Emergent Time from Zero-Point Flux Obstruction

This working paper proposes a hypothetical mechanical framework for the n=4 codimension layer within Push-Theory. We explore the idea that physical time might not be a fundamental dimension but the cumulative geometric record of zero-point energy (ZPE) flux obstructed by matter. In this view, an n=3 matter structure (a topologically closed Möbius loop) continuously obstructs a portion of the surrounding n=0 ZPE flux; the accumulated obstruction traces a four-dimensional phase volume that we propose to identify with the physical passage of time for that structure.

Defining a loop radius r_loop specific to each particle class, we obtain a working relation t_emergent ∼ m · r_loop · ℓ_P / ħ that reproduces the correct qualitative ordering across photons, neutrinos, electrons, protons, and black holes: massless carriers are timeless, light particles age almost imperceptibly, and horizon-scale objects approach a frozen internal clock. We then consider how a local increase in obstruction density (mass concentration) raises an effective refractive index n_eff of the medium, offering a mechanical picture consistent in direction with gravitational time dilation, though the quantitative bridge to the Schwarzschild metric is not established here.

We explicitly flag the largest open problem in this line of reasoning: the summation from single-particle phase accumulation to a macroscopic gravitational field has not been carried out, and the r_loop definition itself requires a distinct physical prescription per particle class rather than a single universal formula. This paper is offered as a working hypothesis, not a finished derivation.