> Maybe we can find some common ground to start with.
Okay, can we agree on the following:
I. The universal wavefunction (UWF) will have some representation
of the form
sum(i) c_i |i>, (1)
where the |i>s are a set of basis states.
II. A complete description of each of the many worlds must be
found somewhere in (1), for the many-world interpretation
to live up to its name.
III. For the concept of 'relative state' to make sense, we
must be able to attach at least two labels to the basis
states, so that the UWF is written as
sum(i,j) c_ij |i;j> (2)
Then we can say that the relative state of subsystem j,
given that subsystem i is in state X, is
sum(j) c_Xj |j>
> But in practice, to try to judge whether a theory matches our universe,
> we need to have a way to map between its predictions and what we see.
I can see only two ways to arrive at this. Either you look for
'what we see' in the |i>'s, the universal basis states, or
you look for 'what we see' in the relative states of subsystems.
The former sounds like many-worlds proper, the latter like
many-minds, since as far as I can tell many minds is all about
focusing on the relative state of the brain.
Neither many minds nor many worlds has any built-in concept of
*history* for an individual 'mind' or 'world', and both require a
statistical weighting to be attached to the various relative
states in order to explain why in this single world we see the
predictions of orthodox QM fulfilled (in the frequencies of
measurement outcomes).
> This topic is discussed in conventional measurement theory, from a
> different point of view. There it is shown that as a quantum phenomenon
> undergoes amplification to large numbers of particles, the nature of
> the wave function changes. It changes from a superposition of states
> to a mixture of decoherent states. This can be derived purely with
> the continuous evolution of the wave function, without introducing any
> notions of wave function collapse.
The Schroedinger equation can't turn a pure state (and a
superposition is still a pure state) into a mixture, which
is a classical probability distribution over a set of pure
states.
Even if you use density matrices rather than wavefunctions,
I don't think what you describe happens; a pure-state density
matrix evolves into another pure-state density matrix.
I think what *is* true is that you can start with a pure-state
density matrix for a coupled system, and the density matrix
of a subsystem will evolve from a pure state into a mixture.
Back at the level of wavefunctions, decoherence does not
explain how observables come to have definite values. All
decoherence does is reduce the correlation between subsystems;
a decoherent state is still a superposition, it's just a
superposition with very little entanglement.
-mitch
http://www.thehub.com.au/~mitch
Received on Sat Jan 31 1998 - 22:21:19 PST