I should warn readers that all my posts on quantum stuff are very, very sketchy. I'm very much learning the material.
In my exploration of many-minds interpretations of quantum mechanics, I’ve been trying to figure out how the many-minds dynamics could work without using problematic notion of a “local” or “effective” wavefunction. Here’s a way I like.
Start with a privileged set O of commuting observables whose values would be sufficient to ground the phenomenal states of all minded beings. Perhaps particle positions will do.
Now let’s suppose we have a modal interpretation with O as the privileged set of observables and with an appropriate dynamics (like the one here).
Attach immaterial minds to the systems described by O, and have them travel along with the systems.
But now do a switcheroo: instead of supposing the observables in O to describe physical reality, ground their values in properties of the minds. If O is phenomenally distinguishable, i.e., if any two distinct assignments of values to the observables in O will result in different ensembles of phenomenal states, then we don’t need to posit properties of minds over and beyond the phenomenal ones here. But if O is too rich to be phenomenally distinguishable, we will need to suppose unconscious properties of the minds to ground the values of the observables in O.
This yields something closer to the Squires-Barrett Traveling Minds variant of Albert and Loewer’s Single Mind View, rather than the many-minds view. (In particular, there is no problem of meeting “mindless hulks”.)
If O determines all particle positions, then the result is a Leibnizified Bohm-like theory where particle positions are grounded in the properties of monads (minds).
If we want many-minds, then we just do the above uncountably infinitely often for each different assignment of values to members of O.