Motivation:
The Standard Model of particle physics has been succesful at uniting three of the four fundamental forces. Its connection to gravity remains mysterious, as does many of the measured physical constants used within the theory. A more complete model would explain the geometric relationships that underlie the values of these constants.
At the heart of the Standard Model is the strong force as described by Quantum Chromodynamics. While successul at matching experiments, it contains within it counter intuitive concepts and redundant symmetries. As a non-abelian gauge theory of SU(3) group symmetry there exists an associated set of generators and a corresponding field. In the case of QCD we find the SU(3) symmetry in both gluon colors and the baryons grouped by flavor, but only one set of generators. Within this structure quarks are confined by the gluons, and even when freed by high energy, they will immediately undergo hadronization due to the strong force increasing in strength with distance. In this way color symmetry is fundamental and flavor symmetry is emergent. QCD also assumes quarks are fractionally charged yet electric charge is always observed to be multiples of the fundamental charge.
Gravitation has been successfully elucidated in the theory of General Realtivity, yet it cannot be quantized or connected to the Standard Model. As a tensor based geometry it does not need force mediating particles, rather the phenomenon is a result of spacetime curvature.
These two disparate models naturally lead to some questions.
If QCD is a field theory with massless bosons, why is it limited to such a short range in contrast to the infinite range of electromagnetism and gravitation?
If the massless photons are neutral, why do the gluons carry charge?
If gravity can not be quantized, can quantum fields be related to spacetime curvature?
Since quark flavor and color charge both exhibit SU(3) symmetry, can they be manifestations of the same geometry?
The following set of equations and diagrams illustrate a model of the proton in which quarks are individual spacetimes containing each other in a cycle of causality. Each quark radiates at the speed of light into the next quark in the cycle. Assiging a frequency to each quark position within this chain results in a Doppler shift from their relative motion. By enumerating the states of the proton we can create a set of superpositions. From the combination of relative quark frequency and proton superpositions we can determine the constants of gravitation and radiation.
\[ π = 3.14159265359 \]
\[ C = 299792458 \cdot {\small \textcolor{grey}{m / s}}\]
Given Pi and C as known constants, we will describe quarks as spherical radiation travelling at the speed of light in 5 spatial dimensions, with electric and magnetic axes combined with the conventional width, height, and depth.
In addition to these constants we will derive our equations from a set of base values:
{ 1/3, 2/3, 1, 8, 10 }
We will proceed to develop an algebra of color and a set of recursive data structures to model discrete superpositions.
\[ Q_l = \frac{1}{3} \]
\[ Q_d = \frac{2}{3} \]
Positions
Each quark is a unique spacetime containing another quark and being contained by the third. Since quantum mechanics is symmetrical with respect to time, we will allow for the spatial dimensions to turn inside out and continue the causal containment heirarchy in the opposite direction.
In this way each quark has two potential directions to radiate in. From here our logic will follow that of a photon traversing a double slit. It will explore all paths until a suitable destination is found.
Since the quarks are radiating into one another, they never leave the space of the proton. From the outside oberver, the proton appears to have one shared interior space with 3 time dimensions. As such we only see one quark at a time as they flow into each other. We will call the observed quark the light quark, and the unobserved quarks the dark quarks.
\[ r = 8 \]
\[ g = 1 \]
\[ b = 10 \]
Primary Colors
The observed light quark is green, with a value of 1.
The dark quark before it is red with a value of 8
The dark quark after it is blue with a value of 10.
While the values here represent frequency, they function as the number of possible states for a quark within a superposition.
Red is moving away from us in the past
Blue is moving towards us in the future
Time moves left to right
Energy moves right to left
r → g
g → b
b → r
\[ R = r^r = 8^8\]
\[ D = b^b = 10^{10} \]
\[ H = b^{2^1 + 2^2 \times 2^3} = 10^{34}\]
Superpositions
By enumerating the possible combinations of dark quarks we can create a set of internal super positions for for the observed proton.
We can define two monochrome states in the form of a three node cyclic graph,one red and one blue.
Retro Positions:
R = 16777216
Duper Positions:
D = 10000000000
Future Tree
Moving forward in time we can define a binary tree of alternating red, green, and blue quarks. The total future positions are a count of the blue nodes and completes at the second level before recurring to the origin.
\[ P ≈ \frac{R}{H} \cdot {\small \textcolor{grey}{kg}}\]
\[ G ≈ \frac{Q_d}{D} \cdot {\small \textcolor{grey}{m^3 / (s^2 \cdot kg) }}\]
\[ h ≈ \frac{Q_d \cdot b}{H} \cdot {\small \textcolor{grey}{(kg \cdot m^2) / s }}\]
Approximations
Ratios of the dark quarks and the proton super positions can approximate the measured constants of mass, gravitation, and radiation.
