Momentum First - A Deeper Foundation from which Physical Limits Emerge

This paper develops the Momentum-First framework, in which Momentum is treated as the primitive physical quantity from which the familiar structures of Relativity are reconstructed. Part I reconstructs the logical structure of Relativity while resolving conceptual circularities concerning mass, proper time, and events, and reducing the need for auxiliary postulates. Starting from Momentum, together with the primitive notions of succession and extension, it reconstructs proper time, proper distance, spacetime, trajectories, events, the energy–Momentum tensor, and gravitation. Beyond this reconstruction, the axiomatic shift provides a wider explanatory power: Proper time under acceleration — a blind spot of Relativity — finds a natural treatment. Because proper time is constructed from Momentum, the universality of the quantum relations defining the photon Momentum ensures proper time universality without requiring the clock postulate. As Aristotle observed, the irreversibility of one's own becoming is among the most fundamental requirements of physics. The standard formulation secures it only indirectly, as a postulate on a derived quantity (P⁰ > 0); in Momentum First, it follows immediately from Momentum's primitive definition as the capacity for change toward one's own future. This primacy of Momentum extends into the quantum domain as well: Heisenberg's physical intuition acquires a natural explanation once position is understood as a quantity reconstructed from Momentum rather than a primitive observable. Part II investigates whether the Momentum-First ontology naturally extends beyond the continuous framework of Relativity. It proposes that Momentum dynamics possesses an intrinsic discrete structure, giving rise to both the discrete structure of spacetime and fundamental physical limits. Two conjectures are introduced: the existence of an elementary proper-time quantum, Δ ₀ = h/(‖P‖c), and a bound on the Momentum norm variation between successive proper-time quanta, leading for massive particles to the maximum four-force = m²c³/h. These conjectures are independently supported by the Margolus–Levitin bound and Zurek's predictability criterion, quantitatively corroborated through QCD confinement, neutron-star stability near the TOV limit, and the Schwinger instability threshold, and give rise to experimentally testable predictions while remaining logically independent and individually falsifiable. Although speculative, they generate experimentally testable predictions while remaining fully compatible with the standard quantum formalism, including the Schrödinger equation. If confirmed, this framework would suggest that both the continuous spacetime structure of Relativity and the stability of physical states emerge from a deeper discrete dynamics of Momentum. The broader cosmological implications of this framework, including a new interpretation of dark matter and dark energy, are developed in the companion paper Momentum-First Cosmology: A New Paradigm for Dark Matter and Dark Energy [31].