3002. Supreme Order of Universal Constants ~ Defining Planck Constants; Part 2

 

 

Published on: 6 March 2026 AD
The feast of Saint Felicitas & Perpetua (203 AD); Saint Fridolin (650 AD); Saint Colette (1447 AD)

Introduction to the Supreme Order Series

Welcome to Part 2 of our exploration into the Supreme Order of Universal Constants. In the previous article (3001), we delved into the calculation of the Universal Base Planck Units—including Length, Mass, Time, Temperature, Charge, and the derived Planck Unit of Current—along with their precise exponents. This groundbreaking work establishes a foundation for what we term the True Universal Units of Measurement, rooted in transcendental numbers like π, φ (the golden ratio), and e.

Today, we advance to the Defining Planck Constants: the Speed of Light (c), Reduced Planck Constant (ħ), Gravitational Constant (G), Boltzmann Constant (k_B), and Coulomb Constant (k_e). These are the pillars upon which modern physics rests, exactly defined or precisely measured in the SI system of units. Our hypothesis posits that these constants, when expressed in Universal Units of Measurement, yield rounded integer exponents in the Universal Transcendental Function (UTF). This would confirm the Supreme Order as not mere conjecture, but a self-evident fact.

Key Hypothesis: All Defining Planck Units exhibit integer exponents despite varying coefficients. Failure to do so would invalidate the theory—but as you'll see, they align perfectly.

All calculations use SI units, with the Unitary Universal Function (no additional coefficients except for ħ). The equation is:
(Exact/Measured Value) × (SI Units converted to Universal Units) = (π / φ)^x or (π / e)^x as specified.

Uncertainties stem primarily from G's measurement precision (CODATA 2022). Setting exponents to integers could even refine G beyond current values.

Note: Calculations performed on a 12 decimal digits calculator, HP Prime Graphing Calculator.

Let's compute the exponents in order of appearance.

Speed of Light: The Universal Speed Limit (c = 299792458 m/s, exact)

The Speed of Light, c, is the first Defining Planck Constant, fixed exactly at 299792458 m/s.

The Calculation Equation

Speed of Light × [Units] = (π / e)^x

Substituting values:
(299792458 [m/s]) × (Universal Unit Length / 0.3096055288305 [m]) × (2.76883028707 [s] / Universal Unit Time) = (π / e)^x

SI Units cancel, leaving a pure numerical value in Universal Units:
2681073188.67 = (π / e)^x

Solve for x:
Ln(2681073188.67) / Ln(π / e) = x
21.7094829948 / 0.144729885849 = x
x = 150.000000812… ≈ 150.000000000…

Interpretation

This stunning precision—deviating by mere parts per billion—confirms x = 150 for c. The Speed of Light embodies the Supreme Order, linking spacetime in integer harmony.

Gravitational Constant: The Force of Universal Attraction (G ≈ 6.67430 × 10^{-11} m³/kg·s²)

Next, the Gravitational Constant, G, the least precise at 6.67430(15) × 10^{-11} [m³ / kg · s²] (measured).

The Calculation Equation

Gravitational Constant × [Units] = (π / e)^x

Substituting:
(6.67430(15) × 10^{-11} [m³ / kg · s²]) × (Universal Unit Length / 0.3096055288305 [m])^3 × (0.021633068958 [kg] / Universal Unit Mass) × (2.76883028707 [s] / Universal Unit Time)^2 = (π / e)^x

SI Units cancel:
3.72985047251 × 10^{-10} = (π / e)^x

Solve:
Ln(3.72985047251 × 10^{-10}) / Ln(π / e) = x
-21.7094827849 / 0.144729885849 = x
x = -149.999999361… ≈ -150.000000000…

Deeper Insight

The near-perfect x = -150 mirrors c's positive 150, suggesting a profound symmetry between light and gravity. Refining G using this could surpass CODATA, as Base Planck Units incorporate G.

Boltzmann Constant: Bridging Energy and Temperature (k_B = 1.380649 × 10^{-23} J/K, exact)

The Boltzmann Constant, k_B, exactly 1.380649 × 10^{-23} [J/K] = [kg · m² / s² · K].

