🚀 go-pugleaf

jbaez@riesz.mit.edu (John C. Baez) writes:

>In article <braham.711770201@physics.ubc.ca> braham@physics.ubc.ca (Stephen Braham) writes:

>> [stuff by me deleted]

>What do you mean by an "intermediate state"?

>By the way, lots of mathematicians use "state" to refer both to pure
>states (typically represented by unit vectors in Hilbert space) and
>mixed states (aka density matrices).

Yes, I'd better be careful- I used state in that sense later. I'm
really talking about an intermediate density matrix or wavefunction
here, vs. a more general quantum state (or quantum description
of the system). By intermediate, I mean intermediate in time, i.e.,
between 'measurements.' In ADH, we try to give meaning to just
HISTORIES, and we bury the idea of a density matrix or wavefunction
at a particular time. For a _Hamiltonian_ ADH (which isn't general
enough for quantum cosmology, probably), one can go to a generalized
approach with both final and initial conditions, and you get a system
that cannot be described by a density matrix at any intermediate time,
but is fully predictive. Wehn the final state density matrix is
just the identity, you get back to pretty standard Copenhagen
style Hamiltonian quantum mechanics, and you can almost say that
each projection operator IS a Cophenhagen style collapse. I prefer
Jim's way of looking at it though, in which you say that you're
looking at a purely conditional question, and the collapse is
nothing except the standard conditional probability rule. This
shouldn't be confused with the _dynamical_ collapse of the
wavefunction, induced by decoherence processes- that's a statement
on a Shroedinger picture density matrix, and ADH is a lot more
general than that.

>What is the most lucid and interesting single reference on the
>alternative decohered histories approach?  I've read a bit about it but
>could stand some more.

Ewww, hard one. I think I'll have to give you two, because things
are in flux, and Gell-Mann and Hartle are redefining their
concept of quasiclassical domains. The Jerusalem Winter School (1989)
notes are probably the best single description, they're in
Quantum Cosmology anb Baby Universes, ed. S. Coleman, J. B. Hartle and
T. Piran (World Scientific, Singapore, 1990). The later, modified,
stuff is Alternative Decohering Histories in Quantum Mechanics,
UCSBTH-90-56.

			Steve 
--
| Name: Stephen P. Braham | Perversion: Quantum Cosmologist|
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