Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sat, 20 Mar 1999 09:09:19 +0200 (EET)
> On Fri, 19 Mar 1999, Stephen P. King wrote:
>
> > Matti,
> >
> > Thanks for your thoughtfull comments. I will be reading and thinking
> > about them. I still do have a bit of difficulty with the math terms. I
> > do best if we could speak about them in terms of either examples or
>> some analogy. I must frustrate you, I apologize. :)
>
> I must confess that my knowledge about LS is almost nil. I hope that
> I will learn something in these discussions.
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 do 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?
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.
*******
"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 spaceetime:
thermodynamics with different temperatures and different
phases at various spacetime sheets. Hydrodynamics flows: turbulent flow at
one sheet, potential flow at second sheet.
*******
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.
********
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!
Later,
Stephen
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