> If reality consists of a sufficiently large multiverse, then we can expect a vast plenitude of parallel universe states which are almost the same, but different only by the position of a single particle, for example.
I agree. Maybe somebody will come up with a better idea tomorrow but as of today I think Hugh Everett's "Many Worlds" is the least bad quantum interpretation; if it is not at the foundation of reality then something even weirder is.
> Such parallel universes contain identical copies of brain states of all the conscious observers
According to Everett a universe splits if there is a change, if everything is identical then there is no split. So in one universe an electron in your lab goes to the left and your instruments register that it went to the left, and the other universe the electron goes to the right and your instruments register that it went to the right, but you would have no way of knowing which universe you are now in until you look at your instruments.
But how would Many Worlds explain bizarre things like quantum erasure and the delayed choice experiment? In Many Worlds a split happens when there is a difference; and normally the universes will never coalesce again because thanks to the butterfly effect even a tiny difference will exponentially growing magnitude so its astronomically unlikely they will ever become identical again, but if the difference between 2 worlds is very small, like the only difference between two universe is that in the two slit experiment in your lab an electron went through the left slit rather than the right, and if you don't wait so long that other effects might change then, then a very skilled experimenter can coax those worlds to become identical again and coalesce back into just one world; but when contemplating the history of that electron you will find evidence that it went through the left slit but equally strong evidence that it went through the right slit, and that is what some call "quantum indeterminism".
The big advantage Many Worlds has over the Copenhagen interpretation is that Copenhagen claims there are two separate laws of physics, one for things that have been observed and another for things that have not been observed, but Many Worlds says there is only one set of physical laws, and it has no need to explain exactly what an "observer" is or how consciousness works because those things have nothing to do with it. So according to Occam's Razor it is superior.
> But once the measurement is made, the observer's mind state changes in a way that partitions the set of similar but not quite identical universe she is a part of. The observer is said to have "collapsed the wave function" but really, she has only adjusted her knowledge
Exactly, until you look at your instrument you don't know which universe you're in. As for downward causality, the trouble with it is that even if the laws of physics are completely deterministic, causality could still be asymmetrical. For example the laws for John Conway's "Game Of Life" are very simple and completely deterministic so if you are given a pattern you can always predict how it will evolve, but you can't determine what pattern produced it. You can predict the future but you can't know the past.
John K Clark