Fig.1. Lateral Motions across the Hypersurface
Weyl’s Hypothesis, as it is known, is not only a hypothesis, but a postulate at the foundation of Standard Cosmology. What makes the Weyl Postulate unique among other fundamental cosmological principles, such as the Mach Principle, is it’s premise that the motions of large collections of matter, such as galaxies and clusters of galaxies, are groups of particles in a fluid that follow non-intersecting, time-like geodesics. That is to say, these groups don’t collide spatially, but more-or-less maintain their particular set of spatial coordinates throughout all time, and all their metric description would be limited to their location along some time scale.
But galaxies do “collide”, but when so, are so transparent to one another that very few stars actually meet head-on; one measures the ratio between the diameter of a star and the distance between these stars at 1:250,000,000; these galaxies basically pass through one another, almost unchanged in the visible structure of their stars’ motion.
If we ignore for the present argument, the subtle changes in the motion of these stars, and the interactions of the visible gases between these stars, and recent observations of gravitational lensing in regions that are distinct and separated from these collections of stars and gases…
That the centers of these “colliding” galaxies may occupy the same set of spatial coordinates -at either different time coordinates or the same- suggests their is a balance of kinetic energy to be summed in their lateral motion across the hypersurface. Although relatively small, this lateral motion may be contained in the motion of larger groups that follow longer paths. For example, members of the Local Group are moving in relatively the same direction. Is this motion due to the Newtonian gravity of the Great Attractor alone, and only a small irregularity that can be ignored, as postulated by Weyl, or is the motion of the Local Group determined by initial velocity components unrelated to neighboring cosmological structures?
Fig.2 Space-Time diagram of the hypothetical go disassociation
go = g + + g -
In the theoretical context hypothesized here these lateral motions are not ignorable: the total motion of these groups, as a sum of directional velocity vectors along the hypersurface of the Universe -with a sign, positive or negative, to some arbitrary origin- although prefer no orientation, and therefore contribute no net force to adjoining groups, have geodesics that are, nonetheless, space-like and would amount to measurable work if summed along finite paths of individual groups.
The source of this work will be discussed in future articles, to paraphrase: a pair of hypothetical particles constitute the go, that follows the non-intersecting time-like geodesic of Weyl, and is merely the midpoint of its previous disassociation into complementary components, the pair g-and g+.
The pair separate following intersecting, space and time-like geodesics. See Figure 2.
Their number, respective properties, and behavior would determine the cosmological structure of the Universe. Of these two particles, the g+ and the g-, one may merely be the “hole” which remains after the latter has appeared, forming a field [Dirac].