Re: No true relativist!

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