Physics

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

Lars Nordmann

Featured August 10, 2026

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Simply

Newton's famous rule $F = ma$ isn't just an observation; it's a necessary truth derived from two deeper ideas: you can't get something for nothing (no perpetual motion), and everything falls at the same rate.

In depth

The paper rigorously derives Newton's Second Law (

F = ma

) as a theoretical identity rather than an empirical axiom. This is achieved by grounding gravitational mass and force as independent primitives using Suppes' measurement framework under the Principle of Excluded Perpetual Motion (PEPM). The synthesis of Stevin's static and Galileo's kinematic inclined-plane analyses then establishes inertial mass as an object-intrinsic quantity, and the Weak Equivalence Principle (WEP) compels the equivalence of inertial and gravitational mass, leading directly to

F = ma

Key Takeaways

1
Newton's Second Law ( $F = ma$ ) is reclassified from an irreducible axiom to a theoretical identity, derived from deeper physical principles.
2
The Principle of Excluded Perpetual Motion (PEPM) and the Weak Equivalence Principle (WEP) are identified as the foundational constraints for this derivation.
3
The derivation provides first-principles grounding for the SI kilogram's location-invariance and unifies different experimental tests of the WEP.

Conceptual Flow

HIGH LEVEL

Methodology: Deriving F=ma from First Principles

The paper shows how a famous physics rule can be built step-by-step from simpler, more fundamental ideas about how things move and balance.

No Perpetual Motion

All Fall Same Speed

Combine Ideas

Define Mass

Define Force

F = Mass x Acceleration

Results: Impact on Physics Foundations

This new way of understanding the rule means we can trust our measurements more, and it helps us decide which new theories about gravity make sense.

F = ma is Derived

Leads To

Stronger Foundations

Validates SI Kilogram

Guides New Theories