So far, we’re still implicitly in a framework where there’s time evolution, so I have described ways of implementing the many worlds vision in that framework. I am a little hesitant to preempt your next step (after all, I don’t know what idiosyncratic spin you may put on things), but nonetheless: Suppose we adopt the “timeless” perspective. The wavefunction of the universe is a standing wave in configuration space; it does not undergo time evolution. My first option means nothing, because now we just have a static association of amplitudes with configurations. The second option is Barbour’s—disconnected “time capsules”—only now there isn’t even a question of linking up the time capsules of one moment with the time capsules of the next, because there’s only one timeless moment throughout configuration space. I don’t know if the third option is still viable or not; you can still compute the phase gradients of the standing wave according to the Bohmian law of motion, but I don’t know about the properties of the resulting trajectories.
There may be a problem for mangled worlds peculiar to Barbour’s model; there are no dynamics, therefore no mangling in any dynamical sense. You will have to come up with a nondynamical notion of decoherence too.
So far, we’re still implicitly in a framework where there’s time evolution, so I have described ways of implementing the many worlds vision in that framework. I am a little hesitant to preempt your next step (after all, I don’t know what idiosyncratic spin you may put on things), but nonetheless: Suppose we adopt the “timeless” perspective. The wavefunction of the universe is a standing wave in configuration space; it does not undergo time evolution. My first option means nothing, because now we just have a static association of amplitudes with configurations. The second option is Barbour’s—disconnected “time capsules”—only now there isn’t even a question of linking up the time capsules of one moment with the time capsules of the next, because there’s only one timeless moment throughout configuration space. I don’t know if the third option is still viable or not; you can still compute the phase gradients of the standing wave according to the Bohmian law of motion, but I don’t know about the properties of the resulting trajectories.
There may be a problem for mangled worlds peculiar to Barbour’s model; there are no dynamics, therefore no mangling in any dynamical sense. You will have to come up with a nondynamical notion of decoherence too.