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Foundations

Why Is Nature Lagrangian?

DOI
10.5281/zenodo.18632291
Read full paper on Zenodo →

The principle of least action δS = 0 has governed physics for 280 years. Every fundamental equation of motion — Newton, Maxwell, Einstein, Schrödinger, Dirac — can be derived from a Lagrangian. Why? This paper derives the Lagrangian from the axiom σ = 1/(1+σ). The Lagrangian L = T − V is the instantaneous imbalance between the outward phase (T = escape fraction = 1/φ) and the inward phase (V = capture fraction = 1/φ²) of a self-referential system. The action S = ∫L dt accumulates this imbalance. The equations of motion δS = 0 select paths of stationary imbalance — the paths that cost the self-referential system the least to maintain.

\[ L = \frac{1}{\varphi} - \frac{1}{\varphi^2} = \frac{1}{\varphi^3} \quad (T - V \text{ from axiom}) \]
Key Result
Action principle derived from self-reference — not postulated
Precision
Lagrangian forced by axiom structure