# [time 208] Re: [time 204] Observation & Obler's Paradox

Stephen P. King (stephenk1@home.com)
Sat, 10 Apr 1999 19:03:20 -0400

Dear Hitoshi,

snip

> > >What one finds in the universe depends on the way he decomposes the universe.
> >
> > Are these decompositions unique?
>
> Not unique.

I suspected so... ;)

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

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

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

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