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