PeterDonis

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The obvious answer to this is that a "world" is a term in the superposition I wrote down in the OP; i.e., each of the terms ##|1>|U>## and ##|2>|D>## is a "world". So "worlds" are picked out by the interaction between the measured system and the measuring apparatus and how the two become entangled.What precisely constitutes a world in MWI?

With the answer I gave above, obviously it's the latter.Are these worlds just ''points of view'' (independent of reality), or are they dynamical objects in time?

Again, with the answer I gave above, this is obvious: the entanglement interaction between the measured system and the measuring apparatus.What precisely constitutes a split of one of these worlds? What triggers a split?

When the entanglement interactions happen. Of course they do. Of course not.When precisely do these splits happen? Do they happen at all? Is it observer-dependent?

If we want to talk about observers, then the kets ##|U>## and ##|D>## would include the brain states of the observers. So each "world" has its own "copy" of the observer, who observes the appropriate state of the measured system. (We could, if we wanted, split out these kets to include kets for the apparatus, the environment, the observer's eyes, the observer's brain, etc., and separately model the interactions that entangle all of these things, but that wouldn't change the substance of the description in the OP. It would just complicate it.)For an observer as a quantum object in the MWI for the whole universe, how is its perceived world characterized among all possible worlds?

Different "copies" of an observer perceive different worlds, because of the way the entanglement interactions work. See above.Do different observers perceive different worlds? If yes, why?

If we want to include multiple observers, then all of their states would be included in the kets ##|U>## and ##|D>## (or we could split out all those entanglement interactions, as above, which would not change the substance, it would just complicate it), so corresponding copies of all observers in the same world would have consistent observations (all of them would observe the "up" or "down" result for the same measurement, in the case described in the OP).

Like any QM treatment of macroscopic objects, including observers, nobody actually tries to describe them in detail; everybody just writes down kets like ##|U>## and ##|D>## and says those kets represent states of the observer (or observers) that correspond to particular measurement results being observed.What object inside a quantum universe described by MWI qualifies as an observer? What as a measurement? What constitutes a measurement result?

A measurement is an entanglement interaction, as above. A measurement result is one term in an entangled output state of such an interaction. (Note that in the OP I have assumed that the interaction is localized in spacetime, i.e., that it happens over a small region of space and a small interval of time, similar to the standard way that scattering is treated.)

All of this seems to me to be straightforward "MWI 101". I'm not trying to argue that it's "right" (or "wrong"); I'm just trying to be clear about what it says.