The Action Principle as the Description Language of Physical Law: From Particle to Field — One Grammar, Not One Equation.
Can the scattered laws of physics be written in one description language? This paper answers: that language is not a constant shared by all laws but a GRAMMAR all laws obey — the principle of least action. Mechanics, electromagnetism, gravity, and field theory are all written in a single sentence: “for an appropriate Lagrangian L, make the action stationary (delta S = 0).” A particle S = -mc times the integral of ds; the electromagnetic field L = -(1/4)F_{mu nu}F^{mu nu}; gravity the Einstein–Hilbert action S = (1/16 pi G) times the integral of R sqrt(-g) d4x — each delta S = 0 yields its equation of motion (Euler–Lagrange, Maxwell, Einstein). Noether (Paper 80) attaches to each continuous symmetry a conservation law, so the grammar carries its own ledger. This extends Paper 84 (least action in mechanics) to fields. IMPORTANT (scope): this is ONE GRAMMAR, NOT ONE EQUATION — each L remains distinct and must be supplied by hand from experiment and geometry; the action principle unifies the FORM of laws, not their CONTENT (the same type of unification as Maxwell gathering E and B into one tensor), and is NOT a grand unified theory. No new mathematics and no new prediction; “why nature obeys an action principle” is not solved (the same humility as Paper 84). The 4pi/8pi factors in the couplings are Paper 86’s topological-root quantities, distinct from the grammar (delta S = 0). The “source-code grammar of the Universe OS” is a Layer-3 non-science lens, and the paper notes that the feeling that it cannot be unseen is a signature, not a proof.
On the making of this work: The ideas and content of this work stem from the author’s own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author’s. Feedback and corrections are sincerely appreciated.
Reference
Yamagishi, Y. (2026). The Action Principle as the Description Language of Physical Law [Paper 87]. Zenodo.
DOI: 10.5281/zenodo.21747287
ORCID: 0009-0006-8587-3450