Relativity and Cosmology

   

The Flatness Problem

Authors: Gene H Barbee

Data from projects that measure and interpret the Cosmic Background Radiation [4][PLANCK] indicate that nature is “fine-tuned” to expand the universe in a way that it does not collapse or catastrophically expand. The currently popular Lambda CDM cosmology model [4] is strongly supported, meaning that critical density is very near 1. There is discussion regarding the components that make up critical density. Besides normal matter there is cold dark matter (CDM) and a Lambda term that stands for Einstein’s cosmological constant. Many appear to believe that we exist in the bottom shape shown above. Is space time really flat? This concept is associated with the hyperbolic nature of a four dimensional universe [18][19]. To understand what flat means, one must study the Robertson-Walker metric and the Friedmann and Einstein-de Sitter models [3]. I have noticed reluctance by authors to state clearly the shape of the universe. They know that curvature is at the heart of gravitation and can calculate a “Hubble length” describing how far expansion has progressed but leave the shape unstated. If it is a four dimensional sphere, its volume is infinite [19]. This document shows a way to side step the above issues. I believe we live in a spherical finite universe and the key is how we measure time. Quantum mechanics measures time and distance around a quantum circle. For light the ratio between distance and time is C, the speed of light. If space time originates in a quantum circle, the shape of the universe could be similar to the composite of many quantum circles (spheres considering the probabilistic nature of position around a circle). The Robertson-Walker metric [18] satisfies the global condition that space time is homogeneous and isotropic (no preferred position) but the surface of a sphere also has these properties. The author developed a model called cellular cosmology and a model of the neutron mass that leads to the source of the gravitational constant [5][6][7][8][12][13][23]. A cell is one neutron (that decays to a proton) and its associated space attracted to a central neutron. Each proton contains kinetic energy that expands the cell against the gravitational field and is converted to potential energy. Breaking a large surface we will call the universe into many small cell surfaces introduces an important degree of freedom. A cell is initially the quantum circle for gravity. The circle expands and defines space. As it expands it becomes non-quantum and protons are allowed inside the sphere. Protons appear to be around us and able to move relative to one another obeying special relativity. The space we exist in incorporates the Lorentz transformation and many call this space time. The general theory of relativity states roughly that “space time is curved by mass and mass follows curvature”, approaching Newtonian gravity. But the other three forces (interactions) of nature are also based on the curvature of quantum circles. The author’s unification theory [12] is reviewed for comparison in Appendix 3.

Comments: 30 Pages. Please contact Gene at genebarbee@msn.com

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Submission history

[v1] 2016-06-24 21:43:31
[v2] 2017-01-22 17:36:46

Unique-IP document downloads: 784 times

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