**Stephen P. King** (*stephenk1@home.com*)

*Sat, 10 Apr 1999 19:03:20 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Hitoshi Kitada: "[time 209] Re: [time 208] Re: [time 204] Observation & Obler's Paradox"**Previous message:**Stephen P. King: "[time 207] Re: [time 206] Observation and infinity"**In reply to:**Stephen P. King: "[time 203] Observation"**Next in thread:**Hitoshi Kitada: "[time 209] Re: [time 208] Re: [time 204] Observation & Obler's Paradox"

Dear Hitoshi,

Hitoshi Kitada wrote:

snip

*> > >What one finds in the universe depends on the way he decomposes the universe.
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*> >
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*> > Are these decompositions unique?
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*>
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*> Not unique.
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I suspected so... ;)

*> E.g., consider a set L={1,2,3}. (In the case of the universe, L may be an
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*> infinite set. At this point, to use the notion "cluster decomposition" b
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*> concerning the universe may be an abuse at least at the present stage of the
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*> theory. This point might be related with Obler's paradox as I mention below.)
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*>
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*> Then the set Q is
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*>
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*> Q={ {{1},{2},{3}},
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*> {{1},{2,3}}, {{1,2},{3}}, {{1,3},{2}},
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*> {{1,2,3}} },
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*>
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*> consisting of 5 elements. b varies over those elements.
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Forgive my mathematical naivete, but is Q here an example of a power

set?

*> b={{1},{2},{3}} is the I-It case (completely classical). The observer sees each
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*> particle as behaving classically.
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*>
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*> q={{1,2,3}} is the I-Thou case. The observer sees L as a QM system consisting
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*> of the particles 1,2,3 with some Hamiltonian like
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*>
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*> H = -\Delta_{123}/2 + \sum V_{ij}(x_{ij})
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*>
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*> with x_{ij} denoting the relative position between the particles i and j.
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*>
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*> Other cases like q = {{1,2},{3}} are partially classical as well as QM case. In
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*> this case, the particles 1 and 2 inside a cluster {1,2} behave as QM particles
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*> with respect to the Hamiltonian of the subsystem consisting of the two particles
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*> 1 and 2:
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*>
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*> H_{12}= - \Delta_{12}/2 + V_{12}(x_{12}),
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*>
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*> while the particle 3 behaves like a classical particle that interacts
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*> classically with the center of mass (CM) of the subsystem {1,2} consisting of 1
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*> and 2. The Hamiltonian which might explain this QM-Classical system is given by
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*> formula (QMG) on page 21 of time_IV.ps, which, however, is a quite rough
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*> approximation.
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*>
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*> On Obler's paradox and Big Bang, my crude idea might be that humans and their
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*> apparatuses cannot see the universe U in completely QM way (i.e. b={ U }),
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*> probably because the universe consists of an infinite number of particles. If
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*> so, they have to see the universe in classical way to some high extent always,
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*> then what they see should look like what we observe, i.e. the observation by
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*> humans and their apparatuses tells us the universe is expanding and thus Obler's
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*> paradox is not observed, even if the total universe might be stationary.
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*> Assumption behind this is that as the number of particles of a system L becomes
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*> larger, it would be more and more difficult to see L as a QM one, by some
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*> reasons related with recognition (or computation in your context).
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Umm, this idea reminds me of the "decoherence" ideas being worked on

http://feynman.stanford.edu/people/ike.html

http://www.df.uba.ar/~hprel/prep_93.html

http://www.reed.edu/~rsavage/environment_decohere.html

etc.

I think that since LSs have a finite number of particles and can thus

encode only a finite amount of information in their configurations (2^N

bits for binary information given N particles?), they can only 'observe'

a finite number of other LSs at any given moment. This "shapshot" idea

is one that I would like to explore further with you guys, since there

is more to it, like there would be a finite bound on the spatial aspect

of the information content.... I wish Robert were still with us, the DSP

point of view is needed here. :(

Onward to the Unknown,

Stephen

**Next message:**Hitoshi Kitada: "[time 209] Re: [time 208] Re: [time 204] Observation & Obler's Paradox"**Previous message:**Stephen P. King: "[time 207] Re: [time 206] Observation and infinity"**In reply to:**Stephen P. King: "[time 203] Observation"**Next in thread:**Hitoshi Kitada: "[time 209] Re: [time 208] Re: [time 204] Observation & Obler's Paradox"

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