From: <[email protected] <mailto:[email protected]>>
On Saturday, May 26, 2018 at 12:06:53 AM UTC, Bruce wrote:
From: <[email protected]
On Wednesday, May 23, 2018 at 8:16:07 AM UTC, Bruce wrote:
From: <[email protected]
OK, but how does one jump to the assumption of other worlds?
Doesn't each "branch" exist in this world? AG
Initially yes. But decoherence diagonalizes the density
matrix FAPP, so the other branches become unreachable. That
is what one means by separate worlds.
*I am tentatively OK with this conclusion (tentatively until I
examine the mathematics and verify it), as long as these separate
"worlds" do NOT contain copies of THIS world. It's the copying
that I find hugely extravagant, ridiculous, and erroneous! Can
decoherence theory be consistent without the "copying" claim? Is
this the view you adopt to keep your sanity? TIA, AG*
The fact that the whole world is copied in each branch of the MWI
is a simple consequence of the mathematics. If one has a state
|psi> = (|+> + |->)
that one measures, which is a superposition of two possible
outcome states, |+> and |->, then schematically this measurement
process looks like
|psi>|A>|O>|e>,
where |A> is the apparatus, |O> is the observer, and |e> is
everything else, namely the environment. Unitary evolution takes
this to:
(|+>|A+>|P+>|e+> + |->|A->|O->|e->)
where |A+> means the apparatus register the |+> result, |O+> means
the observer sees the |+> result, and |e+> means that information
about the |+> result leaks into the environment by decoherence and
is effectively recorded there many times. Similarly for the other
|-> branch.
As one can see immediately, this evolution necessarily means that
everything is duplicated, the apparatus, observer, and the rest of
the world, differing in the two branches only in consequence of
the different measurement results (|+> or |->).
*How does disjointedness of the branches follow? AG*
Decoherence in the separate branches leads to the approximate
diagonalization of the density matrix. Read about it in Wikipedia or
Schlosshauer's paper/book.
Decoherence does not cause the "copying", the copying is a result
of the Schrödinger equation. Decoherence occurs independently in
each branch, as can be seen in the above schematic outline of the
process.
*Not to quibble, but the copying seems to be the consequence of
unitary evolution, not the Schrodinger equation.*
The Scrödinger equation embodies unitary evolution.
*In any event, how does this situation differ from advanced waves in
EM theory, in that the mathematics seems to imply something that
doesn't exist? AG*
There is no connection between the two things.
Look, if you don't want to believe in the many worlds interpretation of
QM, then that is your prerogative. I was merely outlining the
mathematics that leads many people to think that this is the simplest
understanding of the situation.
Bruce
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