QUARKS AND LEPTONS

SPACETIME STRUCTURE OF QUARKS AND LEPTONS
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Gravity: In the combinatorial array below, rishon fundamentals are considered to be the elements of the combinatorial groups. A given order of groups may constitute a spin network (See Video on right). Each subset of groups (relations), in the array, identified by a common beginning letter constitutes the volume at a point in the spin network.The order (r=3) groups identified by a given letter are produced by the lower order (r=2) group, identified by the same letter, with N elements. Note that each subset of groups identified by a common first letter is patitioned into smaller groups with numbers of elements starting at (J=1) and increasing in counting order to N-1. The number of unions and elements (S) produced for each N-1 partitions of the order (r=3) groups will equal [J(J+1)/2]-J. So, For the spin network, equivalent to a set of order r-3 groups, a point or vertex is designated by the letter identifying a subset of partitioned groups. In the spin network graph, each partition of the subset of groups is indicated by a line segment terminating at that point or vertex. The volume, as noted in the video, has a factor equal the squareroot of J(J+1). This factor, as seen, is associated with the count of relations between rishon fundamentals. In this way, the geometry of spacetime volumes, are seen as comprised by the relations of rishon fundamentals. Then, as suggested previously, the expressions of relating rishon fundamentals in this spacetime are the foundational elements of the standard model particles and forces. These foundational elements are the T and V rishon elements as articulated by the phenomenological reasoning on the first page. Relating rishon fundamentals are then the constituents of spacetime and are notable within spacetime as the T and V expressions of that relating. These expressions produce the elements of the standard model, Quarks and Leptons. T's and V's associated with or expressing a given rishon fundamental will not then have dynamic interactions but will only compose the spacetime structure of a quark or lepton. See videos below for more detailed explanation.

See Video to the Right Let's analyze the graphic representing the rishons' T'Groups T^AC and T^CA. These have three colored areas. The colors (yellow and red) of the bottom cones represent the unique series of expressions or T'elements that each relating rishon exhibits as an object. The colors (purple and green) on the left side of the semi-circles represent the eliminations of uniqueness by the V'elements (the binding energy). This dynamic of the elimination of uniqueness or differentiation of rishon expressions is necessary to conserve the fundamental status of rishons as wholely unique. The colors (red and yellow) on the right side of the semi-circle represent the observable relatedness of rishons one to an other rishon. The expressions of relating rishons must combinatorically sum to zero else the existence of rishons as wholely unique is contradicted by the rishons' appearances. Likewise the graphic representing the rishons' V'Groups V^AC and V^CAare similarly organized. Note that the expressions' and eliminations' colors of the rishons' V'Groups (purple and green ) are the opposite of the rishons' T'Groups. Since the wholely unique rishon comprises its T and V elements, the features of of the appearing elements sum to zero.
As suggested before, The expressions of relating rishons must combinatorically sum to zero else the existence of rishons as wholely unique is contradicted by the rishons' appearances. Therefore these appearances can only express partnered with negations, and thereby the set of rishon elements sums to zero. So the rishon groups AC (yellow cone) and CA (red cone) are partnered with the rishon anti-groups AC (purple cone) and CA (green cone). The electromagnetic force then may arise from this necessary negation of rishon elements expressing relatedness of rishons one to an other rishon.
See Video to the Right Every rishon, as an observable or object, comprises a series of order two expressions, the T and V elements of relating rishons. Time-space arises with rishon expressions. In other words, one rishon relates to the expressions of another rishon as the rishon existing in time-space. The observations of expressions may be likened to turning an object in one's hands to reveal its hidden dimensions. The 3d graphics, to the left, organizes the series of expressions composing the muon and muon neutrino, u-quark and d-quark. See Video to the Below The 3d graphics below are animations that demonstrate how fundamental forces may change the fundamental rishon objects: the muon, muon-neutrinos, u-quark and d-quark. You may need to refresh webpage to start apps. The changes in response to the electro-dynamic (electric/magnetic) force are demonstrated by clicking on the arrow keys. Note the change of the spin quanta The changes in response to the chromo-dynamic (strong) force are demonstrated by clicking on the cube, or pressing the space bar. Note the change in the color of the quarks The changes in response to the weak force are demonstrated by clicking on the [x] buttom. Note the change in the type of quark and lepton
You can change the 3d graphics to display the linear arrangement of the proton, neutron, muon and muon-neutrino pictured below. These 3d graphics and other combinations, not including two special groups of 3 T'elements and 3 V'elements, are the field of rishon and anti-rishon expressions, possible by relating 3 fundamental rishons and compose the known stable particle systems. Thereby the composition of exclusively quark and lepton matter systems from equal fields of matter and anti-matter is demonstrated. The T's and V's not included are addressed on other pages to explain the three generations of quarks and leptons. Once you configure the 3d quark and lepton objects to match the linearly arranged stable particle systems, you can explore the the electromagnetic, strong and weak forces as indicated above. Using the arrow keys, space bar or plus and minus keys change the faces of one of the 3d objects. Then find another 3d figure, sharing a face with the changed object, and using the same type keys change the faces on this figure until its faces are again unique. The total electric and spin quantum number should always sum to zero for the particle systems if the faces on each 3d object or unique. With careful observation you will note patterns in the orientations of the 3d objects.


	Red Quark	Blue Quark		Yellow Quark


	Red Quark	Blue Quark		Yellow Quark


	White Lepton		White Lepton
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