mfb said:
As discussed before, there are deterministic
interpretations of quantum mechanics.
Yes and they're primarily MWI and Bohmian, the only others are time symmetric which could certainly be argued to be retro casual and as such, indeterminate or at the very least agnostic. As for many-minds, I consider that interpretation to bad pseudoscience(yes, I think there's good and bad pseudoscience), but a fun interpretation to think about none the less.
mfb said:
The amplitude is a well-defined number you can calculate.
Yes it is entirely deterministic in the sense that the
probability amplitude is well defined. Second order differential equations with boundary conditions. The wave functions of the particles are determined, yes. However once you make a measurement for the location of the particle in relation to it's wave function it becomes probabilistic. In MWI there is no wave function, as everything happens(convenient), however in each individual world only one final objective measurement will be observed, and in that sense it is probabilistic within each individual world(universe), and only deterministic as a whole(the entire multiverse/many-worlds universe). I have no disagreement about the amplitude being well defined, I have a disagreement with statements claiming that the universe(or single world) is fully predetermined by initial conditions at t=0. When quantum mechanics is clearly probabilistic, among other things(random quantum fluctuations, radioactive atomic decay, the weather

, etc). Anyway my point is at the end of the day each single world in MWI would be probabilistic.
mfb said:
That doesn't make sense at all. Do you have a source for that claim?
Just an observation I made while thinking about it, no specific source to speak of. There are a a few working MWI models and eternal inflationary models which are in contrast to this, for example:
http://arxiv.org/pdf/1205.5550v2.pdf and
http://arxiv.org/pdf/1104.2324v2.pdf
In that paper Yasunori Nomura builds a static multiverse model where the eigenvalue of the Hamiltonian is zero. However this still doesn't diminish what I said above about each world/universe being indeterminate throughout it's evolution, however the evolution of the quantum state of the entire multiverse is unitary and deterministic(as a whole). In his model you can take a selection condition at any moment in "time", which you interpret as t=0. You can then determine the state by solving the Schrodinger equation forward and backward in t. Albeit controversially he considers the eternally inflating multiverse and MWI to be one in the same.
Just to be sure I'm getting my point across I didn't mean to state that it
must be that the MWI universe has to have a Hamiltonian greater than 0, only that it
seems that way to me personally. As I said above in contrast to my perspective, I have offered an alternative idea.
Edit: In summary I agree in that the amplitude for the multiverse(in MWI) is well defined and you could predict anything as the evolution of the MW would be fully deterministic. However there is no means of knowing which branches will recombine and diverge/re-branch out into the future, and as such this would be random, along with vacuum energy fluctuations together adding credence to the idea that each world is still intrinsically indeterminate.
So as per my thread title I find the most likely answer to be "it would be different" rather than the same. Also MWI if you think about it logically is a gross violation of Occam's razor if you're talking about entities instead of laws.