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ENTROPY-POTENTIAL ENERGY, How it related to spacetime

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yquantum

Posted: Nov 1 2006, 01:42 AM

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Will we find the Higgs Boson?

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jal, C2, "THEY", NF, bee, et al,

I guess I missed the party, been busy working dealing with a problem that needed to be looked into.

I truly hope everyone will find there place under the SUN, with a cool drink near by.

QUOTE

A body of work such as Pasteur’s is inconceivable in our time: no man would be given a chance to create a whole science. Nowadays a path is scarcely opened up when the crowd begins to pour in.

Jean Rostand

Next time jal, "THEY", "2" [hope the music and physics goes well and you "2" take care.

ciao_
yquantum

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disce quasi semper victurus vive quasi cras moriturus
+ If you can't explain it simply, you don't understand it well enough.

This document was prepared as a service to the the physic community. Neither the United States Government nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, product, or process disclosed, or represents that its use would not infringe privately owned rights.

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jal

Posted: Nov 1 2006, 01:56 AM

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Good Day yquantum

Welcome!

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Nowadays a path is scarcely opened up when the crowd begins to pour in.

I'm going to let the partyer have fun.... I'm going to take a nap near the door to welcome any latecomers.

jal

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yquantum	Posted: Nov 1 2006, 03:05 AM Quote
Will we find the Higgs Boson? Group: Members Posts: 1376 Joined: 19-March 05 Positive Feedback: 74.19% Feedback Score: 14	I wish you the very best, Sir. jal. y -------------------- disce quasi semper victurus vive quasi cras moriturus + If you can't explain it simply, you don't understand it well enough. This document was prepared as a service to the the physic community. Neither the United States Government nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, product, or process disclosed, or represents that its use would not infringe privately owned rights.
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RealityCheck	Posted: Nov 1 2006, 05:55 AM Quote
Advanced Member Group: Members Posts: 5365 Joined: 1-July 05 Positive Feedback: 68.24% Feedback Score: 16	. Hi jal! Hi everyone! Sorry I'm late! Boy, I could hear the racket from all the way down the street....aren't you afarid the neighbours will complain, jal? hehehe. jal, I'm also sorry to come empty handed (except for this virtual bottle of wine). Medical problems, computer problems and sundry distractions have been hampering the finalisation of an ELECTRO-MAGNETIC/PHOTONIC PROPAGATION/STRUCTURE explanation which I was hoping to finish in time to bring to your party. And the TOE 'implications' have also been delayed, so I couldn't bring THEM either. Sorry! But are you going to have ANOTHER PARTY ANY TIME SOON? I think I'll manage to bring something THEN! BTW, who chose the music....TRoc? Wow! It's got a great 'backbeat' to it, hehehe! Gotta go now. Cheers all! See ya at jal's NEXT TIME. RC. . This post has been edited by RealityCheck on Nov 1 2006, 06:43 AM
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fivedoughnut	Posted: Nov 1 2006, 06:49 PM Quote
Member of the "forum mafia" Group: Members Posts: 1667 Joined: 13-November 05 Positive Feedback: 57.14% Feedback Score: 32	Jal, Thanks for everything, we all owe you so much. ....... Sadly my 'spell' @ the party was somewhat brief ..... kids .... 5 of them! ..... I'm afraid they'll always come 1st. Daddy 5-D.
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jal

Posted: Nov 26 2006, 07:05 PM

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TRoc!

It’s a gem!! You came late for the party but you are making it real!
I’m going to enter it into the discussion and summary.

http://arxiv.org/PS_cache/physics/pdf/0207/0207116.pdf
Work functions, ionization potentials, and in-between:
Scaling relations based on the image charge model
Kin Wong, Sascha Vongehr, and Vitaly V. Kresin
Department of Physics and Astronomy,
University of Southern California, Los Angeles, CA 90089-0484, USA
(Dated: July 28, 2006)

QUOTE

1. Cubeoctahedron
The cubeoctahedron is a shape with small surface area which can be cut out of an fcc crystal. The number of hard spheres as a function of the number of shells k is given by65
N = (10/3)k3 − 5k2 + (11/3)k − 1. The outer radius R is given by R = (2k − 1)r0. For
large k this becomes R ≈ 2kr0 ≈ 2(3/10)1/3r0N1/3 ≈ 1.339r0N1/3. The same expression can be derived by evaluating the volume of the circumscribing sphere relative to the sum of the volumes of the small hard spheres67.

