On 7/4/2021 5:30 PM, Tomas Pales wrote:
On Monday, July 5, 2021 at 12:54:45 AM UTC+2 Brent wrote:
It's not that it's necessarily 50/50; it's that there's no
mechanism for it being the values in the Schroedinger equation. In
one world A happens. In the other world B happens. How does, for
example, a 16:9 ratio get implemented.
For example, A happens in 16 worlds and B in 9 worlds. Or in general,
the proportion of worlds where A happens to worlds where B happens is
16/9.
But it's an additional axiom that this is a probability measure and the
split is per the Schroedinger amplitudes. Which then makes it just like
Copenhagen. Note that that the odds ratio 16:9 depends on the
interaction with measuring instruments (some other measurement would
yield different odds) and so it depends on at what point you stop
considering superpositions and say "That's classical enough. Let's just
zero out the cross terms in the density matrix." Something Heisenberg
or Born could have done and essentially what Bohr said. He realized
that any measurement that people could agree on would have to be
classical. So he held that the Heisenberg cut could be anywhere close
enough to consciousness to be quasi-classical.
Brent
There's nothing in Schroedinger's equation that assigns one of
those numbers to one world or the other. You can just make it an
axiom. Or equivalently, if you can show these are odds ratios,
you can invoke Gleason's theorem as the only consistent
probability measure. But all that is extra stuff that MWI claims
to avoid by just being pure Schroedinger equation evolution.
In MWI the odds of being in a particular world depend on the counting
of branches, similarly like the odds of selecting a particular ball
from a basket depend on the counting of balls. But if there are
infinitely many branches in MWI, different ways of counting give
different probabilities, which means there are different possible
probability measures, and so MWI needs an additional axiom that
specifies the measure and thus the way of counting the branches. You
say that the only possible (consistent) measure is the Born rule; in
that case no additional axiom about the measure is needed (beyond the
axiom of consistency, which goes without saying) and the branches must
be counted in such a way that the probabilities result in the Born rule.
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