From: eric@flesch.org (Eric Flesch) Subject: Geometry of the 1/z Universe. Date: 1998/01/15 Message-ID: <34cdc1d8.20966081@news.uni-stuttgart.de>#1/1 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=us-ascii Organization: Internet Company of New Zealand Mime-Version: 1.0 Newsgroups: sci.physics,sci.astro 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