[AntonioLao]

If there is double loop quantum gravity (LQG) it can modify 2D spin networks by extending them into 3D double linked loops networks. However, in this case there are no quanta of volume or area. Since double-loop is fundamentally a genus=2 topology. It is a doubly background independence spacetime structure. Where and when quantized this structure can be used to describe two distinctive spacetime charges in only one dimension with a principle of directional invariance and its 8 directional properties. Logically, the word ‘gravity’ implies a definition of mass as gravitational charge. This mass charge is basically always attractive. On the other hand, the spacetime charges can be both attractive and repulsive with units’ charge of +1/6 and -1/6. Similar to the quarks these are fractional electric charges of the unit charge of the electron. Nonetheless, depending how the spacetime charges are combined both classical mass and charges (e.g. electric and color) can be described by simply using the one dimensional double loop holes geometry (LHG).

LHG is fundamentally equivalent to a Hopf link of knot theory see http://en.wikipedia.org/wiki/Hopf_link and http://mathworld.wolfram.com/HopfLink.html and http://en.wikipedia.org/wiki/Knot_theory. It is the simplest nontrivial knot composed of 2 linked circles. Since it is the simplest it is suitable for describing the ground state of the quantum vacuum of zero-point energy. More complicated knot structures would then represent excited states of the quantum vacuum. The more convoluted and twisted the knots become the more energy they represented. However, where and when their radii also simultaneously shrunk toward zero these newly formed compact structures take the shapes of elementary particles. Odd combinations become fermions. Even ones become bosons. Nevertheless, the total number of positive and negative LHG is always an even number. The simplest combination being that of electron neutrino: 1H+ and 1H-. The muon neutrino: [3H+][3H-]. The tau neutrino: [5H+][5H-]. The electron: [1H+][7H-]. The photon: [4H+][4H-]. The down quark: [1H+][3H-]. The up quark: [5H+][1H-]. The strange quark: [3H+][9H-]. The charm quark: [15H+][3H-]. The bottom quark: [5H+][15H-]. The top quark: [25H+][5H-]. The W+ gauge vector boson: [8H+][2H-]. The W- gauge vector boson: [2H+][8H-]. The Z0 gauge vector boson: [8H+][8H-]. The compositions of H+ and H- can describe every known elementary particle. The group number of LHG is directly proportional to the complexity of the convolution. Furthermore, unequal numbers of LHGs of pluses and minuses represent broken spacetime symmetry and moreover if the group number exceeds 8 then an equivalent Higgs mechanism becomes effective giving the various masses of all the elementary particles.

[Profpat]

Hi Antonio;

My Idea has three linked circles representing the bonding and asymptotic freedom of the quarks. I'll have to view your links to see what I can extract.

Best,

Pat

[Profpat]

I just looked at one of the links and found my three ring circus to my Idea. I'll read the links. Thank you very much for the links Antonio.



The Borromean rings are a link with the property that removing one ring unlinks the others

Best,

Pat

P.S The only difference is that the yellow ring I have it green for the 3rd primary color

[Profpat]

Standard diagram of the Borromean rings




A realization of the Borromean rings as ellipses

[AntonioLao]

Originally Posted by Profpat Borromean rings

At first, I thought these borromean rings could represent the color charges of QCD. Second thought, I noticed that the rings are not really linked together as pairs. Furthermore, it would be difficult to represent them using Hadamard matrices.

[Profpat]

Maybe not but I use them to describe my Idea of QCD. I'm too dumb to know that they should be inpairs. Also I noticed from a link to your link that a crystal structure of molecular Borromean rings have been reported, which to me indicates that perhaps they could form at the subatomic level.

[Profpat]

BTW Antonio, Would the 3 quarks make a tripole, instead of a dipole?

[AntonioLao]

Originally Posted by Profpat should be inpairs

This is necessary for spacetime quantization but maybe not for color charge quantization. However, in QCD there is the physical explanation for the existence of 8 gluons. Gluons would be described by 8 directional invariance properties not by knot structures.

[AntonioLao]

Originally Posted by Profpat Would the 3 quarks make a tripole, instead of a dipole

3 quarks make a baryon such as proton and neutron. 2 quarks make a meson such as pion. See please http://hyperphysics.phy-astr.gsu.edu...es/hadron.html

[Profpat]

Well I'm not too big on gluons, that is why I eliminated them from my theory. They are a theoritical particle which has not been observed yet, and I explain the 8 gluons through 8 dimensions of the mathematical octants inside any 3 D space.