Stephen P. King (stephenk1@home.com)
Sat, 20 Mar 1999 09:57:48 -0500
Dear Matti,
Matti Pitkanen wrote:
>
snip
[SPK]
> The paper co-authored by Hitoshi and Lance Fletcher
> (http://www.kitada.com/time_III.html) explains all of the basic thinking
> involved in LS. It is rather revolutionary and goes against the grain of
> conventional physical thinking, but, that all said, it does provided a
> starting point with which to address many other difficulties in modeling
> consistently our world.
> An example, the primitive ideas are examined:
>
> "1.We begin by distinguishing the notion of a local system consisting of
> a finite number of particles. Here we mean by "local" that the
> positions of all particles in a local system are understood as defined
> with respect to the same reference frame."
>
> Here we do not assume any particular properties of the "particles"
> other than what is explicitly stated and use the standard definition of
> a "particle"; some entity existing at the locus of an set of
> coordinates, but we do not assume any properties yet...
>
> "2.In so far as the particles comprised in this local system are
> understood locally, we note that these particles are describable
> only in terms of quantum mechanics. In other words, to the extent that
> we consider the particles solely within the local reference frame,
> these particles have only quantum mechanical properties, and cannot be
> described as classical particles in accordance with general relativity."
>
> Here we postulate the particles properties.
>
> "3.Next we consider the center of mass of a local system. Although the
> local system is considered as composed of particles which -- as local
> -- have only quantum mechanical properties, in our orthogonal approach
> we posit that each point (t,x) in the Riemannian manifold X is
> correlated to the center of mass of some local system. Therefore, in
> our approach, the classical particles whose behavior is described by the
> general theory of relativity are not understood as identical with
> the "quantum mechanical" particles inhabiting the local system --
> rather the classical particles are understood as precisely correlated
> only with the centers of mass of the local systems."
>
> Here the "center of mass" is distinguished. I think of this as how
> a bubble has a particular "center of mass" defined by the geometry of the
> surface as visible "on the outside", but any observer can not necessarily have
> knowledge of the "internal features." The center of mass is identified
> with a classical particle at some point in a Riemannian manifold X.
> Here I must mention that the usual Riemannian manifold X used is,
> I believe, only a special case. I think that there is much more structure
> involved. Your ideas, I think are an indication of this structure that
> generalizes X. The use of p-adics and ultrametrics would give us ways of
> defining histories, as you well point out! :)
> [MP]
> There is clear analogy with many sheeted spacetime. In TGD elementary
> particles correspond to so called CP2 type extremals of size of order 10^4
> Planck lengths. They have metric with Euclidian signature but lightlike
> curve as M^4_+ projection. These tiny 3-surfaces are glued by topological
> sum to 3-surface which is roughly like a piece of Minkowski space with
> size of order Compton length and possessing outer boundary. This process
> leads to massivation of elementary particle described by p-adic
> thermodynamics. It seems that one could think CP2 type extremal as a
> local system and piece of M^4_+ as spacetime. Am I correct?
Yes! I would like to understand this "topological sum" better. Could
you explain it to us?
[MP]
> Hierarchy continues: for instance, quark like 3- surfaces are glued to
> hadronic 3-surfaces, and so on. At human length scales my body is a
> 3-surface with outer boundary identifiable as my skin glued to a larger
> 3-surface.
>
> By the way, topological sum contacts connecting different sheets
> have induced metric with Euclidian signature and there is surface where
> the signature changes to Minkowskian one: at these surface the value of
> the p-adic prime characterizing effective topology of spacetime sheet
> most naturally changes.
> *******
This strongly reminds me of the discussions of "phase transitions" that
are discussed in connection to symmetry breaking. What I am most
interested in is how "most naturally" is computed by Nature. This is
where I think that computational physics is important.
[SPK]
> "4.It is important to recognize that the distinction we are making
> between local systems and classical particles which are the centers of
> mass of local systems is not a simple distinction of
> inclusion/exclusion. For example, we may consider a local system
> containing some set of particles, and within that set of particles we
> may identify a number of subordinate "sublocal" systems. It would seem
> that the centers of mass of these sublocal systems must be "inside" the
> local system as originally defined, but the sublocal system is at the
> same time a local system, and we have said that the centers of mass of
> local systems are correlated with classical particles whose behavior is
> to be described in terms of relativity theory."
>
> [MP]
> Also this is consistent with manysheeted spacetime picture. Note that
> one must generalize standard physics to manysheeted spacetime:
> thermodynamics with different temperatures and different
> phases at various spacetime sheets. Hydrodynamics flows: turbulent flow at
> one sheet, potential flow at second sheet.
This idea is not unknown in physics since the Unruh effect is
related...
"The equivalence between an accelerated vacuum and a thermal bath, often
quoted as the Unruh effect, and the resulting insoluble paradoxes appear
to be artefacts due to an inadapted representation of accelerated
frames."
http://www.spectro.jussieu.fr/Vacuum/relat_e.html
for more mentions see:
https://members-central.home.net/stephenk1/Outlaw/Unruh.html
(I tend to think spatially, so my use of multiple URLs that appear
unrelated is analogous to the interference pattern seen on a hologram
film... :) )
> *******
[SPK]
> This, to me, indicates how hierarchical ordering can come into
> play, but notice that there is no a priori ordering defined. Histories are
> like orderings of files on a hard drive, there is no absolute ab initio
> ordering, there is only that "stored" at the time of sampling and it is
> subject to revision by the next read/write operation.
>
> [MP]
> In TGD framework ordering by p-adic topologies enters naturally. The
> higher the value of p, the more refined the topology. Amazingly, one can
> understand the evolution as gradual increase of p-adic prime associated
> with the 3-surface characterizing entire Universe.
I am going out on a long limb here, but could this "evolution" be
related to the Universe "computing" the zeros of the zeta function? This
seems to follow your thinking... ;)
> ********
[SPK]
> The act of observing and/or measuring is an interaction that changes all involved,
> but the very nature of 'nondeterminism" is that results can't be known
> before hand, we only can calculate probabilities. The simple proof of
> this is show by the fact that gambling will never discover a "system" to
> cheap the "house". That would allow for a computer to violate
> thermodynamics!
> I have links to the Maxwell Demon information to show how others think
> about these kind of ideas. We are dealing with a very complex situation
> and thus must expect that any complete explanation of it will be even
> more so!
I am saying here that our observations are aspects of this Universal
"computation" mentioned earlier, but I am thinking of computation in
Peter Wegner's terms... ;)
Later,
Stephen
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