**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Tue, 30 Mar 1999 21:26:13 +0300 (EET DST)*

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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

**Next message:**Stephen P. King: "[time 74] Gerald Edelman reference"**Previous message:**Hitoshi Kitada: "[time 72] RE: [time 69] Spacetime & consciousness"**Maybe in reply to:**Ben Goertzel: "[time 69] Spacetime & consciousness"**Next in thread:**ca314159: "[time 70] Re: Geometric transformations & DSP"

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