Newton's Second Law: A Theoretical Identity Derived from the Principle of Excluded Perpetual Motion and the Weak Equivalence Principle

Abstract

For more than three centuries, Newton's Second Law (F=ma) has governed mechanics with undisputed success, yet its epistemic authority has rested on empirical adequacy alone. That empirical contingency vanishes under two physical principles - the Principle of Excluded Perpetual Motion (PEPM) and the Weak Equivalence Principle (WEP) - from which the law emerges as a structural necessity of admissible mechanics. Under the PEPM constraint, Suppes' operational measurement protocol grounds gravitational mass and force as independent primitives. The fusion of Stevin's static and Galileo's kinematic inclined-plane analyses establishes F/a as a well-defined, object-intrinsic quantity - the operational definition of inertial mass. The WEP compels the equivalence of inertial and gravitational mass without presupposing Newton's Second Law. Substituting this equivalence into the definition of inertial mass yields the law as a theoretical identity between independently defined quantities. The derivation is anchored in gravity because weight uniquely bridges statics and kinematics, yet the result is independent of the underlying force mechanism. The derivation carries structural consequences: modified-inertia formulations of MOND are inadmissible under the PEPM-WEP constraint; the location-invariance of the Kibble-balance realization of the SI kilogram is secured on first principles; and under the PEPM alone, torsion-balance and free-fall experiments constitute equally direct tests of the WEP. More fundamentally, Newton's Second Law is not an irreducible axiom of mechanics, but a structural consequence of deeper physical principles: energy conservation and the Einstein Equivalence Principle.