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MWI and particle splitting

  1. Apr 8, 2008 #1
    Hello everyone,

    I have spent the last week furiously searching google for explanations of the many world's interpretation of QM. As such I think I have built up a reasonable conception of the theory (for someone at my knowledge level, I am a 1st year physicist) but I cannot for the life of me find a discussion or explanation on what, to me, is the most baffling part of the whole idea:

    By what mechanism, if any do they propose that the world/history actually physically splits?!

    More specifically, how does every single particle in the "splitting" system physically copy itself in one moment into a stupendous number of different realities. Where does this new matter come from and what catalyzes it's creation?

    What I find even more odd is that in my searching I did not find this most obvious question being asked at all. Which makes me wonder if my understanding is just completely wrong!

    Thanks
     
  2. jcsd
  3. Apr 8, 2008 #2
    Try this site:

    http://www.hedweb.com/manworld.htm

    I believe the explanation given is that when the wave function splits, the portions that have split actually become "thinner" in a sense. So if you were once "n worlds dense", after viewing the outcome of a quantum experiment there would be two copies of you, each "n/2 worlds dense".
     
  4. Apr 9, 2008 #3
    I have actually already ready that page :)

    It doesn't really give a clear answer as it doesn't explain what it means by "split" or "thinner". In the classical sense of the words that would just be non sensical!
     
  5. Apr 9, 2008 #4
    Well, beyond that FAQ, I can't help you, and I suspect no one really has any answers beyond that. But in ALL of quantum theory, not just MWI, the "classical sense" of certain words is nonsensical. "Wavefunction collapse," "spin," "state vector." These are words that get thrown around here all the time that have no classical analogue. You can't take anything in QM literally except one critical thing - the probability of an observation. On that, every interpretation agrees.
     
  6. Apr 9, 2008 #5

    NateTG

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    I don't study this stuff, but my understanding is that:

    The splitting is not observable, so talking about the mechanism for the splitting is like discussing angels on the head of a pin. The 'split' doesn't have to propagate instantly, but only at the speed of light, and the 'split' doesn't have to involve any kind of physical copying.

    This is philosophy stuff, and not science.

    That said, one way to think of the MWI is to imagine that each thing that we observe as a single particle is really an infinite number of 'particle-slices', and whenever particle slices would interact, they only do so if their histories are consistent. Whenever a 'world split' occurs, a 'world split' wave propagates outward at the proper speed of light (once again only affecting things with an appropriate history) adding some measurement result to the history of each particle-slice. (I say proper speed of light because, the geometry of space-time is warped by matter, so the speed of light might also be history-dependent.)
     
  7. Apr 9, 2008 #6
    My understanding of MWI is that it's basically a huge get-around to the then-held view that probabilities only make sense as far as limiting frequencies go. If you're willing to accept the idea that probabilities are subjective things, then there's just no need to go inventing the extra worlds.
     
  8. Apr 9, 2008 #7

    Would you mind expanding on this a little, it sounds interesting, what do you mean by accepting probabilities as subjective?
     
  9. Apr 9, 2008 #8
  10. Apr 9, 2008 #9

    NateTG

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    As a more general notion: the paradoxes in Quantum Mechanics only occur if meaningful probabilities are assigned to things that can't be observed. This existence of probabilities is, in some sense, an artifact of the usual formalism of probability.

    Although there is some ugliness involved, it's not really that difficult to produce mathematical constructs of probability that invalidate Bell's Theorem. (These theories of probability could be described as 'unrealistic'. For a glimpse of the sort of issues this leads, you could look into the Banach-Tarski paradox.)
     
  11. Apr 9, 2008 #10

    Fredrik

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    The worlds don't split in that way.

    One thing that separates the MWI from other interpretations is that it makes sense to consider the Hilbert space of possible states of the entire universe. The time evolution of our universe is described by a curve in this space. (If we know one point on the curve, the Schrödinger equation gives us the entire curve). What the MWI says is that some subspaces of that Hilbert space can be interpreted as representing the states of different worlds, and the projections of the curve onto those subspaces represent the time evolution of those states.

    At least that's how I see it (and it appears to be how Roger Penrose sees it, in "The road to reality"). If I'm wrong, I would very much like to know about it.

    I explained this way of thinking of the MWI in more detail in another forum a few months ago, so I'll just post a link to that thread instead of repeating everything I said there. This is the relevant thread. Check out posts #11 and #23.
     
  12. Apr 9, 2008 #11
    Thanks everyone,

    Fredrik I think your link is wrong, when I click it I just get taken to a reply form for this thread.
     
  13. Apr 9, 2008 #12

    Fredrik

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    Hm, that's strange. I must have overestimated my copy/paste skills. And now I can't edit the link. :rolleyes:

    I'll just have to try again: Link. Yes, that seems to work. Here's another link, to a very readable article about the MWI by Max Tegmark.
     
