From: eric@flesch.org (Eric Flesch)
Subject: Geometry of the 1/z Universe.
Date: 1998/01/15
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The hyperangle rotates linearly with distance. There, I've said it.
That's it. That's all. No no, really, there is no more. OK?
That's all it takes to solve the 1/z cosmology which yields the
correct static model of the universe. Just one little rule.
Here is how this rule builds the universe (the term "hyper" refers to
projection into a 4th dimension orthogonal to 3-D space):
1) THE REDSHIFT: Rotation of the hyperangle leads to a hyperbolic
universe, thus space expands hyper-orthogonally with distance. While
not a problem for travellers, photons, having no classical existence
between emission and absorption, display their initial
hyper-orientation (i.e. orientation on the surface of the
hyper-circle) upon registration. The effect is hyper-polarization,
and only cos^2(A) of the photon's energy is received, where A=relative
hyperangle. The rest (sin^2(A)) is returned to the hyper-domain.
This causes the cosmological redshift, and redshift (z) = tan^2(A).
2) THE INVERSE THETA - Z CORRELATION: A little-publicized aspect of
hyperbolic geometry is that "shells of space" appear more distant than
actual travel-time, compared with flat Euclidean, because the larger
hyperbolic volumes are re-mapped into our Euclidean 3-D perspective.
Thus distances approaching hyperangle pi/2 are manifested as many
(apparent) distances which bear redshifts inversely linear to the
angular size (theta). Thus, the 1/z criterion is met.
3) THE PHYSICAL HYPERSPHERE: The *linear* rotation of the hyperangle
with distance shows a hypercircle, but the required space is
hyperbolic (as Einstein postulated), not hyperspherical. However, a
boundary point to the hyperbola can be thought of as an asymptote
(line in the cone) h^2 - x^2 - y^2 - z^2 = 0. It follows that the
boundary (del)H^4 is a sphere. Thus the hyperbolic space is bounded
by a physical hypersphere. The hypercircle demonstrated by the linear
hyper-rotation is a circular hyper-torus (i.e. a donut) with a
vanishingly small center, nested contiguously within the hypersphere.
The hypertorus is excluded, the remainder maps the hyperbolic
curvature of space within the physical hypersphere. The curvature
mapping places the observer at the center, with a covariant
description at the opposition point where the hypertorus meets the
hypersphere, at the surface.
A simpler model uses just the surface of the hypersphere, without any
hypertorus. But this may not match observation of the theta-z
correlation. If it can be reconciled to observation, then the simpler
model is naturally to be preferred.
Note that at hyperangle pi/2 the visible terminus of the universe (T)
is reached. Travelling 4T (i.e. 2*pi) in any direction returns you to
your starting point.
4) THE NATURE OF GRAVITY: It is immediate to posit that the surface
of the hypersphere is the 4-D playing field on which Einstein's GR
rules. Thus massive bodies depress the surface of the hypersphere.
Thus the hypersphere attracts massive bodies. Thus the hypersphere
gravitates. Thus, by Occam's Razor, massive bodies do not gravitate
as this assumption is unnecessary to the functioning of gravity. Thus
gravity is no longer a law of our universe, but of the hypersphere
exclusively. This explains the failure of all attempts at grand
unification theories & quantum gravity.
It is immediate that gravity is a function of distance from the center
of the hypersphere. Thus G is not constant, but varies according to
hyper-topography, although homogeneous on a large scale.
Specifically, in our universe, G increases in the presence of large
masses. This simplifies GR equations and provides a basis for
experimental comparison.
Eric Flesch
15 January 1998