From: <[email protected] <mailto:[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 |->). 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.
Bruce
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