Quantum Chromo Relativity
A Color Theory of Matter, Space, and Time

Sean Orelli
seanorelli@protonmail.com
2025




Abstract:
A 5 dimensional model of the proton unifies the constants of general relativy and quantum mechanics to reveal the source of gravitation and radiation.

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.


Part 1:
The relationship between the constants of relativity and quantum mechanics suggest a geometry divided in three parts. Considering the uncertainty principle we can infer the existence of three dimensions of time.

Speed Of Light:

The speed of light is defined as a ratio of meters to seconds. One may wonder why it is eactly this ratio and what does it say about the geometry of space time.

Special relativity tells us that light does not experience time. Since velocity is a measure of distance over time, how can something experiencing 0 time have any speed at all?
What is its speed in reference to?

-----
Why is it this ratio?
Why is it a whole number?
Why is it close to a third?
How does light have a speed if it does not have time?
\[ C = 299792458 \ m / s \]
\[ C ≈ \ \ 3 \cdot 10^8 \ \ \ \cdot m / s \]

\[ \frac{1}{C} ≈ 1/3 \cdot 10^{-8} \cdot s / m \]
\[ \sqrt{\mu\varepsilon} ≈ 1/3 \cdot 10^{-8} \cdot s / m \]
Quantum and Gravitational Constants:
Scientific notation hides the fact that these constants are used as scalars within their respective equations. When expressed as a number between 0 and 1 we see that they are both close to 2/3
- 2 dimensions of space, 1 time
- 3 dimensions of space, 2 time
- quantum effects occur over an area - gravitational effects occur over a volume
\[ h = 6.626 \cdot 10^{-34} \ m^2 \ kg/ s\]
\[ G = 6.6743 \cdot 10^{-11} \ m^3 / kg \ s^2 \]

\[ h ≈ 2/3 \cdot 10^{-33} \cdot m^2 \ kg/ s\]
\[ G ≈ 2/3 \cdot 10^{-10} \cdot m^3 / kg \ s^2 \]

Planck Units:
In 1900 Max Planck showed how these constants can be combined to define canonical units of mass, length, and time.


The planck units combine three physical constants
and a periodic function to determine the limits
of mass, length, and time
Gravity and quantum mechanics can be combined algebraically without the need for calculus or probability

space
time
mass
circular geometry
\[ pm = \sqrt{\frac{hC}{2πG}} \]
\[ pl = \sqrt{\frac{hG}{2πC^3}} \]
\[ pt = \sqrt{\frac{hG}{2πC^5}} \]

Planck Operator:
-periodic function

\[ pr = \sqrt{\frac{h}{2π}} = \ \sim \]


Simplified Units:
remove the geomtetric
only three constants
Dimensions of C, 1, 3, 5
Spacetime has C in denominator
Mass has C in numerator
reflects the inside and outside
space of the spherical geometry
\[ pm \sim \frac{C}{G} \ \ \ kg\]
\[ pl \sim \frac{G}{C^3} \ \ \ m\]
\[ pt \sim \frac{G}{C^5} \ \ s\]

Planck Temperature:

temperature
boltzman constant to kelvins
reciprocal of planck time
\[ pT = 1/kB\sqrt{\frac{hC^5}{2πG}} \]
\[ kB pT = \sqrt{\frac{hC^5}{2πG}} \]
\[ kBpT \sim \frac{C^5}{G} \]

Ideal Gas:

Energy of a single atom
reciprocal of 2/3 planck time

The energy of a single atom is the reciprocal of 2/3 the planck time

\[ E = \frac{3}{2} \ kBpT \]
\[ E ≈ \frac{3}{2} (\sim \frac{C^5}{G})\]

Uncertainty Principle
ħ = h / 2π
energy time relationship
frequency time relationship
three time dimensions

\[ \Delta x \ \Delta p \geq \frac{h}{4π} \]
\[ \Delta E \ \Delta t \geq \frac{h}{4π} \]
\[ h \Delta f \ \Delta t \geq \frac{h}{4π} \]
\[ \Delta f \ \Delta t \geq \frac{1}{4π} \]
\[ \frac{\Delta t_1 \ \Delta t_2}{{t_3}^2} \geq \frac{1}{4π} \]
Part 2:

A basic quark model of the proton in 5 dimensions can approximate the fundamental constants.
3 Quarks

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.

