From: braham@physics.ubc.ca (Stephen Braham)
Newsgroups: sci.physics
Subject: Re: Quantum Cosmological Boundaries and Determinisim?
Date: 23 Jul 92 17:24:21 GMT
Organization: University of British Columbia, Vancouver, B.C., Canada

MRG3@psuvm.psu.edu writes:

> [stuff deleted]

>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.


Yes, at, in some sense, ADH goes even further; once you define everything
in terms of decoherence functionals, you can even get rid of the
idea of a density matrix, or the concept of a state at a given time.
It's this that interests us in QC, of course, where time is a dirty
word.

> 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.

Exactly, and this connects up with an earlier statement by Jase on
the difficulty is getting perfectly decohered histories. Approximate
decoherence seems to be the way to go, but it's hard to QUANTIFY
it. I really worry that coarse graining may not preserve approximate
decoherence (unlike perfect decoherence). We can almost see what
needs to be done in the old density matrix, S-picture, type decoherence,
but, as I said in another post, the ADH off-diagonal terms are not
really connect to the off-diagonal terms in the effective density
matrix (when that matrix exists, which, in general, it doesn't).
There's a DYNAMICAL connection- the same squeezing together of the
trajectories in the configuration space path integral produces
both types of decoherence, but that's not enough for an _interpretation_.
It helps, though :).

>  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.

Oh goody, I get to be in wormie mode for a bit; yeah, I know tend to
believe that wormies don't help as much in that regard. On the other hand,
I think we're pushing our paradigm a little far when we talk about
information going down 'em- it's hard to give them a physical meaning
outside the Euclidean path integral, and the interpretation of THAT
is getting tougher. At a certain point, I'd go along with Jim Hartle
and say let's define QM _by_ the decoherence functional, and forget
about fields at a particular time.

>mike gallis
>mrg3@psuvm.psu.edu

			Steve

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