The trouble with many worlds, for me at any rate, is say you have a mirror where the photons go one way 94% of the time, the other 6% of the time. How does that work? 94 worlds of one type and 6 of the other? Everett did some hand wavy, we assign a probability P to each outcome stuff but you still wonder how on earth that works physically. If the universe branches with one version of you seeing it go one way and one the other is one of you more existy or what?
The only thing that's fundamental, that's physically "real", is the wavefunction. So you have your mirror and your photon and you, and all that's described according to some wavefunction |P(t)>, evolving according to the laws of quantum mechanics.
Now we observe that after the photon passes through the slit, we can decompose the function as |P(t)> = sqrt(0.94)|Q(t)> + sqrt(0.06)|R(t)> where Q and R are independent, each individually evolving according to the laws of quantum mechanics. This is already derived rather than fundamental, but the phenomenon is real, because the causality relation is real. Our neurons under Q (and of course a "neuron" isn't really fundamental, it's an interpretation of a particular group of particles behaving in a particular way, i.e. of particular aspects of the wavefunction) have no effect on our neurons in R and vice versa.
All that is physically real; the only remaining question is what we should expect to subjectively experience. Since our neurons in Q have no effect on our neurons in R and vice versa, it seems like we'd experience either being in Q or being in R. With what probability? Well, whatever it is it had better be conserved; it makes no sense to say that we'd experience R with 4% probability in 5 minutes and then 8% probability in 10 minutes. If we send another photon through in Q, splitting the wavefunction further into |S(t)> + |T(t)> + |R(t)> where Q = S + T, then our subjective probabilities should be such that the probability we find ourselves in S or T = the probability that we found ourselves in Q before sending the second photon.
What's the probability-like quantity that's conserved by quantum evolution of a system? Why, it's the norm, ||P>|^2. I guess that's what we'd expect to be the subjective probability then.
It uses the (uncollapsed) wave function to have a mass density on physical space. There are many realities, if you like, implied, but they all move about in a self-consistent way. The analogy is that it is as if two tv channels were overlying each other. You can follow each separately if you watch the evolution, but at any one time it would look a bit like a mess.
The problem with just having the wavefunction and nothing else is that it is not at all clear what the probabilities would be about. You need something that the theory describes that makes contact with our 3 dimensional experience.