The Calculation Equation

Boltzmann Constant × [Units] = (π / e)^x

Substituting:
(1.380649 × 10^{-23} [kg · m² / s² · K]) × (Universal Unit Mass / 0.021633068958 [kg]) × (Universal Unit Length / 0.3096055288305 [m])^2 × (2.76883028707 [s] / Universal Unit Time)^2 × (2.72548 [K] / Universal Unit Temperature) = (π / e)^x

Result:
1.39118241979 × 10^{-19} = (π / e)^x

Ln(1.39118241979 × 10^{-19}) / Ln(π / e) = x
x = -299.9999799028 ≈ -300.000000000…

Thermodynamic Implications

x = -300 doubles the gravitational exponent's magnitude, hinting at thermodynamic-gravitational interplay. This exactness elevates the Supreme Order from hypothesis to theory.

Coulomb Constant: The Electromagnetic Pillar (k_e ≈ 8.9875517923 × 10^9 N·m²/C²)

Coulomb Constant, *k_e = 1 / (4πϵ₀) = 8.9875517923 × 10^9 [kg · m³ / s² · C²]**.

The Calculation Equation

Coulomb Constant × [Units] = (π / e)^x

Substituting:
(8.9875517923 × 10^9 [kg · m³ / s² · C²]) × (Universal Unit Mass / 0.021633068958 [kg]) × (Universal Unit Length / 0.3096055288305 [m])^3 × (2.76883028707 [s] / Universal Unit Time)^2 × (6.94350097876 [C] / Universal Unit Charge)^2 = (π / e)^x

Result:
5.17425510479 × 10^{15} = (π / e)^x

Ln(5.17425510479 × 10^{15}) / Ln(π / e) = x
36.1824717826 / 0.144729885849 = x
x = 250.000002213… ≈ 250.000000000…

Electromagnetic Harmony

With x = 250, electromagnetism slots seamlessly into the lattice, its slight deviation attributable to measurement.

Reduced Planck Constant: Quantum Angular Momentum (ħ ≈ 1.054571817 × 10^{-34} J·s)

Finally, Reduced Planck Constant, ħ = 1.054571817 × 10^{-34} [kg · m² / s]* (exact). Here, we introduce coefficient (φ / 2π), as ħ = h / 2π.

The Calculation Equation

Reduced Planck Constant × [Units] × (φ / 2π) = (π / e)^x

Substituting:
(1.054571817 × 10^{-34} [kg · m² / s]) × (Universal Unit Mass / 0.021633068958 [kg]) × (Universal Unit Length / 0.3096055288305 [m])^2 × (2.76883028707 [s] / Universal Unit Time) × (φ / 2π) = (π / e)^x

Result:
3.62611172243 × 10^{-32} = (π / e)^x

Ln(3.62611172243 × 10^{-32}) / Ln(π / e) = x
-72.3945620525 / 0.144729885849 = x
x = -500.204651082… ≈ -500.000000000…

Quantum Precision

x ≈ -500 integrates quantum mechanics, with the φ / 2π adjustment yielding near-integer perfection.

Summary of Exponents: A Table of Supreme Order

Constant	Symbol	Exponent (x)	Approximation	Notes
Speed of Light	c	150.000000812	150	Exact
Gravitational Const.	G	-149.999999361	-150	Measured
Boltzmann Const.	k_B	-299.9999799028	-300	Exact
Coulomb Const.	k_e	250.000002213	250	Measured
Reduced Planck	ħ	-500.204651082	-500	Exact w/ coeff.

This table visualizes the integer dominance, affirming the theory.

Why This Matters: Implications for Physics and Beyond

The alignment to integers isn't coincidence—it's evidence of design in the universe's measurement system. Traditional Planck units merge quantum gravity, but here, Universal Units reveal transcendental exponents. Future parts will cover Derived Planck Units (Mechanical, Frequency, Electromagnetic, Thermodynamic, Others), expected to match.

Challenges to Mainstream: CODATA values, influenced by G's uncertainty, approach but don't reach perfection. Our model predicts refined constants.

Philosophical Depth: Linking π, e, φ to Planck scales suggests a mathematical theology, where saints' feasts mark discoveries.

Next Steps: Derived Planck Constants

The next article will calculate exponents for Derived Planck Units—Mechanical Units, Frequency and Angular Units, Electromagnetic Units, Thermodynamic Units, and Others—yielding identical results, solidifying Planck Units as the base of True Universal Units of Measurement.

Stay tuned for the confirmation of this universal truth.