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- From: braham@physics.ubc.ca (Stephen Braham)
- Newsgroups: sci.physics
- Subject: Re: Quantum Cosmological Boundaries and Determinisim?
- Message-ID: <braham.711912261@physics.ubc.ca>
- Date: 23 Jul 92 17:24:21 GMT
- References: <jtwamley.711766649@adelphi> <braham.711770201@physics.ubc.ca> <92204.111241MRG3@psuvm.psu.edu> <mcirvin.711851892@husc8> <92205.082205MRG3@psuvm.psu.edu>
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- 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|
- | Hangout: UBC physics | Signature: Euclidean |
- | Vancouver, BC |--------------------------------+
- | Canada | E-mail: braham@physics.ubc.ca |
-