On 3/2/2015 12:46 PM, LizR wrote:
On 2 March 2015 at 17:24, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
Russell Standish wrote:
On Sun, Mar 01, 2015 at 07:48:49PM -0800, meekerdb wrote:
On 3/1/2015 6:29 PM, Russell Standish wrote:
I remain unconvinced that that probabilities are undefined.
Tegmark gave an interesting version of how to get Born's rule
from
MWI, which seemed to have legs. Deutsch gave one based on
decision
theory that is admittedly unsatisfying.
My own derivation simply assumed that observers had measure. The
probability of an outcome is proportional to the measure of the
observers
What's "the measure of the observers"? That's usually where the
implicit assumption of Born's rule sneaks in.
It's not implicit, but quite explicit that observers are drawn from an
ensemble of all possible observers with an associated
measure. Somewhat later, we identify that measure with the complex
magnitude of the QM state vector. It is still problematic that the
measure turns out to be complex, rather than say quaternionic or
something more general, though.
I don't see it as implicitly assuming Born's rule, though. The exact
functional dependence of probability on the observer's state could be
anything, but it turns out it has to be given by Born's rule (assuming
Kolmogorov's probability axioms, of course).
In other words, it doesn't appear to avaoid the problem with MWI pointed
out by
Dawid and Thebault:
http://philsci-archive.pitt.edu/9542/1/Decoherence_Archive.pdf
You effectively assume the Born rule in order to get your ensemble of
observers out
of the superposition.
Do superpositions still occur in the MWI? I thought they were supposed to be branches
(which are perhaps able to recombine) ?
Sure, it's an interpretation of the mathematics. It doesn't change the mathematics. A
pure state that's not a superposition in one basis is a superposition in a different
basis. Deutsch's argument that a conscious quantum computer will confirm MWI depends on
the computer being in superposition of different worlds so that they can interfere during
its computation.
Brent
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