bhobba said:
My opinion is the breaking of a system into subsystems is entirely arbitrary - basically you choose it for convenience. You can choose not to break it into subsystems, or into as many as you like with any boundaries you like. If however you choose a not particularly good one then the interaction Hamiltonian, Lagrangian, or whatever formalism you use is more complicated, however if you break it into subsystems such that the interaction term (or terms) is non existent or at least simple then you have chosen a good one. You would, or should anyway, obtain exactly the same results either way - its just a suitable choice will make life easy.
I would expect the results (the preferred bases) corresponding to two different decompositions to
not be exactly the same. In fact, I would expect them to have almost nothing in common. For example, I don't see any reason to think that "the silver atom in my Stern-Gerlach experiment + everything else" and "an iron atom in the sun + everything else" should give us similar results. That article seems to confirm that, by showing that there's always a decomposition such that the two subsystems do not interact with each other. If we choose that decomposition, no preferred basis will emerge.
What I expect all this to mean (this is what I've been thinking for a few years, so it doesn't have anything to do with that article) is e.g. that a claim that a classical world is being split in two is never objectively true or false. It can be true relative to one decomposition, and false relative to another. Worlds can be splitting in one way relative to one decomposition, in an entirely different way relative to another.
I also expect this "non-objectiveness" to go very far beyond this. The worlds relative to one decomposition could perhaps be very different from the worlds relative to another decomposition. Note that a decomposition doesn't have to be "this chunk of matter + everything else". Every countable orthonormal basis and every bijection from ##\mathbb Z## (the set of integers) into ##\mathbb Z\times \mathbb Z## defines a decomposition, as described (briefly and not very pedagogically) in the article. Basically, you take a basis ##\{e_i\}## and relabel the basis vectors ##\{e_{ij}\}##. Then for each j, ##\{e_{ij}\}_{i=1}^\infty## spans a subspace, and if I understand this idea correctly, the original Hilbert space can be viewed as a tensor product of (something isomorphic to) that subspace and (something isomorphic to) its orthogonal complement. These spaces can then be considered the Hilbert spaces of "subsystems".
There could be decompositions such that a description of what's happening is
completely different from what we'd get from a typical decomposition. It seems entirely plausible to me that such a description could describe worlds where you and me don't even exist. The "exponentially multiplying" copies of you will only exist in the descriptions corresponding to a specific sequence of decompositions. Relative to other decompositions, you may not be splitting in the same way, and you may not even exist. Since these ideas haven't been explored (as far as I know) it's hard to tell how deep this goes. Is it possible that the same chunk of matter that we think of as "bhobba", is a Coca-Cola machine relative to another decomposition? I have no idea, and I think its funny that I can't even tell if such things can be ruled out.
Note that I'm not saying that this is what's actually happening. I still prefer to think of QM as just an assignment of probabilities to possible results of experiments. I'm just saying that it seems to me that the consequences of assuming that QM describes what's actually happening are very different from what people seem to think.
I don't consider this a reason to dismiss the MWI. I don't consider it a reason to favor the MWI. I just think it makes the MWI much more fascinating than it seemed at first.