    Last edited: Apr 9, 2008
  14. Apr 10, 2008 #13

    Fredrik

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    I would be interested in some comments about my take on the MWI. Perhaps it's too much work to go to another forum to read what I said :wink:, so I'll just post it here.

    Someone said that the MWI "requires the creation of at least one entire new universe every time any two particles interact". I replied:

    The other guy didn't find it convincing, so I wrote a second post to clarify a few things:

    Thoughts? Did I get this right, or am I just nuts? Also, since I'm asking questions, why do people always link to that many-worlds FAQ whenever the MWI is mentioned in any forum on the Internet? Was that FAQ really written by some "MWI expert"? (I still doubt that MWI experts exist. Every time I read something about it I get the impression that no one has really thought things through). That FAQ looks pretty bad to me. I didn't find any of their arguments convincing (any of the ones that I actually tried to understand, that is), and I think it's often not even clear what they mean.
     
  15. Apr 11, 2008 #14
    It makes sense but it's a little hard to envisage, if you've got some spare time could you explain this, possibly in metaphorical terms:

    "According to the MWI, the state vector always evolves according to the Schrödinger equation, and never gets projected onto a proper subspace. In the MWI, a measurement is just an interaction with a unitary time evolution like everything else, that through some mechanicsm (possibly decoherence), give certain orthogonal subspaces a significance of their own. In other words, this mystery mechanism just selects a preferred basis of the omnium.

    So all those "worlds" don't get created when a measurement is performed. They are orthogonal subspaces that were always there, but after the measurement they get interpreted as different worlds, instead of as degrees of freedom in "the" world."

    Are you saying that the new worlds are not actually new at all, just copies of the one world into different dimensions of the same universe? Like two 2-d worlds (pieces of paper for example) separated by a 3rd dimension (one is above the other).

    Thanks again!
     
  16. Apr 11, 2008 #15

    Fredrik

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    I have started writing an explanation but it's difficult to tie the pieces together. I'll try to finish it tomorrow.
     
  17. Apr 11, 2008 #16

    Ken G

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    I think you got it right. But the further point is that the problem with the MWI is that it is simply not the way we do science, it is kind of a pretense about how science works. One thing we can all agree on is that the MWI you describe is certainly correct for a collection of entangled quantum systems that do not include us, and do not include any systems that contain degrees of freedom we do not wish to include in our model. So at that level, we would not call it "MWI", we'd call it "entangled multiple particle quantum mechanics", possibly with additional complications like the need for the total wave function to be antisymmetric to exchange of identical Fermions.

    What makes it "MWI", as you pointed out, is when we include ourselves within the framework of the closed system we are imagining will unfold unitarily (that is, will obey the Schroedinger equation and remain always in a pure state if it started in one). Here's where we depart from science. In my view, the way a wave function is used in science is to make predictions. It is a tool used by a physicist, so the physicist cannot be part of that wave function and still do demonstrable science. The MWI gives with one hand and takes away with the other-- it gives us the warm fuzzy philosophical sense that our equations transcend our experience, and we are living in a subspace of a larger unitarily evolving universe. Lovely, how nice to imagine that. But what it takes away is science itself-- the demonstrability of objective evidence. The "objective" in objective science comes from the fact that we are not part of the wave function. The Copenhagen Interpretation allows us to remain separate from the closed-system wave function when the Schroedinger equation applied, and then we make our entrance in a nonunitary phase when we intentionally decohere the system in a way that we can accept as a measurement.

    That last bit is actually the way we define science. So the rub is, the projection of the MWI onto the scienific method results in the Copenhagen Interpretation. Given that, I frankly see no point in it at all-- not as science anyway. It is a fine way to generate a pedagogical picture that might help imagine what is happening in an untestable way, and it can also be used to go to town on a philosophy of reality, but it is not scientifically testable, and is not distinguishable from other nonscientific avenues for making pictures about reality.
     
  18. Apr 12, 2008 #17

    Fredrik

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    Not quite like that. I'll try to explain. It would be easier if I could draw a picture, but I suck at making cool graphics so I'll just try to describe the mental picture I keep in my head when I think about these things.

    We usually think of a measurement as a process that "collapses" the wave function, i.e. as a process that projects a superposition onto one of the eigenstates of the observable being measured. For example, if the system is a spin-1/2 particle in a superposition [itex]|\psi\rangle=a|+\rangle+b|-\rangle[/itex] and we measure the z-component of the spin, the measurement changes the state of the particle into either [itex]|+\rangle[/itex] or [itex]|-\rangle[/itex].

    The "measurement problem" of quantum mechanics is the conflict between this description of a measurement and the claim that physical systems change with time according to the Schrödinger equation. Wave function collapse contradicts the Schrödinger equation, so it appears that we have two different types of time evolution in quantum mechanics, and no clear way to tell when we should use the first kind and when we should use the second kind.

