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Scerir,

This a a very interesting bunch of related topics... the idea of the

Cosmological Principle (in its strong & weak forms); the idea that no

observer is "special"; and the related idea that no coordinate system

(..ultimately, in the Strong C.P., even a higly derived one, eg that of a

system space...) is paramount.

Such a situation might be deriveable from consistency constraints on

compression models of the universe. In other words, any empirical physical

description of the Universe, including a local coordinate system, is a

"model".

The traditional 4 dimensions of spacetime might simply be a consequence of

modelling... because of consistency requirements, everything works out, so

we're convinced that "THIS" is the physical world.

But one can imagine some wierd machine entity; that for reasons based on its

structure, chooses to interpret its local universe as an n-dimensional

system space. Where n, of course could be 256 or 1000; or whatever.

It would deal with "our" insistence on an absolute 4-space as a contrivance!

The Strong Cosmological Principle is indeed a curious thing!

cymm

-----Original Message-----

From: scerir <scerir@libero.it>

To: extropians <extropians@extropy.com>

Date: Sunday, July 23, 2000 12:07 PM

Subject: The Fractal Universe

*>The basic hypothesis of a post-Copernican cosmological theory is that all
*

*>the points of the universe have to be essentially equivalent. This
*

*>hypothesis is required in order to avoid any privileged observer.
*

*>
*

*>This assumption has been implemented by Einstein in the s.c. *cosmological
*

*>principle*: all the positions in the universe have to be essentially
*

*>equivalent, so that the universe is (at least mathematically)
*

*homogeneous*.

*>This situation implies the condition of some (spherical) symmetry about
*

*>every point, so that the universe is (at least locally) *isotropic*.
*

*>
*

*>But an *hidden* assumption seems to be in the formulation of the
*

*>cosmological principle. In fact, the condition that all the points are
*

*>(statistically) equivalent (with respect to their environment) corresponds
*

*>to the property of a local *isotropy*. And it is generally accepted that
*

the

*>universe can not be *isotropic* about every point without being also
*

*>*homogeneous*.
*

*>
*

*>But local *isotropy* does not necessarily implies *homogeneity*. In fact a
*

*>topological theorem states that homogeneity requires (at least local)
*

*>isotropy together with the assumption of the *analyticity*. Analyticity
*

was

*>an usual assumption in any physical problem: before the *fractal* geometry!
*

*>
*

*>Actually a *fractal* structure has some local isotropy but has not
*

*>homogeneity. In simple terms one observes the same mix (structures and
*

*>vacua) in different directions (statistical isotropy). This means that a
*

*>*fractal* structure satisfies the cosmological principle! In the sense that
*

*>all the points are essentially equivalent (no center, no special points).
*

*>But this does *not* imply that these points are distributed uniformly!
*

*>
*

*>Now astronomy showed some intrinsically *irregular* structures for which
*

the

*>analyticity assumption might be reconsidered and fractal properties might
*

be

*>investigated.
*

*>
*

*>The space distribution of galaxies and clusters, the cosmic microwave
*

*>background radiation, the linearity of the redshift-distance relation
*

*>(Hubble law), the abundance of (light) elements in the universe: each of
*

*>these four points provides independent experimental facts. The objective of
*

*>a cosmological theory of the universe (fractal or not) should be to provide
*

*>a coherent explanation of all these facts together. An important point in
*

*>the theoretical investigation concerns the distribution of the
*

gravitational

*>force inside structures which could be irregular or fractal.
*

*>
*

*>But the recent statistical analysis of the experimental data already shows
*

*>also that *the distribution of galaxies is fractal* up to the deepest
*

*>observed scales. In the near future one could describe structures in which
*

*>intrinsic *self-similar* irregularities develop at *all* scales and
*

*>fluctuations cannot be described in terms of *analytical* functions. The
*

*>theoretical methods to describe this situation could not be based on
*

*>ordinary differential equations because *self-similarity* implies
*

*>singularities and the absence of analyticity.
*

*>
*

*>About the fractal universe:
*

*>http://pil.phys.uniroma1.it/astro.html
*

*>http://pil.phys.uniroma1.it/debate.html
*

*>http://pil.phys.uniroma1.it/
*

*>http://pil.phys.uniroma1.it/eec1.html
*

*>
*

*>The Nobel laureate (1977) P.W. Anderson is working on this field (now at
*

the

*>Princeton University and also at the Rome University, La Sapienza).
*

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