From: MRG3@psuvm.psu.edu
Newsgroups: sci.physics
Subject: Re: Quantum Cosmological Boundaries and Determinisim?
Date: 23 Jul 92 12:22:05 GMT
 <92204.111241MRG3@psuvm.psu.edu> <mcirvin.711851892@husc8>
Organization: Penn State University

Matt (mcirvin@husc8)writes:
>MRG3@psuvm.psu.edu writes:
>>A quick comment on the role of the wavefunction/density matrix
>>in consistent histories (ala Hartle & Gell-Mann):
>>There is an initial condition (i.e. initial density operator) to be specified
>>in the decoherence functional.  The initial conditions will determine in part
>>which histories decohere, and are quasi-classical. The specific dynamics, and
>>choice of coarse graining will also be important.

>This is interesting.  I assumed that the initial density operator was
>in fact a partial description of some pure state, unknown because of
>our ignorance of the microscopic variables-- like an ensemble of experiments
>repeatedly performed in which controllable variables interact with a
>complicated environment.  You get a diagonal density matrix for the
>macroscopic variables after decoherence, but in this view the state
>after any one measurement would actually be some unknown superposition of
>the various eigenstates of the measured observable, with the density
>matrix giving average results.  Someone recently mentioned that in
>quantum cosmology, though, there might be such a thing as a truly mixed
>state-- that the universe might be describable only by a density matrix,
>not a single state vector or wave function.  Is this related to the idea
>of degrees of freedom disappearing behind event horizons?  What does
>it mean?  Am I babbling?

You are certainly not babbling, but suffer from a cultural bias in the way
QM is generally taught.:)  Generally, when the density matrix is introduced,
it is in terms of some level of ignorance (unknown measurement results, quantum
entanglement with other systems, etc.). While this may be a useful viewpoint
at first, I tend to think it results in confusion in the long run.
QM can be expressed solely in terms of density operators, without ever
referring to a state vector.  A pure state is merely a minimum entropy
density operator.  Evolution of isolated systems (in normal QM) is unitary
and preserves entropy (i.e. pure states stay pure), although alternatives
to standard QM, such as Quantum Mechanics with Spontanious Localization,
have nonunitary evolution(where we can only say entropy is nondecreasing).
In open quantum systems, there has a great deal of work done on
phenomenological evolution equations.  When you start looking at
quantum open systems, or variants of the Schroedinger equation, paying
attention to things like "where did the information go" is distraction and
irrelevant (unless you are considering foundational issues). I think a
fairly good intro to density operators can be found in von Neuman's
Mathematical Foundarions  of Quantum Mechanics.

 The effective dynamics of an  open quantum system tend to
reduce the coherence terms of the density operator of the
system of interest.  They don't go away in a finite time, rather, the
the decoherence decays away (hopefully exponentially) with time.
The density operator can never be diagonal in a continuous
basis (such as position): it would not be normalizable.
Decoherence and the "superselection" are necessarily
approximate.
  With regards to quantum coherence down the wormhole:
This strikes me as just another open quantum system with inaccessible
regions (to the observable universe, as opposed to the entire universe).
A minor point is that it is not degrees of freedom that go down the wormhole,
but rather, there is quantum entanglement between degrees of fredom (field
amplitudes) out here and degrees of freedom down in there.
There is still no dynamical mechanism for collapsing the wave function.

mike gallis
mrg3@psuvm.psu.edu