[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.