now I have a totally different set of worlds. That doesn’t make sense.”
(I figured I’d reblog this since it’s a good explanation and I’ve been mentioning this without explaining it)
