Matti Pitkanen (email@example.com)
Sun, 21 Mar 1999 16:18:06 +0200 (EET)
On Sat, 20 Mar 1999, Stephen P. King wrote:
> Dear Matti,
> Matti Pitkanen wrote:
> > 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?
Topological sum for two n-dimensional surfaces is formed as follows.
Cut balls D^n from both surfaces. The boundaries of these
holes are spheres S^(n-1). Connect the boundaries of the
holes by the cylinder D^1xS^(n-1) along its ends. In two dimensional case
you remove disks from the two surfaces and connect them by a cylinder by
gluing its ends to the boundaries of the holes.
I looked at the references you mentioned. There seems to be also a
difference. Local clocks are introduced at each spacetime point
by replacing X^4 with X^4xR^6 (R^6 phase space of particle).
I do not attach local system to *every point* of background spacetime.
Local system would represent topological nonhomegenuity of
spacetime surface in TGD approach. But these spacetime sheet 'glued'
to background space represent in good approximation their own universes
and in good approximation one can construct their physics discarding
the interactions with external world. In this manner one obtains
QCD, low energy hadronic physics, nuclear physics, atomic physics,...
Also our starting point could be seen as same. The failure of Newtonian
spacetime applied in standard QM in General Relativistic context.
My solution is to give up totally the idea about physical state as
time=constant snapshot and describe quantum state as quantum history
and try to understand the emergence of psychological time ('clocks')
as a problem of consciousness theory: why the contents of conscious
experience is located around some value(s possibly) and why this value
of time tends to increase at least locally. Here the nondetermism of
Kahler action, which generated this discussion, is in fundamental role.
Quantum jumps for which nondetermism is located in finite time interval
give conscious information about that time interval and hence conscious
experiences with time localized experiences become possible. Without
nondeterminism experience would contain information diffused over entire
intial and final quantum histories.
What troubled me in local system approach were the following points.
Dirac equation for atoms gives predictions which are verified
experimentally and replacing Dirac equation with Schrodinger equation does
not seem promising. Secondly, Why R^6, why not only R^3 if local system
obeys nonrelativistic QM?
> > 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.
One could say that different values of p represent different phases: the
nature of classical nondeterminism is different. I have proposed
p-adic phase transitions in which region of new p grows gradually from
pointlike seed as solution to some anomalies of physics.
In TGD based model of sonoluminesence the expansion phase is assumed to
involve increase of p (see the chapter 'Quantum antenna hypothesis' of
TGD inspired consciousness'
In TGD top quark belongs to scaled up up hadron physics for which hadrons
correspond to Mersenne prime M_89 (ordinary hadrons correspond to M107).
Top quark decay involves phase transition increasing the p-adic prime M_89
of top quark (http://www.physics.helsinki.fi/~matpitka/padtgd.html).
These are not the only applications. In cosmology this kind of phase
transitions would involve the emergence of entirely new spacetime sheet in
temperature of order 1/L_p, L_p the p-adic length scale (L_p =about
10^4*sqrt(p) Planck lengths).
> > "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
> "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
> for more mentions see:
> (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... :) )
> > *******
> > 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... ;)
This evolution is real. The origin is p-adic unitarity and quantum jumps
between quantum histories scenario. I do not see any evolution in
deterministic classical time development: I believe that quantum jumps
between quantum histories are needed for evolution and self organization.
space of 3-surfaces decomposes into sectors D_p such that the effective
topology is p-adic in sector D_p. S-matrix elements for the transitions
leading to states localized in D_p belong to C_p since integration
over D_p gives rise to p-adic number.
b) One must assume that quantum jump
leads to a definite sector D_p since otherwise the amplitude for
transition would be superposition of p-adic numbers belonging to different
p-adic number fields. Hence the sequence of quantum jumps between
histories can be regarded as a sequence labelled by p-adic primes
c) p changes quantum jump by quantum jump: each quantum jump is
preceded by real time evolution
with infinite lightcone proper time interval represented by exponent of
Virasoro generator and this causes dispersion of configuration space
spinor field from initial sector D_p to other sectors.
d) Since for given prime there is much more primes larger than p than
primes smaller than p, p increases in the long run. This means evolution
at topological level: the larger the p, the more refined the
p-adic topology. Also evolution of consciousness is involved: the
maximum negentropy gain in quantum jumps scales as log(p) and increases
with p. This negentropy gain is related to Shannon information of density
matrix. Also the cognitive resources of 3-surface, measured by the
logarithm of the number of 3-surfaces X^4(X^3) having same value of
absolute minimum of Kahler action, increase as log(p).
These arguments can be found in the last 'TGD inspired theory of
Riemann Zeta function emerges in the heuristic argument leading to
a precise estimate for the value of Kahler coupling strength. The argument
involves arithmetic quantum field theory. I must admit that I do
not have the needed computationalistic intuition to answer your question.
For instance, the p-adic length scale hypothesis putting primes near prime
powers of 2 in special position might be related to some kind of
computation: you could perhaps give examples of the special role of
numbers of form N= 2^n-1 in computation.
> > ********
> > 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... ;)
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