From: CYMM (cymm@trinidad.net)
Date: Mon Jul 24 2000 - 04:33:16 MDT
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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