On Mon, Feb 10, 2025 at 11:12:36AM -0800, Brent Meeker wrote:
>
> There are ways MWI can be saved. For example Julian Barbour's idea that a
> single macroscopic world consists of an enormous number of parallel worlds
> that
> are microscopically distinct, and a measurement divides this stream of
> microscopic worlds into macroscopically distinct worlds. Then the division
> can
> reflect instantiating uneven probabilities. There's a paper by Pearle which I
> cited in reply to JC which puts some mathematics on a similar idea.
I think it _has_ to be something like this. Division into microscopic
worlds can be done arbitrarily, of course, since they're
indistinguishable wrt observers, however to get a meaningful measure
by branch counting, it has to be done is such a way that a symmetry
relation is preserved, and then the indifference principle
applied. Just like a classical 6 sided die is modelled as symmetric
with respect to each face, so we can assign a probability of 1/6 to
each outcome.
My comment to Bruce is that he is inappropriately applying the
indifference principle in his setup. In order to recover the necessary
symmetry, it is necessary to include observers who rotate their
apparatus -θ as well as θ. And once you do that, the probability of 0
being observed by anyone from the union of the two sets of observers
is 1/2. For every observer in the θ set seeing a give sequence x, there is
an observer in the -θ set that sees the complementary sequence.
I don't know whether Kent's setup suffers the same flaw, but I will
look into it when I get a spare moment. (Or a round tuit).
>
> But is certainly not "just the Schroedinger equation". It's interesting to
> think how the Born rule may be realized. Barandes, Weinberg, and Pearle have
> ideas worked out in different degrees. Generally they begin by rejecting the
> Hilbert space picture and adopting the density matrix as fundamental,
> recognizing that that a real state is never completely isolated.
>
Actually getting the Born rule from the MWI is obviously non-trivial,
and possibly impossible, given the large number of attempts by bright
people that have failed. However, it does seem that once you assume a
complex measure over the system states, the Born rule arises quite
naturally - it is, after all, the only bilinear relationship between
two states that is normalised to unity.
--
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Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders hpco...@hpcoders.com.au
http://www.hpcoders.com.au
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