What question did this study set out to answer?

This work seeks to establish energy as the fundamental basis of all physical phenomena and forces.

June 15, 2026Open Access

On the Origin of Energy

Key Points

This work seeks to establish energy as the fundamental basis of all physical phenomena and forces.
Proposed a geometric theory (Origin Of Energy) linking all forms of energy through a conservation equation.
Derived key constants and relationships from tetrahedral geometry in three-dimensional space.
Validated the model by reproducing known physical constants with minimal error rates.
Reproduced the lepton mass spectrum with an error of 0.014%.
Derived the fine-structure constant with an error of 0.000012%, confirming its emergence from the geometric structure.
Validated gravitational constant G (error 0.011%) and the deflection of light by the Sun (error 0.05%).

Abstract

This paper is grounded in a single foundational principle: energy is always conserved. We propose that energy is the primordial basis of all nature and the universe — the one quantity that is universally preserved across every scale and every phenomenon. This work is motivated by the desire to understand that foundation, and to ask whether all known forces and structures might emerge from it. We propose a geometric theory — the Origin Of Energy (OOE) — in which all forms of energy (mass, electromagnetism, strong nuclear force, weak nuclear force, and gravity) are derived from a single energy conservation equation: Eₜotal (θ, φ, ρ) = Efamily·cos²θ − k·cosφ / ρ − k·sinφA·sinφB / ρAB − (3/4) ·k·cos²θ / ρ³ + p²/2m = constant Here θ is the mass angle, φ is the charge angle, and ρ is the spatial scale. These three variables are fully determined by the vertex geometry of two dual regular tetrahedra embedded in three-dimensional space. The framework reproduces the lepton mass spectrum via the Koide relation (error 0. 014%), the gravitational constant G (error 0. 011%), the deflection of light by the Sun (error 0. 05%), and the W boson mass (error 0. 52%). Several results — particularly in gravity and the strong nuclear sector — are exploratory in nature; this is stated explicitly throughout. v2 update The fine-structure constant α = 1/137. 03598 is derived from OOE tetrahedral geometry via 24πα (1 + 3α/2n + α²/n) = arccos (23/27), n = ln (2/α). Error 0. 000012% — within experimental uncertainty (±0. 000021%). α is no longer an empirical input; it emerges from the dual tetrahedron structure (Section 2A). v2. 1 update Added exact geometric derivation of arccos (23/27) via the cosine triple-angle identity: arccos (23/27) = 3·arccos (1/3) − π. This confirms that the electron solid angle Ω — and through it α — arises from three quark phase rotations. Numerical verification: difference 3. 3×10⁻¹⁶ (machine precision). This is an exact trigonometric identity, not a numerical fit (Eq. 2A. 1b, Section 2A. 1).

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