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From: Thomas Heger <ttt_heg@web.de>
Newsgroups: sci.physics.relativity
Subject: Re: No true relativist!
Date: Tue, 12 Nov 2024 09:05:07 +0100
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Am Dienstag000012, 12.11.2024 um 06:06 schrieb LaurenceClarkCrossen:
> Mr. Hertz: The article, "Poincaré and Cosmic Space: Curved or not?" by
> Helge Kragh gives the history of how the elementary error of reifying
> space became respected and prestigious thanks to Schwarzschild and
> Einstein carrying it over the finish line. Most scientists knew it was
> fallacious and it only gained acceptance slowly. From the article it
> appears that the key is the idea that non-Euclidean geometry is more
> empirical than Euclidean. After all, no one has been able to prove the
> fifth postulate that parallel lines never meet. However, no one has ever
> proven that they do. The idea that the universe is spherical given the
> vast extent of it now known would make the curvature infinitesimal so it
> is non-falsifiable. This shows that non-Euclidean geometry is not more
> empirical.
> 
> Elementary logical analysis remains sufficient to disprove non-Euclidean
> geometry. Obviously spherical geometry and geometry describing other
> shapes is valid. It is only the reifying space that is absurd.
> 
> Poincare correctly understood that geometry cannot be reified (in
> Einstein's words, "'geometry alone contains no statements about objects
> of reality, but only geometry together with physics.'"["Poincaré and
> Cosmic Space: Curved or not?" Helge Kragh]


You understand 'geometry' as 'relations in euclidean space', while 
actually higher dimensions have also an embedded geometry.

Therefore you are right, that Euclidean geometry does not tell anything 
about material objects.

But what about spaces with higher dimensions, from where our observable 
universe is an observable subset?

Since our universe contains matter, the superset of our observable space 
must have a connection to matter, too.

Such a space could be build from the equivalent to a point (but with 
more features than than only three spatial dimensions).

This had to look from any perspective like a valid universe, because our 
current position in it is not supposed to be that special.

So: what construct would fulfill this requirement???

My view:

I assume spacetime of GR would exist and was build from 'elements', 
which behave 'anti-symmetric'.

E.g. assume, that each 'point' is actually a bi-quaternion, which are 
connected to their neighbors in a multiplicative fashion according to
p' = q * p * q^-1

Than local time would be a so called 'pseudoscalar' and imaginary to the 
so called 'hyperplane of the present' as if that was rotated by a 
multiplication with i.

Then matter could be ragarded as 'timelike stable patterns of/in spacetime'.

(a somehow better behaviour seem to have so called 'dual-quaternions').

....


TH