Most reasoning about many worlds, by physicist fans of the interpretation, as well as by non-physicists, is done in a dismayingly vague way. If you want a many-worlds framework that meets physics standards of actual rigor, I recommend thinking in terms of the consistent or decoherent histories of Gell-Mann and Hartle (e.g.).
In ordinary quantum mechanics, to go from the wavefunction to reality, you first specify which “observable” (potentially real property) you’re interested in, and then in which possible values of that observable. E.g. the observable could be position and the values could be specific possible locations. In a “Hartle multiverse”, you think in terms of the history of the world, then specific observables at various times (or times + locations) in that history, then sets of possible values of those observables. You thereby get an ensemble of possible histories—all possible combinations of the possible values. The calculational side of the interpretation then gives you a probability for each possible history, given a particular wavefunction of the universe.
For physicists, the main selling point of this framework is that it allows you to do quantum cosmology, where you can’t separate the observer from the physical system under investigation. For me, it also has the advantage of being potentially relativistic, a chronic problem of less sophisticated approaches to many worlds, since spatially localized observables can be ordered in space-time rather than requiring an artificial universal time.
On the other hand, this framework doesn’t tell you how many “worlds” there are. That depends on the choice of observables. You can pick a single observable from one moment in the history of the universe (e.g. electromagnetic field strength at a certain space-time location), and use only that to define your possible worlds. That’s OK if you’re only interested in calculation, but if you’re interested in ontology as well (also known as “what’s actually there”), you may prefer some kind of “maximally refined” or “maximally fine-grained” set of histories, in which the possible worlds are defined by a set of observables and counterfactual properties that are as dense as possible while still being decoherent (e.g. without crowding so close as to violate the uncertainty principle). Investigation of maximally refined, decoherent multiverses could potentially lead to a new kind of ontological interpretation, but the topic is little investigated.
Most reasoning about many worlds, by physicist fans of the interpretation, as well as by non-physicists, is done in a dismayingly vague way. If you want a many-worlds framework that meets physics standards of actual rigor, I recommend thinking in terms of the consistent or decoherent histories of Gell-Mann and Hartle (e.g.).
In ordinary quantum mechanics, to go from the wavefunction to reality, you first specify which “observable” (potentially real property) you’re interested in, and then in which possible values of that observable. E.g. the observable could be position and the values could be specific possible locations. In a “Hartle multiverse”, you think in terms of the history of the world, then specific observables at various times (or times + locations) in that history, then sets of possible values of those observables. You thereby get an ensemble of possible histories—all possible combinations of the possible values. The calculational side of the interpretation then gives you a probability for each possible history, given a particular wavefunction of the universe.
For physicists, the main selling point of this framework is that it allows you to do quantum cosmology, where you can’t separate the observer from the physical system under investigation. For me, it also has the advantage of being potentially relativistic, a chronic problem of less sophisticated approaches to many worlds, since spatially localized observables can be ordered in space-time rather than requiring an artificial universal time.
On the other hand, this framework doesn’t tell you how many “worlds” there are. That depends on the choice of observables. You can pick a single observable from one moment in the history of the universe (e.g. electromagnetic field strength at a certain space-time location), and use only that to define your possible worlds. That’s OK if you’re only interested in calculation, but if you’re interested in ontology as well (also known as “what’s actually there”), you may prefer some kind of “maximally refined” or “maximally fine-grained” set of histories, in which the possible worlds are defined by a set of observables and counterfactual properties that are as dense as possible while still being decoherent (e.g. without crowding so close as to violate the uncertainty principle). Investigation of maximally refined, decoherent multiverses could potentially lead to a new kind of ontological interpretation, but the topic is little investigated.