A triple double slit


\[ q = 3 \]
3 Quarks

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.

A triple double slit


\[ l = 1 \]
\[Q_l = \frac{1}{3} \]
\[ d = 2 \]
\[ Q_d = \frac{2}{3} \]
Color Shift

doppler

expanding universe

acclerating light source
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 { r, g }
g { g, b }
b { b, r }


\[ r = 8 \]
\[ g = 1 \]
\[ b = 10 \]
Super Positions

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.
\[ R = r^r = 8^8\]
\[ D_g = b^r = 10^{8} \]
\[ D = b^b = 10^{10} \]
Hyper Positions

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.

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.
\[ H = b^{2 + 2^5} = 10^{34}\]
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.
\[ C ≈ q b^r \cdot {\small \textcolor{grey}{m/s}}\]
\[ G ≈ \frac{Q_d}{D} \cdot {\small \textcolor{grey}{m^3 / (s^2 \cdot kg) }}\]
\[ h ≈ \frac{Q_d \cdot b}{H} \cdot {\small \textcolor{grey}{(kg \cdot m^2) / s }}\]
\[ P ≈ \frac{R}{H} \cdot {\small \textcolor{grey}{kg}}\]
Part 3:

By evaluating the recursive containment of quarks we can refine our model and improve the accuracy of our algebra
2 Quarkini
The quarks inside the quarks

when observing the proton, the green chanel contains at most one red quark which in turn contains the green quark

Since the future is not yet determined, there are two possible blue quarks. within them is a red quark



\[ Q_s = Q_l^{\ \ 2} = 1/9 \]

\[ Q_r = \frac{Q_s \cdot b }{d} = 10/18 \]
Secondary Colors
CMY complementary colors of RGB
Second Order RGB
Transforming a color to its complement
swaps the order of contained quarks.
\[ m = \frac{b + r}{d} = 9 \]
\[ c = m Q_l = 3 \]
\[ y = m Q_d = 6 \]
Super Position

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.
\[ D_m = d^m = 2^{9} \]
Hyper Position

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.

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.
\[ H_r = 10^{2π}\]

Proton Mass

Mass is created by subtracting
the blue from the red.


\[ Rr = \frac{r^2}{d b} \]
\[ Rg = gb^{3}\]
\[ Rb = \frac{b^5}{d}\]
\[ P = \frac{R + Rr - Rg - Rb}{H} \]

Timespace
The photon has no clock, the proton is the clock
A broken clock is right twice a day

It may seem that this ratio is arbitrarilty determined by the definition of the meter. One must remember that mass, space, and time can all be converted to energy. Since energy is conserved and all units of the metric system are base 10, the ratio is a fundamental property of spacetime.


circular rainbow, empty center
null, now, past, future
\[ n_u = b - r = d\]
\[ n_s = \frac{br}{d} \]
"Light Speed" = Causality
The photon has no clock, the proton is the clock
A broken clock is right twice a day

It may seem that this ratio is arbitrarilty determined by the definition of the meter. One must remember that mass, space, and time can all be converted to energy. Since energy is conserved and all units of the metric system are base 10, the ratio is a fundamental property of spacetime.


circular rainbow, empty center
null, now, past, future
\[ C_t = d + \frac{br}{d}\]
\[ L_s = \left(r - \frac{g}{d}\right)b^3 \]
\[ D_s = d b^5 \]
\[ C = qb^r - C_t - L_s - D_s \cdot {\small \textcolor{grey}{m / s}}\]
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.

