Re: The weirdness of the Many Worlds Interpretation

From: Robin Hanson (rhanson@gmu.edu)
Date: Fri Jul 04 2003 - 13:33:36 MDT

  • Next message: Lee Corbin: "RE: The weirdness of the Many Worlds Interpretation"

    On 7/4/2003, Hal Finney wrote:
    > >... In many worlds, you have a straightforward way
    > > to calculate probabilities, namely counting worlds, that gives a
    > > *different* answer, which is a much more serious problem. You can deal
    > > with this problem by positing an infinity of "minds" per "world", which
    > > then split during measurements due to some unknown process. Or you can
    > > state decision theory axioms that declare that we do not care about
    > > counting worlds. Neither of these is very satisfactory in my opinion.
    >
    >I think the decision theory approach is relatively promising. I don't
    >know that the axioms really declare that we don't care about counting
    >worlds. In the end, it's true, we conclude that rationally we should
    >act as though the standard QM "Born" probabilities hold and ignore
    >the simple mechanism of counting worlds. That is a deduction from the
    >axioms and is therefore implicit in them. But the axioms are intended
    >to present a plausible definition of what constitutes rational behavior.
    >They don't start right off declaring that we ignore world counts.

    But they don't seem very plausible to me. They are just what you need
    to get the Born rule.

    >A simpler approach just occured to me. Let's consider a photon which is
    >emitted in a polarized state and encounters a polarizer tilted to give
    >a 10% chance of passing. As Damien describes, if each photon splits
    >the world into two, then the fraction of worlds that see the 10/90
    >probabilities becomes vanishingly small.
    >But does it really split like this? ...
    >... even a single emission and polarization-measurement of a photon
    >does not actually split the universe into two parts; it splits it into
    >an infinite number of parts. Even if it turns out that photon emission
    >is not truly continuous, that it can only happen at multiples of the
    >Planck time or whatever, that's still a truly enormous number of parts.
    >And the point is that among this humongous split, 10% of the universes
    >will see the photon pass through the polarizer, and 90% will see it
    >be absorbed. Given this reality, a simple counting rule does in fact
    >reproduce the Born probabilities. It was only because we abstracted away
    >the enormous additional complexity of the world in order to focus on the
    >polarizer interaction that we thought the universe split into two just
    >two branches.

    You say it works in this example, but I don't see it. Can you show us
    explicitly how you can calculate your 10%/90% figure in this example.

    Robin Hanson rhanson@gmu.edu http://hanson.gmu.edu
    Assistant Professor of Economics, George Mason University
    MSN 1D3, Carow Hall, Fairfax VA 22030-4444
    703-993-2326 FAX: 703-993-2323



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