4. Icosahedron
The icosahedron has the highest symmetry of all discrete point groups. Although due to it’s five-fold symmetry, the icosahedron does not form bulk crystals, it can be considered as a slightly distorted fcc crystal. The icosahedron structure has been observed for small clusters of inert-gas clusters, Ca, and Mg clusters (see references in 65). The relationship between the number of hard spheres and the number of shells is the same as for the cube-octahedron65: N = (10/3)k3 − 5k2 + (11/3)k − 1. The radius is also given by the same expression as for the cube-octahedron R = (2k − 1)r0. The resulting expression for the cluster radius is therefore the same as for the cube-octahedron. For large k the radius is:
R ≈ 2kr0 ≈ 2(3/10)1/3r0N1/3 ≈ 1.339r0N1/3.

VI. SUMMARY
The main results of this work can be summarized as follows.
(1) Starting with an expression for the electron removal energy in terms of the image charge potential for an isolated spherical particle and a surface cutoff parameter [Eq. 3], we explored how this model may be consistently applied to metallic systems ranging from bulk surfaces to finite clusters and down to individual atoms.
(2) We showed that this approach provides a transparent physical explanation for the empirical fact that the atomic ionization potentials and polycrystalline work functions of the metallic elements exhibit an almost constant ratio of ∼ 2 over the periodic table [Eqs.
(1, 10)].
(3) We found that for most elements there is a remarkably close numerical correlation between the values of the nearest-neighbor distance in a crystal, the cube root of the atomic polarizability, and the image force cutoff parameter. This correlation may be rationalized qualitatively, but appears worthy of further study.
(4) Taking advantage of this correlation, we formulated simple expressions for the cut-off distance [Eq. (7)] and the atomic and cluster radii [Eqs. (11,14,15)]. They yield good estimates for the work function, the ionization potential, and the cluster electron removal energies by using only a single input parameter, the atomic polarizability. No extra adjustable parameters are required.
(5) Generalizing the scaling argument to the case of binary alloys, we found that it can simulate the shape of the concentration dependence of work functions of continuous bulk solutions [Eq. (12)].
(6) We also provided an analytical derivation of the connection between the geometric structure of a cluster of close-packed spheres and its outer radius. It is described by an equation of the type (13), but the precise numerical coefficient is shown to depend on the packing structure.

By generalizing, this work has application to the TOE project.

QUOTE

A significant number of first-principles calculations have been performed for work functions of metallic systems6,7,8. In addition, simple models based on semi-empirical approaches combined with classical electrostatics have been rather successful at reproducing WF trends and values9. This suggests that some features of the desired scaling law may be found by employing such a model.

In a similar spirit, let us now consider the image-force expression for the energy required to remove an electron from an isolated finite metal particle, modelled as a conducting sphere of radius R. The particle is assumed initially neutral, i.e., after the removal of the electron it acquires an unit positive charge.

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jal

Posted: Nov 27 2006, 04:24 PM

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http://arxiv.org/ftp/nucl-th/papers/0309/0309035.pdf
The double tetrahedron structure of the nucleus
Jozsef Garai
Department of Earth Sciences Florida International University University Park,
E-mail: jozsef.garai@fiu.edu
4 Oct 2003

QUOTE

Expanding a double tetrahedron formation of equal spheres arranged in fcc structure correlation between the positions of the nucleons and quantum numbers has been detected. The number of protons in the structure is not simply consistent with all the corresponding quantum numbers but also bears the same physical meaning as in quantum mechanics. The detected correlations between lattice positions of the protons and quantum numbers raise the possibility the solid nuclear structure might be able to provide an explanation for the single particle properties of the nuclei.
Other nuclear properties supporting a double tetrahedron nuclear structure are the followings.
These correlations are consistent with the physical meaning of the quantum description; therefore, a random coincidence should be excluded. The detected correlations raised the possibility that the double tetrahedron crystalline model might provide the first comprehensive description of the nuclei by combining the individual particle, collective, and clustering characteristics of the nuclei.

http://www.npaci.edu/successes/2001_tetra.html
http://www.hno.harvard.edu/gazette/2001/08.16/06-atomic.html
http://www.npaci.edu/enVision/v17.3/students.html#chemical

QUOTE

Chan used a variation of a well-known mathematical technique to discover a novel arrangement of atoms missed by other scientists. He found that 78 neutral atoms could theoretically settle into the shape of a particular double icosahedron.
Leary and his colleagues use a variety of modeling techniques to examine how 10 to more than 100 neutral atoms arrange themselves into the lowest energy states possible. Their method works like an explorer scanning new countryside. An algorithm hops from one possible energetic state to another, each of which corresponds to a different cluster geometry, looking for the one with the deepest valley.
"This new double-icosahedral structure has a lower potential energy than the other structure," said Chan. This means that his structure, not the single icosahedral structure previously reported, may represent the actual 3-D structure of 78-atom clusters in nature.