\[ \mu = \frac{4 \pi }{b^{r - g}} \cdot {\small \textcolor{grey}{m^3/ ( s^2\cdot kg )}}\]

\[ \varepsilon = \frac{g}{\mu C^2} \cdot {\small \textcolor{grey}{ s^2 / ( m^3\cdot kg)}}\]
Alpha
vol(r) = 4/3πr^3
area(r) = 4πr^2
blue and red quarks
mix into magenta

vol_1(r) = 2r
vol_4(r) = r^4 * π^2/2
\[ r \cdot m \cdot b = 8 \cdot 9 \cdot 10 \]
\[ dR = \frac{b^5}{m^3} \]
\[ dV = \frac{vol(b) - vol(m)}{\pi^2 b^3} \]
\[ dA = \frac{area(b) - area(m)}{b^4} \]
\[ dI = \frac{ r^2 + (b - r)^2}{b^5} = \frac{ r^2 + d^2}{b^5} \]
\[ dE = \left(\frac{1}{\sqrt{2} \cdot b^4}\right)^2 = \frac{g}{d b^r} \]

\[ A = dR - dV - dA + dI + dE \]

\[ Á = A - (A \% 1) = 137\]

\[ \alpha = \frac{1}{A} \]

\[ \alpha' = \frac{1}{Á} = \frac{1}{137}\]
Entropy

the second generation of quark states

bottom half/quarter of the future tree
\[ S = (2^r - r^2) b^4\]

\[ S_r = H_r + D_m + g/d \]
Gravitation

The obscured quarks over the super duper positions, including the dark quarks and the shadow quark as seen through the alpha lens. The entropy must be removed from the shadow quark as it goes through the alpha function


The second order superposition that remains
unknown relative to the green origin
1.996 / 10 ^22 J/K.
\[ G = \frac{Q_d + \alpha (Q_s - S/C)}{D} \]
Flux Capacitance

The energy transferred between quarks
and conserved by the proton
during the alpha function.

1 F= s^4 /kg⋅m^2

\[ Y = \frac{b^2 + b}{b^3} \]
Radiation
Quantum of Action The unit of action in a radiating body. The darks quarks and current path without radiating or fluxing energy as a fraction of the hyper positions.
\[ h = \left(Q_d + \frac{g}{b^r} - \alpha' Q_r - Y \left(\frac{S}{C}\right)^2 \right) \frac{b}{H} \]

Elementary Charge
The units of charge squared are equal to those of the quantum constant.

6-8-10 triangle

\[ \tilde{e} = \sqrt{C h \alpha r^{1/3}g \varepsilon } \cdot {\small \textcolor{grey}{\sqrt{ kg \cdot m } / s }}\]
Electron
Electron charge and mass are balanced
by the yellow channel

Proton charge results from the difference
between Secondary and Primary Colors
(r + g + b ) - (c + m + y) = 1

\[ \hat{e} = \frac{P}{y \pi^5} \cdot \textcolor{grey}{kg}\]

\[ \ddot{e} = \hat{e} \cdot \sqrt{1 - \alpha' ^{\ 2}} \]

\[ e = \ddot{e} + \frac{\hat{e} - \ddot{e}}{\pi} - \frac{y}{H b^3} - \frac{d - Y}{H b^5} \]
Neutron
A free neutron has no charge and
does not radiate. It decays when all
of its possible energy states have
filled and reaches maximum entropy
Mn = c^y + y^c - mc
Mn = 0x396 // 12 bits
Mn = 918