    This "problem" isn't really a problem if we adopt the view that quantum mechanics is just an algorithm that we can use to predict the probabilities of the possible results of any experiment. This view is of course perfectly valid, but it's not the one that proponents of the MWI prefer. The MWI proponents believe that quantum mechanics isn't just an algorithm that tells us probabilities of possibilites, but also an accurate description of reality. In other words, they think that state vectors represent something that actually exists. The problem with this view is that it promotes the measurement problem into a real paradox...unless...the second kind of time evolution is really just a special case of the first.

    So let's assume that all physical systems evolve according to the Schrödinger equation and see where this takes us. (It will more or less force us to accept the existence of many worlds, if we also believe that quantum mechanics describes reality). If the assumption is correct, then the entire universe evolves according to the Schrödinger equation, and it makes sense to consider the wave function of the universe.

    Now let's try to visualize the state of the universe. :smile: The possible states of the universe are represented by vectors in a complex Hilbert space. Unfortunately, we can't really visualize complex dimensions, or a large number of real dimensions. The best we can do is to visualize three real dimensions, so let's do that. Imagine three axes, labeled x, y and z. We will let the x-y plane represent the spin state of a single spin-1/2 particle, and let the z direction represent the state of the rest of the universe (including other properties of that particle). Yeah, I know, we're omitting absurd amounts of information from this picture, but we don't really have a choice.

    In this picture, [itex]|+\rangle[/itex] is a unit vector in the x direction, and [itex]|-\rangle[/itex] is a unit vector in the y direction, so an arbitrary linear combination [itex]|\psi\rangle=a|+\rangle+b|-\rangle[/itex] is a vector in the x-y plane. (Note that even the picture of the x-y plane omits information, since a and b are really complex numbers). The vector that describes the state of the universe is a vector of the form [itex]|\phi\rangle|\psi\rangle[/itex], where [itex]|\phi\rangle[/itex] represents the state of the rest of the universe.

    Now suppose that we measure the spin of that particle. We know that we will always find the spin to be either "up" or "down", so the time evolution of the state of the universe is going to be approximately

    [tex]|\phi\rangle|\psi\rangle\longrightarrow a|\phi_+\rangle|+\rangle + b|\phi_-\rangle|-\rangle[/tex]​

    There are other terms on the right-hand side, but they are very small. I put a + or a - subscript on the state of the "rest of the universe" to indicate that it has also changed (since a measurement is a physical interaction between the system and the rest of the universe). The state [itex]|\phi_+\rangle[/itex] includes the happy observer from my previous post, and [itex]|\phi_+\rangle[/itex] includes the sad observer.

    Now, here's the point I've been trying to make: The first term is a point in the x-z plane, and the second term is a point in the y-z plane. Those two planes are now the Hilbert spaces of possible states of two different worlds.

    Note that the state vector of the universe isn't really projected onto one of these subspaces. It continues to evolve according to the Schrödinger equation, tracing out a curve in the x-y-z space, but after the measurement, there are two subspaces of the Hilbert space we started with that have a significance of their own. Those subspaces, weren't created by the interaction. They were always there. The interaction simply made them relevant to physical systems that include brains.

    We can't possibly represent the difference between [itex]|\phi_+\rangle[/itex], [itex]|\phi_-\rangle[/itex] and [itex]|\phi\rangle[/itex] in the picture we've made, so in the picture, the states of the two worlds are just the projections of the state vector of the universe onto two subspaces that were selected by the physical interaction that the observer thought of as a measurement.
     
  19. Apr 12, 2008 #18

    Ken G

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    That's all correct, and the real swindle in the MWI appears when we now ask, what is the associated magnitudes of those two projections? (They are amplitudes of the pure state, but since their coherences have been destroyed, they will serve as magnitudes along the diagonal of the matrix representing the full Hilbert space.) If we take the view that "there is a universal wave function", then these magnitudes keep getting smaller and smaller, cascading downward toward truly infinitesmal levels. But when we do science, we are not interested in those vanishing amplitudes, we renormalize them so that our concept of "what happened" has magnitude 1. In the process, we zero out all the other diagonal elements that don't conform to the "information of the experiment". There is no possible way we could do science if we couldn't do that renormalization-- we could never "set up an experiment" according to some "initial conditions". The MWI is therefore untrue to all the language of science. I'd say that is a devastating price to pay to simply be able to elevate a set of axioms to the level of "reality". When has that ever worked in the history of science? We'll never learn, apparently.
     
  20. Apr 12, 2008 #19

    Fredrik

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    Thanks for confirming that. It's nice to get some confirmation from someone who seems to know what he's talking about. :smile: I enjoyed reading your posts, and I agree with what you said in them.
     
  21. Apr 12, 2008 #20

    Ken G

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    Thanks. I have no authority beyond the sense I make, so feel free to form your own opinions. I'm glad we agree.
     
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