Re: When Worlds Collide

From: Robin Hanson (
Date: Thu Aug 16 2001 - 14:46:24 MDT wrote:

> > or .ps
> > When Worlds Collide: Quantum Probability From Observer Selection?
> Exciting as this is, I think the more likely possibility is the suggestion
> that the small worlds would be effectively eliminated by this influence,

A reasonable guess.

> The paper describes a simple case with one large and one small world.
> Does the math still work if there are enormously more small worlds than
> large ones, as I believe is expected to be the case? Is it necessary
> to consider the ratio of numbers of small to large worlds?

The basic linear equation i dr/dt = rh-hr can be decomposed across more than two
worlds, and then you get the evolution of a world being the self term plus,
instead of the single interaction term as in the equations I gave, there is a sum
of terms like that for each of the other worlds.

> ... Presumably there are "medium" worlds where the
> probabilities are somewhat different from what they should be, worlds of
> low probability (say, one in a billion) but still much higher than the
> probabilities relating to environmental coherence effects ...

If you make a billion measurements and your probability is one in a billion
relative to a max probability world, your measured frequency is *very* close to
that predicted by the Born rule. I don't think you'd notice the difference. If
you stare at a window and see the fraction of photons that come through, you are
implicitly making a vast number of measurements.

> Does the math still work in the case of an infinite dimensional set?

Me, I don't trust results you get with infinities that aren't the limit of finite
results. We only ever see a finite amount of data, and should seriously consider
the hypothesis that the world is finite as well. All the decoherence analysis
I've seen looks at finite sets of states decohering. Deutsch and others (eg "many
minds interpretation") do try to play something like your infinite set game

> In effect Robin's paper says that if all worlds make an equal contribution
> then you can still get the Born probabilities (modulo the various caveats
> and assumptions). This is a step forward as it is a simpler assumption
> than others which have been made. But I am not very comfortable with
> this assumption (that all worlds should be counted equally).

I'm not sure I follow you, but I think your discussion is only relevant for your
infinite case, right? For a finite set of worlds, I think I'm fine.

> Nevertheless, if an explanation like Robin's can work, it does seem to cut
> the knot and eliminate much of the difficulty. If stable observers can
> exist only in universes which match the predictions of QM, or if observers
> in bizarre universes somehow nevertheless experience only sane events,
> then there seems to be nothing left to explain and the issue is solved.

Yes, the hope is to have a simple mechanical solution that avoids most
philosophical complexities.

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