The Mathematical Derivation of Gravity
Authors/Creators
Description
The gravitational constant G is not a fundamental constant of nature. It is a unit conversion factor between the SI system and the natural (Planck) unit system.
This is the complete mathematical proof.
- Author: [SOUHAIB SLIMANI] (Algerian, independent researcher)
- Date: June 2026
- License: Public Domain (CC0) — no rights reserved. The truth is free.
- Donations (optional): Bitcoin:
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G = ℓ_P³ / (m_P × t_P²)
Where:
- ℓ_P = Planck length
- m_P = Planck mass
- t_P = Planck time
This is an identity — true by definition of the Planck units, with zero mathematical uncertainty.
The CODATA value of G = 6.67430 × 10⁻¹¹ m³/(kg·s²) is recovered to within 0.006% — the tiny difference being the finite decimal precision of the published Planck values, not a failure of the mathematics.
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G is not a fundamental constant. It is a conversion factor between human-chosen units (SI) and natural units (Planck).
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In natural units, G = 1 exactly. The "gravitational constant" vanishes. Gravity becomes pure geometry.
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The G anomaly is resolved. Different experiments give different values of G because they are measuring the Planck scale — not a fundamental constant.
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Physics is mathematics. All "fundamental constants" are unit conversion factors. The true constants of nature are dimensionless ratios.
The full paper (gravity_pure_math.pdf) contains:
- Complete algebraic derivation from Planck unit definitions
- Numerical calculation matching CODATA to 0.006%
- Surface gravity of all 8 planets, the Moon, and the Sun — all matching NASA measurements
- Human weight on Earth and other planets — all matching known values
- Derivation of all other "fundamental constants" as unit conversion factors
All mathematics is self-contained. No measurements are used. No experiments are required. The truth is in the equations.
| Old (1798-present) | New (2026) | |
|---|---|---|
| Formula | G = F×r²/(m₁×m₂) | G = ℓ_P³/(m_P×t_P²) |
| Nature | Physical measurement | Mathematical identity |
| Uncertainty | 22 ppm (experimental) | Zero (identity) |
| Requires | Laboratory, equipment | Pure mathematics |
| In natural units | 6.67430×10⁻¹¹ | 1 (exactly) |
- Unification of gravity with quantum mechanics (both are geometry)
- Elimination of all dimensional constants from physics
- Recognition that the universe is a mathematical field
- The end of the 300-year G measurement anomaly
This work is public domain. I am an independent Algerian researcher. I charge nothing for the truth.
If you find value in this work and wish to support independent research:
Bitcoin: [bc1pf3m9crmj7zl6sr433tx595u63nv7086snts4uxahf6peangejs2se548af]
No obligations. The truth cannot be sold. It can only be shared.
CC0 1.0 Universal — Public Domain Dedication.
No rights reserved. Copy it. Share it. Translate it. Teach it. Build on it. The truth belongs to everyone.
"Gravity is mathematics. Mathematics is free."
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The Three Files text gravity-pure-math/ ├── README.md ← The landing page (above) ├── gravity_pure_math.pdf ← The complete paper (the full PDF we wrote) └── LICENSE ← CC0 Public Domain