THIS IS THE MAIN LINK IN THIS PILE OF SOUP, THIS HAPHAZARD AGGREGATE OF LINKS.
We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d
conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually
described by a geodesic in spacetime, becomes instead a choice of ways to reverse the conformal
compactication of a Euclidean vector space up to scale. The observer’s `current time,’ usually
given by a point along the geodesic, corresponds to the choice of scale in the decompactication.
We also show how arbitrary conformal 3-geometries give rise to `observer space geometries,’ as
dened in recent work, from which spacetime can be reconstructed under certain integrability
conditions. We conjecture a relationship between this kind of `holographic relativity’ and the
`shape dynamics’ proposal of Barbour and collaborators, in which conformal space takes the
place of spacetime in general relativity. We also brie y survey related pictures of observer
space, including the AdS analog and a representation related to twistor theory.
THE REST OF THIS POST IS A MENAGERIE, sort of like a Bar-Kays discography. And look at this because Brain Freeze:
Use this link above about lengths to visualize generalized hamsters, or to classify magnitudes of decompactification in terms of spacetime. If you’re all up in Cartan spacetime like R.Kelly up in a bucket of fetid doodoo butter, please look into info about 4th dimensional representations of spheres, which is easy to visualize if you can visualize a sphere being turned inside out, which I think you can do by focusing on the Eötvös effect.
“You are the music of the spheres heard from the particular vantage point that is you.”
― Julian B. Barbour
And waste an hour, because it doesn’t exist, anyways.