# UNIVERSE MODEL EXPANSION (cont.)

Posted Jun12-08 at 11:19 AM by jal
Updated Dec20-09 at 12:18 AM by jal

Sphere Packing and Inverse Square law
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You can use a High Tech approach, paper and pencil or a Low Tech approach, a computer.
Use 12 sticky circles on an orange. Make sure that all the circles are separated by another circle of a different color to represent the minimum length separations. This will result in you having 6 white and 6 colored circles on the circumference, plus 6 on the top and 6 on the bottom. These are the shadow projections of the kissing point on the 13th inner sphere.
You have established the length of the circumference (12 minimum lengths) and so you can get the radius of the sphere by using a calculator from the web. You have also established that the smallest sphere has 24 units.
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2. Now, let’s do the expansion.
Get some graph paper. Draw that circumference then draw another circle at 2R and 4R.
These circles will represent the expanding circumferences at the inverse square law.
Draw 6 lines from the center. ( 0, 60, 120, 180, 240, 360 degrees) These lines will be going through the center of each kissing spheres that are on the circumference.
On those lines, ( 0, 60, 120, 180, 240, 360 degrees r, 2r, and 4r) draw the minimum length circles. You will notice that there is a lot of room for more circles in between the lines.
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Those using a computer program will get a more accurate number because they will be able to “jiggle” the location of the spheres in 3d.
What is the “jiggling” formula to get the densest packing?
What “jiggling” formula did the universe use as it expanded?
At what step do the spheres get back to their original positions on the 0, 60, 120, 180, 240, 360 degrees lines?
Does the expansion always increase or are there any backward steps before going to the next expansion level?
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For those that are really advanced,
1. Using 2d surfaces of one unit diameter, you can place those surfaces at different angles and different positions within each “cubes/spheres” as long as they do not violate minimum length. They cannot remain “locked” in that position as the sphere expands. They could come back to that position if there is “room” for them to move without violating the minimum length between the units.
2. Is the Inverse Square Law violated.
3. Can you think of an experiment to verify if the densest sphere packing does or does not violate the Inverse Square Law?
4. Can we get an accuracy to 15 decimal places? (The proton is at about 10^-15 m and the planck length is at 10^-33 m ).

Search the web …. Maybe someone has already done all of this work and found all kinds of “unusual behaviors”.

Let me know what you find.

If you figured out that this could apply to an expanding Black Hole … give yourself a pat on the back.

You could make a model with beads. From a center disc, string your beads of alternating colors or spacers at 60 degree.

Work on the model … you will have fun!
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Some cool references!
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http://arxiv.org/abs/hep-ph/0611184
Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
Authors: D.J. Kapner, T.S. Cook, E.G. Adelberger, J.H. Gundlach, B.R. Heckel, C.D. Hoyle, H.E. Swanson
(Submitted on 14 Nov 2006)
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http://arxiv.org/abs/hep-ph/0611223
Particle Physics Implications of a Recent Test of the Gravitational Inverse Square Law
Authors: E.G. Adelberger, B.R. Heckel, S. Hoedl, C.D. Hoyle, D.J. Kapner, A. Upadhye
(Submitted on 16 Nov 2006 (v1), last revised 7 Feb 2007 (this version, v3))
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http://arxiv.org/abs/0706.3898
Scalar modifications to gravity from unparticle effects may be testable
Authors: Haim Goldberg, Pran Nath
(Submitted on 27 Jun 2007 (v1), last revised 4 Dec 2007 (this version, v3))
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http://arxiv.org/abs/hep-ph/0608078
Evading Equivalence Principle Violations, Cosmological and other Experimental Constraints in Scalar Field Theories with a Strong Coupling to Matter
Authors: David F. Mota, Douglas J. Shaw
(Submitted on 7 Aug 2006 (v1), last revised 1 Dec 2006 (this version, v3))
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http://arxiv.org/abs/0805.3430
Beyond the Chameleon Mechanism
Authors: David F. Mota, Douglas J. Shaw
(Submitted on 22 May 2008)
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http://arxiv.org/abs/hep-th/0609155
Gauss-Bonnet Quintessence: Background Evolution, Large Scale Structure and Cosmological Constraints
Authors: Tomi Koivisto, David F. Mota
(Submitted on 22 Sep 2006 (v1), last revised 3 Nov 2006 (this version, v2))
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http://arxiv.org/abs/hep-ph/0303057
Current Short-Range Tests of the Gravitational Inverse Square Law
Authors: Joshua C. Long (Los Alamos National Laboratory), John C. Price (University of Colorado)
(Submitted on 7 Mar 2003 (v1), last revised 4 Apr 2003 (this version, v2))
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~~~ Since I’m learning … I reserve the right to change my mind ~~~
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