12 bits are left unchanged, 4 bits, or 1/4 total are reused
This provides a corollary to the black hole entropy
And matches the Einstein-Maxwell theory
M = -917
\[ M = g - c^y + mc - y^c\]

\[ N = \frac{R + g - c^m + Mm - y}{H} \]

\[ \beta = Á\left(b^3 + Q\right) \frac{S}{C} \cdot \textcolor{grey}{s} \]
Muon
\[ \mu_n ≈ \ e \ \frac{Á + l - Q_s}{Q_d}\]
Tau
\[ \tau ≈ \ \mu_n \ \frac{Á + Q_s - d - Q_d}{r}\]
Z
\[ Z ≈ P \left( Á + Q_s - \frac{r}{db}\right)\]
W
\[ W ≈ P \left( Á - C_t - m - Q_l\right)\]
Higgs
\[ h_b ≈ P \left(Á + Q_l - \frac{r}{d}\right)\]
Up / Down

uQ = P/(ns*b+c^c)
dQ = P/QD*b**2
green
magenta

\[ dQ ≈ \frac{P}{d b^2} \]
\[ uQ ≈ \frac{P}{r - g + Ct \cdot b}\]
charm / strange

cQ = P*(A-QD)/b**2
sQ = P/b

\[ sQ ≈ \frac{P}{b}\]
\[ cQ ≈ P \frac{Á - d}{b^2}\]
truth / beauty
tQ = P*(A+QD*b+c^c)
bQ = P(m-Y)/b**2
\[ tQ ≈ P \left(Á + C_t + b/d\right)\]
\[ bQ ≈ P \frac{m - Y}{b^2}\]
Cosmological Constant
\[ \Lambda = \frac{\frac{b^2 + b + g/d}{b^3 - g/d}}{H^{q/d}} \cdot {\small \textcolor{grey}{1/m^2}}\]
Color Containment

Transforming a color to its complement swaps the order of contained quarks.
r { r, g, c }
g { g, b, m }
b { b, r, y }
c { c, y, r }
m { m, c, g }
y { y, m, b }


Conclusion:
A simplified quark model of the proton can reveal the source of mass, gravity, and black body radiation.
mass gap is from 1/10^34 in position space and 1/10^35 in momentum space

Javascript:

π=Math.PI
function vol(rad){return (4/3)*π*(rad**3);}
function area(rad){return 4*π*(rad**2);}

Q=3
QD=2
QL=1
Ql = QL/Q
Qd = QD/Q
r = 8
g = 1
b = 10
m = (b+r)/2
c = m*Ql
y = m*Qd
C = Q*b**r - QD*b**5 - (r - g/2)*b**3 - r*g*b/2 - QD
R = r**r
D = b**b
H = b**(2**1 + 2**2 * 2**3)
Y = (b**2+b)/(b**3)
S = (2**r-r**2)*b**4
Qs = Ql**2
Qr = Qs*b/2
dR = b**5/m**3
dV = (vol(b)-vol(m))/(π**2*b**3)
dA = (area(b)-area(m))/(b**4)
dI = (r**2+(b-r)**2)/(b**5)
dE = (1/(2*b**r))
A = dR-dV-dA+dI+dE
Á = A-(A % 1)
α = 1/A
ά = 1/Á
G = (Qd + α*(Qs - S/C)) / D
h = (Qd + g/(b**r) - ά*Qr - Y*(S/C)**2) * b/H
P = (R + r**2/(2*b) - g*b**3 - b**5/2) / H
μ = 4*π/b**(r-g)
ε = 1/(μ*C**2)
ẽ = Math.sqrt(2*α*h*ε*C)
ê = P/(y*π**5)
γ = Math.sqrt(1-ά**2)
ë = γ * ê
e = ë + (ê - ë)/π - y/(H*b**3) - (2-Y)/(H*b**5)
M = (y**c+c**y)-m*c
Mb = g-c**y+m*c-y**c
N = (R + g - c**m + m*Mb - y )/ H
β = Á * S/C * (b**3 + c)
Λ = (b**2+b+g/2)/(b**3-g/2)/(H**(c/2))

Conclusion:


References:

Lenz, F. (1951). The Ratio of Proton and Electron Masses.
Physical Review, 82, 554.
DOI: 10.1103/PhysRev.82.554.2