Octblog 2024
Welcome to the upgraded site. The new ‘Hamburger’ icons in each section open up their various subsections.
The Geometry, Topology, and Chirality of the Universe.
This crude visual aid for a private lecture on the geometry of the universe.
Shows how a sphere can stereographically project onto a plane.
(Hockey ball with many drill holes for galaxies, black paint and a torch.)
This gives a lower dimensional representation of how a hypersphere can stereographically project into a sphere. Imagine that the plane into which the sphere projects represents a plane bisecting a sphere. Although this reduced dimensional visual aid represents a hypersphere by a sphere, and a sphere by a plane, it does show how distances in a hypersphere will become exaggerated to observers who assume that they inhabit a gravitationally flat universe and deceive them into hypothesising an expansion driven by some mysterious dark energy.
See Hypersphere Cosmology equations 16 and 17 and Septblog 2024 on this site, which make a seemingly overwhelming case for the Hypersphere model of the universe.
This month’s Apophenia concerns the Chirality (handedness) of the Universe.
We can represent a Hypersphere by a Hopf Fibration which shows it as decomposed into a fibre bundle of circles each of which passes inside all of the other circles. In Hypersphere Cosmology the galaxies all Vorticitate around the circles of the Hopf Fibration. This gives the universe no net angular momentum although it allows it to conform to the Godel metric. The circles of the Hopf Fibration each pass within all of the other circles.
Few if any seem to have noticed that a hypersphere submits to two possible Hopf Fibration modes as shown in the following picture.
These keyring models lay flattened onto a surface for clarity, but in reality, the rings can lie a bit more separate from each other to form more of a spherical type of configuration.
Notice that the two Fibrations remain distinct, and we cannot superimpose them by any form of re-orientation in three dimensions, they constitute mirror images of each other. The one on the left has a Left Handed Fibration and the one on the right has a Right Handed Fibration.
Which chirality corresponds to the universe we inhabit?
Almost certainly we inhabit a universe with a Left Chiral Vorticitation - a Left Handed Universe!
The supporting evidence seems strong but kind of weird: -
1) The weak nuclear force remains exclusively left handed. All neutrinos (the simplest matter particles) rotate anticlockwise.
2) Most terrestrial chiral biomolecules show a preference for left handedness.
3) Rotating spiral galaxies all over the universe show a preference for left handed (anticlockwise) rotation.
4) Galaxies all over the universe seem predominantly aligned with respect to their nearest three neighbouring galaxies, in left handed tetrahedral orientations.
Just how the anticlockwise (left handed) vorticitation of the entire universe could induce these mysterious microcosmic, midi-cosmic, and macrocosmic symmetry breakages remains an interesting question, yet it seems a fair bet to predict from Hypersphere Cosmology that this universe has a Left-Chiral Vorticitation. It will however probably take a lot of long timescale observation of the relative movements of far distant galaxies and some heavyweight computer analysis to confirm this.
Topology clarification. The keyring models of the Hopf Fibration do perhaps not make the left or right twists of the fibre bundle entirely apparent. We can easily make it more apparent with three pieces of string. Three pieces of string can represent the spacetime world lines of three bodies in a hypersphere.
So, flip one piece of card over twice in the same direction to rotate it by 360 degrees and then free the ends from the cards and tie them together. This makes three interlinked circles, showing how within a hypersphere all particles and bodies move along great circles which (over vast timescales) all pass within each other.
It works with any number of strings, and the result looks oddly similar to various mystical figures from the Vesica Piscis to various Celtic and Tibetan knotwork designs.
Magic News.
https://www.amazon.co.uk/This-Chaos-Embracing-Future-Magic/dp/1578638739