Relational Foundations: Fundamental Constants, Relative Phase, Action, and the Persistence Principle

This paper proposes a pregeometric foundation in which fundamental physical quantities are understood not as isolated 'absolute quantities' but as relations among multiple quantities. The point of departure is not philosophical relationalism. Rather, equations describing the speed of light, the fine-structure constant, the Planck constant, momentum, energy, and action—either standard relations or relations proposed in this research—repeatedly take the form of ratios, differences, gradients, and phase differences. In the preceding paper, a fundamental speed c₀ = ℓ₀/τ₀ was defined from a spatial quantum ℓ₀ and temporal quantum τ₀; under the hypothesis c₀ = c, synchronization of C₂ and C₃ gives Δφrel = π/3 and α = (rrel/ℓ₀)Δφrel = (π/3)(rrel/ℓ₀). Taking these results as a starting point, the present paper places dS = ℏdφ, dS = p·dx − E dt, p = ℏ∇φ, and E = −ℏ∂φ/∂t in the same relational sequence. In this organization, c connects space and time, ℏ connects phase and action, and α connects a relative spatial scale and relative phase. A further hypothesis, the Persistence Principle, is introduced: relational structures that cannot maintain self-consistency do not persist over long times, whereas self-consistent relations remain. The possibility is then examined that, in a continuous limit, this principle leads through phase stationarity δφ = 0 to stationary action δS = 0. The central thesis is not to assume in advance that relation is fundamental, but to observe that, when the equations of physics are traced toward a lower level, space, time, phase, action, and fundamental constants become linked as relational quantities.