Matti Pitkanen (matpitka@pcu.helsinki.fi)
Tue, 30 Mar 1999 21:26:13 +0300 (EET DST)
Dear Ben,
Ben Goertzel wrote:
>
> 3 particles? 9372? Obviously there is no magic number. But what then?
> do we have to view the GR perspective as fuzzy, as having more and more
plausibility as there
> are more and more particles in the system, and as their mean becomes
more and more stable (in
> a highly dynamic, high-variance quantum system there may be no reliably
detectable center of
> mass over finite time scales).
In short, YES! :) There is the possibility of a truncation or
cut-off of the number of LSs interaction in a single "cosmos" system, (I
find Matti's work covering this!) but that is a subject of its own. ;)
[Matti]
Perhaps I can explain a little bit what the analogy of local system
in TGD is. TGD:eish spacetimes are 4-surfaces in 8-dimensional space
M^4_+xCP_2: Cartesian product of future light cone and complex projective
space of real dimension 4 (CP_2= SU(3)/U(2)).
TGD:eish spacetime is manysheeted (here manysheetedness has nothing to do
with Riemann surfaces) consisting roughly of pieces of Minkowkski
space glued by topological sum contacts to larger sheets of Minkowski
space. [For illustrations see my homepage
http://www.physics.helsinki.fi/~matpitka/)
Pne could actually say that there is entire hierarchy of local systems
inside local systems with increasing size and labelled by the p-adic prime
characterizing the effective p-adic topology of spacetime sheet.
At the top of this hierarchy are elementary particle 3-surfaces, which
are so called 'CP2 type extremals' with size of order 10^4 Planck lengths
glued to elementary particle like spacetime sheets with size of order
Compton length. CP2 extremals have metric with Euclidian signature
and their lightcone projection is random light like curve: randomness
is possible since vacuum extremal of Kaehler action is in question.
Amusingly, the quantization of the lightlikeness condition leads to
Virasoro algebra of string models: this observation led to the realization
that Super Virasoro invariance and other symmetries of super string models
generalize to TGD context. CP2 type extremals are to TGD what black holes
are to General Relativity: even the area law for black hole entropy
generalizes to corresponding law for elementary particle p-adic entropy.
The crucial property of the spacetime sheets is their finite size: this is
forced by the special features of classical gauge fields obtained by
inducing CP2 spinor connection to spacetime surface. If one tries to imbed
arbitrary gauge field, say em field, as induced gauge field, imbedding
typically fails at some surfaces. For instance, the gauge potential
created by constant charge density fails to be imbeddable at certain
critical radius. Spacetime surface generates spatial boundaries as a
consequence. Gauge flux must be conserved however and the only
possibility is that it flows to a larger spacetime sheet
via the topological sum contacts, which are like extremely small wormholes
(Einstein-Rosen bridges) connecting two spacetime sheets.
The consequences are nontrivial in all length scales. For instance,
our bodies are 3-surfaces with finite size and our skin corresponds to
the boundary of our spacetime surface at which our spacetime sheet
ends: the exterior spacetime corresponds to a larger spacetime sheet
'below it' (only visually). The first thing what wormholes bring into mind
is prototype for a nervous system since they mediate gauge fluxes and
interaction between two different worlds (my internal world and exterior
world). It indeed turns out possible to construct a model of nerve pulse
and EEG based on the idea that wormholes behave like elementary particles
(bosons) and form Bose Einstein condensate.
p-Adic length scale hypothesis makes this picture quantitative. One can
associate to each spacetime sheet p-adic topology as an effective
topology. p-Adic number fields are labelled by primes. The spatial size
of the sheet with given p-adic prime p is typically L_p =about sqrt(p)*l:
l=about 10^4 Planck lengths. This estimate follows from p-adic mass
calculations using p-adic mass formula M propto 1/l_p using uncertainty
principle.
To sum up, the finite size of the p-adic spacetime sheet implies
that the particle number of given sheet is finite for finite p. The
hierachy however continues and one can wonder, what happens when one
considers entire universre presumably having infinite size: is the p-adic
prime infinite? This question could have led to the theory of infinite
primes, which I discovered few months ago: actually I ended up with the
theory of infinite primes from
TGD inspired theory of consciousness rather than from this question.
Best,
Matti
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