This preprint develops a substrate-based framework in which several familiar structures of relativistic quantum field theory emerge from a finite-speed site-link medium. The starting point is a discrete substrate with: directional propagation channels local channel mixing local phase or internal-basis comparison rules on links a distinction between exclusive site excitations and shareable link excitations From these ingredients, the manuscript builds a coherent emergence ladder: Dirac-like dynamics from a finite-speed substrateIn one spatial dimension, a two-channel propagation model with local mixing yields a 1+1 dimensional Dirac equation in the continuum limit. The universal speed ccc is set by the substrate update rule, while the mass term is interpreted as local channel mixing. Higher-dimensional spinor structureExtending the same logic to two and three spatial dimensions naturally introduces Pauli and then Clifford/gamma-matrix structure, yielding the standard relativistic dispersion relation. Gauge emergence from local redundancyLocal phase redundancy leads to Abelian link variables and gauge-covariant derivatives. Local multi-component internal-basis redundancy leads to matrix-valued links and non-Abelian connection fields. Maxwell / Yang–Mills structure from curvature costThe simplest local plaquette curvature cost on the substrate reproduces Maxwell- and Yang–Mills-type gauge dynamics in the continuum limit. Hamiltonian, Lagrangian, and action formulationThe paper writes an explicit site-link Hamiltonian with fermionic matter modes on sites and bosonic connection modes on links, then derives the corresponding continuum Lagrangian and action. Quantum histories and measure splitThe action is interpreted as the cumulative propagation/reconfiguration cost of a substrate history. Quantum amplitudes arise from summing over admissible histories weighted by phase. In this picture, fermionic Grassmann measures are associated with exclusive site excitations, while bosonic measures are associated with shareable connection/link modes. The manuscript is presented as a derivational framework, not as a finished fundamental theory. It does not yet derive the full Standard Model, select the observed gauge groups and particle representations, derive chirality or the Higgs sector, or provide a complete first-principles proof of spin-statistics or Born’s rule. Its aim is narrower: to show that a surprisingly large amount of the formal grammar of relativistic quantum field theory may arise from a compact finite-speed substrate architecture.
Danut Antoche-Albisor (Wed,) studied this question.