I can’t parse what you mean by perspectives here- do you mean different non-relativistic observers (no relativity, we are using Schroedinger quantum), or do you mean putting a different basis on the Hilbert space?
Hm. So what I mean is that if you have several particles entangled with each other, and you want to know what that “looks like” to one subsystem (or, experimentally, if you’re going to produce a beam of these particles and do a bunch of single-particle measurements), then you have to trace over the other particles in the entangled state. This gives you a reduced density matrix, which is then interpreted as a mixed state. A mixed state between what? Well, “worlds,” of course.
This the definition of “world” I meant when I said “if that’s your definition of world...”
But anyhow, why did I say that different observers will see different lists of worlds? Well, because when you take the partial trace, what you trace over depends on which perspective you want (experimentally, what partial measurement you’re making). If you’re an electron, your worlds are boring—we traced all the complicated externals away and now your perspective just looks like a distribution over single-electron states. If you’re a person, your perspective is much more interesting, your density matrix is much bigger. Or to put it another way, you have more “worlds” to have a distribution over.
You still are implicitly thinking about worlds,
And you’re implicitly thinking about waterfalls, because every cognitive algorithm is isomorphic to a thoght about a waterfall :P
Hm. So what I mean is that if you have several particles entangled with each other, and you want to know what that “looks like” to one subsystem (or, experimentally, if you’re going to produce a beam of these particles and do a bunch of single-particle measurements), then you have to trace over the other particles in the entangled state. This gives you a reduced density matrix, which is then interpreted as a mixed state. A mixed state between what? Well, “worlds,” of course.
This the definition of “world” I meant when I said “if that’s your definition of world...”
But anyhow, why did I say that different observers will see different lists of worlds? Well, because when you take the partial trace, what you trace over depends on which perspective you want (experimentally, what partial measurement you’re making). If you’re an electron, your worlds are boring—we traced all the complicated externals away and now your perspective just looks like a distribution over single-electron states. If you’re a person, your perspective is much more interesting, your density matrix is much bigger. Or to put it another way, you have more “worlds” to have a distribution over.
And you’re implicitly thinking about waterfalls, because every cognitive algorithm is isomorphic to a thoght about a waterfall :P