[time 413] Re: Symplectic Geometry and GR

Stephen P. King (stephenk1@home.com)
Sat, 19 Jun 1999 13:09:04 -0400

Hi Hitoshi, Matti and friends,

        Reasserting some questions:

Sat, 20 Mar 1999 03:47:34 +0900
Hitoshi Kitada wrote:
> Dear Stephen,
> Maybe the problem you raised is concerned with the nature of observation. Or
> it might be said that the observation is possible only for a finite number of
> "classical particles." So we cannot define any metric effective globally in
> the universe. Thus we cannot deduce from this metric any "definite
> connections" valid throughout the universe.

        We need a theorem proving that observation is an action (O act)
only a finite number of "classical particles" can perform. The term
"classical particles" speaks to the "outside" aspect of a local system
(LS)... Since the Universe (Totality) has an infinite number of
particles it would be disallowed from having O acts. Matti's quantum
jumps involve aspects that may be illuminating as to the nature of this
"theorem"... :)
        The relationship between metrics and observations, I believe, is
inherent in the "Clocking" nature of LSs. We do need to discuss this
> The metrics and hence connections appear only as subsidiary quantities at each
> observation. My postulate that "we do not introduce any connections among
> Euclidean geometries inside local systems" is not violated because of this ad
> hoc-ness of determining the metrics. At each observation, the observer may
> feel from their measurements that "it seems that the 'global metrics' may
> exist." But such a feeling might be an illusion. For we cannot gather the
> whole of observations to construct the metrics among "infinite number of
> classical particles" due to the gap between an "infinite number" and "the
> finite number of procedures of observation." The finite sum of the latter is
> always finite.

        I think that metrics and their related connections are implicit
in the
way observations (by LSs) "frame" an event. The selection of scale,
orientation, and ordering are not "given from above", they are local
acts of the LS. I completely arguer with this comment that the
appearance that an observer "feels from their measurements that "it
seems that the 'global metrics' may exist."" is an illusion, but it is
helpful to consider why the illusion can occur.
        Hitoshi, Your last two sentences here are very close to my
that time has a computational aspect! :) I ask: 1) How many steps or
separate actions are needed to "construct the metrics among "infinite
number of classical particles""? 2) How many different finite sets of
"procedures of observation" exist? I believe that the quantities in 1)
and 2) are closely analogous to the quantities the Malthus considered in
his famous essay: Population and Resource availability
        The former increases at an exponential rate and the former
increases at
a polynomial rate: Malthus said: "Population, when unchecked, increases
in a geometrical ratio. Subsistence increases only in an arithmetical
ratio. A slight acquaintance with numbers will shew the immensity of the
first power in comparison of the second."
        The issue of NP-completeness in computation is very much related
this last discussion! I hope that in the near future we can get into
this subject. :)
> -----Original Message-----
> From: Stephen Paul King <stephenk1@home.com>
> To: hitoshi@kitada.com <hitoshi@kitada.com>
> Date: Saturday, March 20, 1999 2:33 AM
> Subject: Re: Symplectic Geometry and GR
> >Dear Hitoshi
> >
> > I just found this. it claims a relation between metrics and
> >connections. I fully understand your postulation of no connections
> >between LSs, but would this not be equivalent, under special
> >conditions, to saying that *any possible connection* is equiprovable?
> >
> >Later,
> >
> >Stephen
> >

Onward to the Unknown,


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