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Overlapping vs Non-overlapping worlds in Many Worlds/Everettian Interpretation

  1. Jun 23, 2012 #1
    As the poll on this forum from 2011 that has recently been resurrected shows, there are a portion of the users here who adhere to the modern reading of the Everettian interpretation.

    What I have never seen discussed here though is the issue of whether the worlds split(overlap) or diverge(non-overlap).
    It's a distinction David Lewis made clear when discussing worlds in modal realism.
    Either worlds are identical, but seperate from the beginning (big bang) and then diverge as the worlds differentiate OR there is only one world in the beginning from which the other worlds split/branch 'out of' as time goes on.
    The latter view is the one most people have heard of, but there is nothing in the quantum formalism that prefer this over non-overlap.

    Alastair Wilson is one of the few who has written several papers on this issue and he prefers non-overlap.
    His papers on the matter can be found here: http://alastairwilson.org/
    Another prominent proponent of the modern Everettian reading of QM is Simon Saunders, he also advocates the non-overlap view in his chapter in the 2010 volume called Many Worlds?: Everett, Quantum Theory, & Reality

    So Many-Worldians of PF.com, which view do you prefer and why?
     
  2. jcsd
  3. Jun 25, 2012 #2
    Bump
    Where did all the Many Worlds proponents go?
     
  4. Jun 25, 2012 #3
    They're in another world I guess.
     
  5. Jun 25, 2012 #4

    Hurkyl

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    If I'm understanding your description, "non-overlapping" worlds is a notion is an unrelated notion to MWI, or even to quantum mechanics.

    "Separate" worlds already fits easily into classical mechanics, especially where probability distributions are used. However, the fact they are separate leads most people to think in terms of 'ignorance' -- the worlds don't describe a universe smeared out across parallel worlds , but instead represent our information about a single world.

    But trying to reinterpret classical mechanics in terms of 'separate' worlds is a good warm-up for trying to understand MWI -- nearly every misconception I've seen people have about MWI would translate directly into a misconception about classical 'non-overlapping' worlds. Trying to sort these issues out in the purely classical setting is useful.

    The central point of MWI is that unitary evolution tends to drives subsystems into mixed states, and that one ought to understand this process if one is to understand unitary evolution -- especially the question of the emergence of classical-seeming behavior. This is very much the non-separate case.

    Purely internal interactions within a subsystem will preserve a mixture, though, so in this very restricted case MWI could be said to talk about 'separate' 'worlds'. But really, the most interesting questions which prompt one to consider the MWI involve two subsystems interacting with each other, or a system interacting with its environment.
     
  6. Jun 26, 2012 #5
    Hmm, not sure what to make of your answer.
    It seems you think that the divergence view is just a nice mental model that fits the classical scale?

    I'm not really debating whether or not MWI is true in this thread.
    *If* we assume that many worlds is true, which view do you support? Divergence or Branching / Non-overlap vs Overlap.
    In the overlap view the worlds share initial segments, whilst in the non-overlap view you have qualitatively identical worlds who have numerically distinct initial segments.
     
  7. Jun 27, 2012 #6

    Hurkyl

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    The notion of 'non-overlapping worlds', as I understand from your description, has nothing to do with MWI in particular. It can be layered on top of anything, even formal, purely mathematical structures.

    The motivating consideration of MWI is emergence of classical probabilities by the unitary evolution of subsystems -- i.e. the idea you are trying to describe as 'overlapping worlds' (but do still seem to have some misconceptions about).

    MWI can certainly treat 'non-overlapping worlds' to an extent -- in terms of physical questions it's more or less equivalent to the state of the 'universe' being a mixed state -- but each of the 'non-overlapping worlds' would still contains 'overlapping worlds' within.


    However, if you tried to apply the approach of MWI to interpret classical statistical mechanics, you would only get 'non-overlapping worlds' -- I suppose that could be the origin of your misconception.
     
  8. Jun 27, 2012 #7

    Fredrik

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    The only kind of MWI that makes any sense to me is the idea that the purely mathematical part of QM is an accurate description of the time evolution of a single physical system (sometimes called "the omnium"), and the worlds correspond to grokable descriptions of what that system is doing. In other words, QM describes a single physical system in a very counterintuitive way, and the only way to describe what that system is doing in terms that we can understand intuitively, is to describe the individual worlds.

    This is analogous to how we use coordinate systems to describe things in relativity. There is a coordinate-independent mathematical representation of reality (spacetime, and the curves in it, that represent the motion of matter), but we must choose a coordinate system before we can say things like "the chair is to the left of the table". That statement can be true in one coordinate system, while "the chair is to the right of the table" is true in another (because the meaning of terms like "left" and "right" are fixed by the coordinate system).

    In the quantum theory of the omnium, we need more than just a coordinate system to be able to describe things in intuitive terms. We need at least

    1) a decomposition of the Hilbert space of the omnium, into a tensor product of the Hilbert space of the relevant subsystem and the Hilbert space of "everything else",
    2) a basis for the Hilbert spaces of these two subsystems.

    In most cases that we are interested in, 2 may not be necessary, because (I think) that decoherence will select the bases for us.

    The (enormous) difference between a QM description in terms of a decomposition and a basis, and a classical description in terms of a coordinate system, is that two different descriptions in QM can appear to describe two entirely different things, while two different classical descriptions will never be interpreted as anything more than two different "points of view".

    If we look at QM this way, then questions like "do worlds split?" don't seem to make sense. At least I don't see how to make sense of them. I don't think there are any events where worlds split in an objective sense. There are events where in terms of one decomposition and basis, worlds are splitting, but in terms of another decomposition and a basis, nothing like that is happening.

    Edit: Note that I'm not saying that this is what reality is like. There's no evidence that QM can be thought of as a description of reality. There isn't even a meaningful definition of what it means for a theory to "describe" reality. Still, the concept of what it means to describe something seems fundamental enough to treat as a primitive, i.e. something we can leave undefined. So it doesn't seem to be nonsensical to consider the idea that QM can be applied to the whole universe (=omnium) and thought of as a description of what it's doing. We're not doing science when we're thinking about that idea and its consequences, but we are exploring what seems to be a valid way to think about a scientific theory.

    Edit 2: I should also add that what I'm talking about isn't Everett's MWI. Everett dropped the Born rule from the definition of QM and wanted to recover it from the other assumptions. What I'm talking about is a straightforward interpretation of the standard version of QM (with the Born rule intact) as a description of what's actually happening to a physical system that includes everything.
     
    Last edited: Jun 27, 2012
  9. Jul 5, 2012 #8
    hi i am trying to understand the quantum mechanics many world theory / interpretation. do the alternate universes split off from only our universe as if this universe is the initial universe from which all others derive or do other universes split off in billions of ways at once as well? also are our conciousness' allowed to travel among these alternative universes or is the conciousness set on one univese and in the billions of universes spliting off from our universe or the other universes another completely new conciousness formed.
     
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