- From the combinatorial formula for the number of elements (t) for a given number of order 2 combinations (s), I use the vector addition of these variables to model particle system compositions and interactions. I let (s,t) correspond to (x,y) . Introduction Below
- I Mapped to these (s) and (t) variable quantities the rishon-like T and V doublet assemblies: the number of T's in an assembly or group I set equals the (t) variable and the number of V's in an assembly or group I set equal 2 times the (s) variable. Ordered Pairs (s, t) Since reading a paper by Piotr Zenczykowski, (see link below at strategem 5) I have come to interpret the combinatorial variables (s, t) as the respective count of space and momenta vectors (x, p) in triplets suggested in Piotr Zenczykowski paper linking space and matter.
- Each of theses assemblies, I then designate a T-group or V-group of which emerges four unique doublets. T&V Groups
- I let the electric charge of a group (Q) equal 1/3 times (t). And thereby assigned quanta to the T anv V groups with the formula Q = Iz +[ (B+(S+C+B+T)) /2 ], but I let (R) the rishon number supersede B the baryon number, so Q = Iz +[ (R+(S+C+B+T)) /2 ] T&V Groups
- The mass/energy problem challenging any so called preon models I suggest may be addressed by considering the T and V groups not to be objects in spacetime but as dimensional constituents of the spactime structure of quarks and leptons. I Imagine each quark or lepton as 3d objects turning in spacetime and presenting varying dimensional faces to an observer. the varying faces are its constituent T and V groups. I have found a similar idea explored more rigorously by Piotr Zenczykowski. Click Matter Space and Rishons to view their paper.
- I there, then see emerge logical generic quarks and leptons compositions of the T-groups and V-groups as well as scalar bosons that account for the standard model particles, symetries and broken symetries. Compositions & Decays
A constituent or preon model of leptons and quarks must phenomenologically produce all particles of the standard model. In addition, the preon constituents of this model must demonstrate the symmetries and broken symmetries of the standard model. The following suggested constituent preon elements seems to meet these criteria. It provides a detailed phenomenological accounting of the standard model.
Though I proceeded from a logical rather than mathematical foundation, I arrived at *rishon-like preon elements. My preon elements are similar to the prequark candidates developed by Haim Harari, Michael A Shupe and Nathan Seiberg.
Correspondence of Combinatorics and Rishons
I represented possible fundamentals quantitatively as the ordered pairs of numbers (s , t) in a standard (x , y) orientation. Where (t) is a number of combining elements and (s ) is the number of unique unions exhibited from the order 2 combining pairs of (t) elements. Let t=N-2s , where N equals an integer value constant and s is a multiple of (1/2). So as s varies t varies. The vector addition of these ordered pairs allowed me to explore possibilities for particle interactions that compositionally account for the standard model. I was able to initially associate the quanta of electric charge with the ordered pair as Q = (t/3).
When I happened upon a Scientific American article on rishons, I noted the following possible correspondences. The (T) rishons could correspond with the number of elements (t) participating in order 2 combinations. The (V) rishonss could correspond with twice the number of order 2 combinations (s) of (t) elements.Therefore an assembly of V and T elements would map to the corresponding numbers of the ordered pair (s , t) or as noted above the count of space and momenta vectors in triplets.
I was then able to further articulate the quanta for T and V rishons using the relation. (t/3) = Q = Iz+(B/2).
Learn more on next page.
For this representation of fundamental physics I suggest the geometry of spacetime arises from the combinatorial relations of fundamental rishons just as do the rishon T and V elements. The T and V elements then relate in the spacetime of rishon fundamentals. T and V elements are not thought to be dynamic constituents of quarks and leptons but rather the spacetime structural components of quarks and leptons.
To learn about the Standard Model, view video on the right or continue below.
Click link to Explore example below with the rishon elements display program and See Video Demonstration.
See Video To Learn About The Standard Model
When you left click on an ordered pair, in the boxes above, the number to the left or right of the comma will cycle from 0 to 3 or from 0 to -3.
In the light blue panel, see the text (+/-1*VEE) or (+/-1*TEE).
When the text reads VEE the number to the left of the comma representing the value of (s) will cycle.
When the text reads TEE the number to the right of the comma representing the value of (t) will cycle.
Half way down the panel are buttons that determine which numbers change.
The R-ELEMENT button sets the VEE or TEE side.
The +/- buttons set the sign of the numbers.
As you cycle through the numbers, note that associated assemblies of V and T elements are displayed.
Click R-Elements until +/-1*VEE is displayed then click the (+/-) button depending on the (s) sign of the quark,lepton or boson ordered pair you want to display.
Click the green topmost ordered pair to display the (s) number. For example (3/2) for the Boson Minus to begin combinatorial model.
If you click mouse over another ordered pair.
when you return to the current ordered pair your numbers will zero.
Next click R-Elements until +/-1*TEE is displayed then click the (+/-) button depending on the (t) sign of the quark, lepton or boson ordered pair you want to display. For example (-3) for the Boson Minus.
Sum the displayed series of +/-V elements and sum the displayed series of +/-T elements.
Each element counts as +/-(1) and opposite signed rishon elements sum to (0).
The sums will equal the left and right numbers of the ordered pairs respectively.
There is either two V's above and one T below or two T's below and one V above.
Each triangle is designated as a V or T group by the single element above for V's and below for T's.
The negating or anti-elements are (+V's) and (-T's), V and T.
Thereby you can see the Boson Minus includes the groups ( ,V' , T') V-Prime and T-Prime.
With -1*TEE still displayed click on the bottom yellow ordered pair square until (0/2 , -2) displays.
Click on R-Element and then the (+) button to display 1*VEE.
Click on the yellow ordered pair square until (1/2 , -2) displays to represent the anti-Uquark.
The top yellow ordered pair will display (2/2 , -1) representing a Dquark(-1/3). The Boson now comprises a Pion Minus.
With -1*TEE still displayed click on the bottom ordered pair of the blue square until (0/2 , -3) displays.
The top blue ordered pair will display (3/2 , 0). Mouse over to see assemblies. These two pairs and V and T assemblies represent repectively the anti-muon neutrino and the muon (V ,V, V ) and (T ,T , T). The Pion above will zero to a quark anti-quark pair.
Click Muon Decay Or Kaon Decay