The units of gravitation show it functions over a volume while the quantum units define an area.
\[ Rr = \frac{r^2}{2b} \]
\[ Rb = \frac{b^5}{2} + b^3\]
\[ P = \frac{R + Rr - Rb}{H} \]
Retro Tree
The retro tree runs backwards.
Mass is created by subtracting
the blue from the red.
\[ \mu = \frac{4 \pi}{b^{r - g}} \cdot {\small \textcolor{grey}{m^3/ ( s^2\cdot kg )}}\]
\[ \varepsilon = \frac{g}{\mu C^2} {\small \textcolor{grey}{\cdot s^2 / ( m^3\cdot kg)}}\]
Electromagnetism
The containment of color reveals the magnetic and electric constants.
When specifying in units of kilograms, meters, and seconds we can see the magnetic and gravitational constants have identical units, with the electric constant reversing space and time.
\[ Q_s = Q_l^{\ \ 2} = 1/9 \]
\[ Q_r = \frac{Q_s \cdot b }{2} = 10/18 \]
Quarkini
The quarks inside the
quarks
The red at the third level is the shadow quark
The blue at the fifth level is the radiant quark
We consider the green node in the center the origin. The quark at the origin has come from the red node above it. The quark will traverse all possible paths. Eventually one blue node at the bottom will complete a circuit. The blue is redshifted to magenta as the
shadow returns to the origin and the radiant quark is released.
\[ m = \frac{b + r}{2} = 9 \]
\[ c = m Q_l = 3 \]
\[ y = m Q_d = 6 \]
Secondary Colors
CMY complementary colors of RGB
Second Order RGB
r |
→ |
{ g, c } |
g |
→ |
{ b, m } |
b |
→ |
{ r, y } |
c |
→ |
{ y, r } |
m |
→ |
{ c, g } |
y |
→ |
{ m, b } |
\[ vol(r) = 4/3πr^3 \]
\[ area(r) = 4πr^2 \]
Electric Flatland
Radiation expands in 5 Dimensions
width, height, depth, electric, magnetic
The least action between photons
occurs on their 4D intersection
We live in an electric flatland
only seeing the 3D volume and
2D surface area of matter
\[ r \cdot m \cdot b = 8 \cdot 9 \cdot 10 \]
\[ dR = \frac{b^5}{m^3} \]
\[ dV = \frac{vol(b) - vol(m)}{\pi^2 b^3} \]
\[ dA = \frac{area(b) - area(m)}{b^4} \]
\[ dI = \frac{ \sqrt{ r^2 + (b - r)}^2}{b^5} = \frac{ r^2 + (b - r)}{b^5}\]
\[ dE = \left(\frac{1}{\sqrt{2} \cdot b^4}\right)^2 = \frac{g}{2 b^r} \]
\[ A = dR - dV - dA + dI + dE \]
\[ Á = A - (A \% 1) \]
\[ \alpha = \frac{1}{A} \]
\[ \alpha' = \frac{1}{Á} \]
Alpha
blue and red quarks
mix into magenta
\[ S = (2^r - r^2) b^4\]
\[ G = \frac{Q_d + \alpha (Q_s - S/C)}{D} \]
\[ Y = \frac{b^2 + (m+g)}{b^2 \cdot (m+g)} = \frac{b^2 + b}{b^3} \]
\[ h = \left(Q_d + \frac{g}{b^r} - \alpha' Q_r - Y \left(\frac{S}{C}\right)^2 \right) \frac{b}{H} \]
\[ \tilde{e} = \sqrt{2 \alpha h \varepsilon C} \cdot {\small \textcolor{grey}{\sqrt{ kg \cdot m^2 / s }}}\]
\[ \hat{e} = \frac{P}{y \pi^5} \cdot \textcolor{grey}{kg}\]
\[ \ddot{e} = \hat{e} \cdot \sqrt{1 - \alpha' ^{\ 2}} \]
\[ e = \ddot{e} + \frac{\hat{e} - \ddot{e}}{\pi} - \frac{y}{H b^3} - \frac{2 - Y}{H b^5} \]
Electron
The units of charge squared are equal to those of the quantum constant.
\[ N = \frac{R + g - c^m + m (g - c^y + m c - y^c) - y}{H} \]
\[ \beta = Á\frac{S}{C} \left(b^3 + c\right) \cdot \textcolor{grey}{s} \]
Retro Future Tree
combined past and future trees
\[ \Lambda = \frac{\frac{b^2 + b + g/2}{b^3 - g/2}}{H^{c/2}} \cdot {\small \textcolor{grey}{1/m^2}}\]