The Law of Intrinsic Formulation - Beyond General Covariance: A Criterion for Fundamental Physical Laws

The Law of Intrinsic Formulation proposed in this paper arises from a simple but far-reaching observation: all intrinsic physical realities presently known admit intrinsic representations. Making this empirical observation explicit through the Postulate of Intrinsic Representability, together with Einstein's Principle of General Relativity, naturally leads to the Law of Intrinsic Formulation. The principal contribution of the present work is therefore epistemological. To the author's knowledge, the LIF provides the first general operational criterion for assessing whether a physical law is fundamental from the intrinsic character of the physical concepts and operations on which it is built. In doing so, it addresses the limitation revealed by Kretschmann: while General Covariance guarantees the invariance of a formulation, it cannot distinguish genuinely fundamental laws from mathematically covariant reformulations relying on auxiliary structures. The LIF resolves this limitation by requiring that every object entering a fundamental law represent an intrinsic physical reality and that all operations remain intrinsic. This requirement extends to the conceptual foundations of any physical theory: all its essential primitive concepts must be intrinsic, although non-intrinsic auxiliary ones may still be introduced provided that they are not constitutive of its fundamental laws. Recognizing intrinsic formulation as a genuine law rather than as an implicit methodological preference also has important pedagogical consequences. Once established as a law, the LIF can be applied systematically both as a precise discriminating test and a powerful guide for the construction of relativistic laws: non-intrinsic quantities are replaced by their intrinsic counterparts that correspond to physical entities and reduce to the classical quantities up to negligible relativistic corrections when . The direct derivation of the four-Momentum and, from it, the celebrated relation illustrates the power of this approach. The simplification achieved is not a shortcut that comes at the expense of physical insight; it results from adopting a fundamental principle with broad implications: the Law of Intrinsic Formulation. More generally, by emphasizing the importance of intrinsic notions, the LIF encourages students to master them, thereby supporting sound reasoning while preventing recurrent conceptual misconceptions. The historical development of modern physics suggests that intrinsic formulation has long served implicitly as a guiding principle in the construction of fundamental theories. By making this principle explicit and formulating it as a law, the present work provides a unified epistemological foundation for the formulation, analysis, and teaching of fundamental physics. A companion articles applies this approach: “Momentum-First — A Deeper Foundation revealing Physical Limits.”