Stephen P. King (stephenk1@home.com)
Sun, 11 Apr 1999 11:17:46 -0400
Hi Guys,
I found this while reading a post on sci.physics.research:
Re: Non-continuous space
On 10 Apr 1999 18:33:57 GMT, jmperrochat@csi.com wrote:
>Edward Startsev a ecrit dans le message
><3707C7C2.620FE101@me.rochester.edu>...
>
>>Could anyone give me some pointers on using non-continuous space (say
>>fractal-like) to model the physical space continuum?
>
>You could check works by El Naschie (cantorian space-time)
>and Moulin (arithmetic relators).
>
>L.Nottale dropped the hypothesis of differentiability
>(but not continuity) in his generalization of GR called
>scale relativity.
>In his theory, particles are geodesics in a non-differentiable
>(fractal) space-time.
>
>The new nondifferentiable mechanics uses a special
>scale-covariant derivative.
>Newton's equation of dynamics, once made scale-covariant
>by replacing the usual time derivative by the new covariant one,
>is integrated in terms of a Schr=F6dinger equation.
>See predictions/results :
>http://www.daec.obspm.fr/users/nottale/ukmenure.htm
>
>Meilleures salutations
>
>Jean-Michel
>
I am looking at the site:
http://www.daec.obspm.fr/users/nottale/ukmenure.htm
I like this:
"The fundamental principle of ScR:
It is an extension of Einstein's principle of relativity. It can be
stated as follows: The laws of nature
must be valid in every coordinate systems, whatever their state of
motion and of scale. The
results obtained show once again the extraordinary efficiency of this
principle at constraining the
laws of physics."
Peter Wegner wrote:
>
> Stepehen and Ben
>
> I hesitate to come in in the middle of the discussion about finiteness versus infiniteness of the universe.
>
> But I have a preference for an infinite model, at least from the subjective viewpoint of observers, for the > following kinds of reasons.
>
> 1. From the viewpoint of general principles of relativity, observable properties should not depend on > whether you are near the edge of the universe or near the center.
> If the observer cannot detect the edge of the universe this suggests an infinite model, at least from the > subjective viewpoint of any observer.
>
> 2. I prefer to think of the universe as an open rather than a closed system
> in that any part can be subject ot forces from unknown parts.
> An open universe is subject to nondeterministic external forces, while a closed universe can be modeled at > some level in a deterministic (algorithmic) way.
> The existence of a closed deterministic universe seems to violate a general relativity principle.
> Openness is better matched by an infinite than a finite universe.
> This notion of openness is like that in topology.
> Topology allows us to clearly see that open sets can be finite, for example the open unit sphere, while > still having the property that the complete set cannot be effectively defined.
Peter, I assume that the unenumerability of possible interactions of
MIMs related to this openness. Do you think that Hitoshi's LS can be
characterized as MIMs?
> 3. Mandelbrot sets are an attractive model for an infinite universe.
> This would allow a principle of relativity for scale, in that structures at any
> particular scale would replicate themselves at both lower and higher scales.
> Some of Eddington's work suggests that the scale factor for replication might be about 10**80.
> If the universe has relativity of scale like a Mandelbrot set it is an infinite universe.
>
> Ben, has there been work on modeling the universe in terms of Mandelbrot sets?
> Are there models that focus especially on open versus closed systems?
>
> peter
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