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April 26, 2008

Comments

OK, so let's say I measure a spin with 50% chance of up and 50% chance of down. By my understanding I can now make a tiny adjustment of my basis designed to multiply the number of worlds by a factor of "just" one trillion after I measure spin up (but perhaps by some completely different factor if I measure spin down). So now the ratio of probabilities for observing spin up and spin down has changed by a factor of a trillion (perhaps divided by some completely different factor). But the ratio should be indistinguishable from 1. How is this not fatal? (Is my second sentence wrong?)

I'd just like to comment that assuming a *continuum* of worlds is a perfectly reasonable thing to do. If done properly, it provides results that are independent of the basis.

Suppose you start with some initial coherent state. Consider some region of finite volume V. Now, as the wavefunction evolves, evolve the region V under the hydrodynamic flow: map the point x to the point q(t), where q(t) is a Bohmian/hydrodynamic trajectory with q(0)=x (call the new region UV). This is independent of your choice of basis.

In this perspective, we suppose that all worlds *exist* at all times. But most of them (different q(t)'s which are close together) are indistinguishable macroscopically.

Now measure the ratio of the volumes, |UV|/|V|. This is, in a certain sense, a measure of branching. It measures whether nearby (indistinguishable) trajectories have separated, and become macroscopically distinguishable.

What alternate account are they defending?

I recommend reading, for example, Wallace's 2003 paper Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation.

Since the standard probability rule can be derived using fairly innocuous (imo) assumptions, if you believe in a uniform probability rule (which will disagree in principle even if it does work out to close to the same in practice), you must either find these arguments faulty or disagree with an assumption.

The mangled worlds idea has the same problem that the Copenhagen interpretation does: it postulates an additional physical process that is not needed to explain observations.

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