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http://www.rwgrayprojects.com/synergetics/s06/p2200.html
R. Buckminster Fuller

QUOTE

624.03 Both the positive and negative tetrahedra can locally accommodate the 45 different energy exchange couplings and message contents, making 90 such accommodations all told. These accommodations would produce 30 different "apparent" tetrahedron position shifts, whose successive movements would always involve an angular change of direction producing a helical trajectory.

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There is a thread in all of those approaches.

It leads to the "SPOT".

jal

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jal

Posted: Nov 30 2006, 05:07 PM

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Does there exist a mathematical approach that can analyse the "SPOT"?
Try sheaf cohomology, Abstract Differential Geometry
http://arxiv.org/PS_cache/hep-th/pdf/0610/0610065.pdf

Discretising differential geometry via a new product on the space of chains
Vivien de Beauc´e and Siddhartha Sen
† Department of Physics, Hokkaido University, Sapporo, 060-0810 - Japan
E-mail: debeauce@particle.sci.hokudai.ac.jp
‡ I.A.C.S Jadavpur, Kolkatta 700032 - India
‡ School of Mathematical Sciences, UCD, Belfield, Dublin 4, Ireland
E-mail: sen@maths.ucd.ie
05 Oct 2006

QUOTE

5 Discussion
In order to test the usefulness of the method in concrete applications, we propose three concrete
applications:
• Topological field theory: calculation of the Reidemeister torsion in a combinatorial way.
• Simplicial gravity: comparing with 2D random surface models for gravity, for Nambu-Goto and for actions including matter fields.
• Electromagnetic theory: discretising Maxwell’s equations.

http://arxiv.org/PS_cache/gr-qc/pdf/0607/0607038.pdf
A Dodecalogue of Basic Didactics from Applications of Abstract Differential Geometry to Quantum Gravity
Ioannis Raptis_
July 10, 2006

QUOTE

We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG)

Comments, Discussion welcomed
jal

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jal

Posted: Mar 24 2007, 11:02 PM

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The paper that you have all been waiting for.

"SPOT" HAS MADE IT IN THE arxiv.org

http://arxiv.org/PS_cache/gr-qc/pdf/0610/0610056.pdf
Quantum Mechanics and the Generalized Uncertainty Principle
Jang Young Bang_ and Micheal S. Berger†
01 Dec 2006

QUOTE

VI. SUMMARY AND CONCLUSIONS
We have derived the generalized uncertainty principle from a toy model of discretized space by considering quantum mechanics on a circle where the compacification involves the momentum. This model may be useful in exploring how the ultraviolet limit is approached in more realistic models of discrete spacetime or models of quantum gravity with a fundamental or minimum length. This may result in an improved understanding of the origin of the generalized uncertainty principle in theories of quantum gravity.

THIS IS ONLY THE BEGINNING OF WHAT IS TO COME.

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jal	Posted: Jun 12 2007, 02:06 PM Quote
Advanced Member Group: Members Posts: 1459 Joined: 23-October 05 Positive Feedback: 64.29% Feedback Score: -15	THE "MATH KIDS" ARE WORKING ON MY APPROACH -------------- http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.1534v1.pdf Coupling gauge theory to spinfoam 3d quantum gravity Simone Speziale∗ Perimeter Institute, 31 Caroline St. N, Waterloo, ON N2L 2Y5, Canada. June 11, 2007 ----------------- If you got trouble understanding this paper then go look at my simple presentation in my blog and the spinning double tetra. ------------------- Previous papers http://arxiv.org/PS_cache/gr-qc/pdf/0606/0606074v2.pdf A semiclassical tetrahedron Carlo Rovelli and Simone Speziale_ CPT†, CNRS Case 907, Universit´e de la M´editerran´ee, F-13288 Marseille Perimeter Institute, 31 Caroline St.N, Waterloo, ON-N2L-2Y5, Canada March 31, 2007 http://arxiv.org/PS_cache/gr-qc/pdf/0611/0611097v1.pdf Grasping rules and semiclassical limit of the geometry in the Ponzano–Regge model Jonathan Hackett and Simone Speziale 17 Nov 2006 --------------- jal Any discussion welcomed -------------------- Moved 10 June 2008 JAL'S BLOG http://www.physicsforums.com/blog.php?b=2
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