> I think decoherence is a relationship between branches, not between
> subsystems, so it doesn't have anything to do with correlation. To quote
> Price's FAQ:
> Worlds, or branches of the universal wavefunction, split when different
> components of a quantum superposition "decohere" from each other [7a],
> [7b], . Decoherence refers to the loss of coherency or absence of
> interference effects between the elements of the superposition. For two
> branches or worlds to interfere with each other all the atoms, subatomic
> particles, photons and other degrees of freedom in each world have to be
> in the same state, which usually means they all must be in the same place
> or significantly overlap in both worlds, simultaneously. [end quote]
> It seems to me that the modern MWI has more to do with relationships
> between branches (i.e. decoherence) than with relationships between
> subsystems (i.e. correlation or relative state), even though Everett
> originally stressed the concept of relative state.
What is a branch? It's a component of a wavefunction. The total
wavefunction is therefore the sum of the branches. This means that
the branches all inhabit the same Hilbert space, which means that
they are different quantum states of the same system.
Decoherence means loss of coherence, which amounts to loss of
correlation, which is a relation between different systems.
Price says for two branches or worlds to interfere, all their
degrees of freedom must be in the same state - but in that case
they would be the same world.
I note that in the answer to Q4, "What is a 'world'?", he does
*not* say that it's a state of the universe; instead he says
it's a state of a set of subsystems which don't significantly
interact with other systems. I find this a completely unsatisfactory
definition. The concept of 'world' is supposed to be fundamental
to a new, clear interpretation of QM. But now 'world' itself is
defined in terms of the undefined concept of 'significant interaction'.
(Indeed, under Q6, he speaks of "worlds, or branches of the
universal wavefunction..." ... !)
So I stand by my original claim: the many-worlds interpretation
has not been clearly enunciated. Crucial concepts remain undefined
in any rigorous way.