Threshold Emergence of Physical Laws: A Scale-Relative, Field-Dependent, Infinitely-Layered Quantization Framework

Modern physics has long treated the tension between continuity and discreteness as a fundamental duality: wavefunctions and fields appear continuous, while measurement outcomes remain sharply quantized. Yet, as the article emphasizes, this duality is not intrinsic to nature but a consequence of observational scale and field dominance. Drawing directly from the text — “both continuity and discreteness are relative to the energy scale of observation and to the dominant field at that scale” — the framework proposes that no continuous layer is truly fundamental. Instead, every continuous regime is the coarse-grained limit of a deeper discrete structure governed by fields not yet discovered. The paper introduces an infinitely recursive hierarchy of layers — “discrete → continuous → discrete → continuous… with no floor and no ceiling” — where each transition is controlled by a normalized energy-scale parameter \( \varepsilonF = E / Ec(F) \). At the critical point \( \varepsilonF \approx 1 \), each field generates a field-specific horizon \(HF\), which simultaneously acts as a boundary of informational inaccessibility and the only communication channel between adjacent layers. This framework reinterprets foundational physical concepts: virtual photons become momentary openings of the electromagnetic horizon; entanglement becomes a persistent sub-layer connection; and black-hole interiors become continuous limits of deeper discrete fields rather than singularities. By analyzing residual vacuum properties—such as Planck’s constant, nonlocality, and CPT symmetry—the article argues that these unexplained quantities are fingerprints of undiscovered sub-substrate fields. Overall, the work proposes a unified, scale-relative, horizon-based architecture of physical law in which quantization, mass, geometry, and even spacetime itself emerge from recursive discretization and field dominance.