Discrete electromagnetism in a finite-information space–time framework

Building on previous work that models space–time as a discrete network of finite-information cells, we develop a gauge-covariant formulation of electromagnetism within this framework. Each Planck-scale cell carries a finite-dimensional Hilbert space that stores local quantum imprints of fields and interactions. Embedding U(1) gauge symmetry through link variables and gauge-covariant imprint operators ensures unitarity, strict locality, and exact charge conservation at the microscopic level, while Lorentz and gauge invariance are recovered in the continuum limit. The resulting effective operator expansion predicts Planck-suppressed but potentially observable modifications to photon propagation, including parity-odd birefringence and parity-even refractive shifts. These effects influence charged black-hole evaporation through non-thermal correlations in Hawking radiation, modify vacuum polarization and coupling flows near the Planck scale, and may leave imprints in the cosmic microwave background, fast radio bursts, or large-scale magnetic fields. By preserving unitarity through strictly local information storage, the framework provides an intrinsic ultraviolet regulator and a falsifiable mechanism for information retention. Although direct Planck-scale experiments remain infeasible, indirect probes such as primordial black-hole searches, gravitational-wave ringdowns, precision cosmology, and quantum-simulation analogues offer potential avenues to test the theory. • We construct a gauge-invariant embedding of U (1) electromagnetism into the Quantum Memory Matrix (QMM) framework, demonstrating that exact local gauge symmetry, locality, and unitarity can be preserved on a Planck-scale discretized space–time with finite-dimensional Hilbert cells. • We derive a continuum effective operator expansion from the underlying lattice theory, obtaining Maxwell–QED at leading order together with Planck-suppressed corrections proportional to ( ∂ S ) F F ̃ and ( ∂ S ) 2 F 2 , thereby linking microscopic memory imprints to observable photon propagation effects. • We show that finite Hilbert-space capacity per cell provides a structural ultraviolet regulator, replacing divergent loop integrals by finite sums and softening trans-Planckian behavior without introducing an ad hoc cutoff. • We identify falsifiable phenomenological signatures, including parity-odd birefringence, parity-even refractive index shifts, and non-thermal correlation patterns in charged black-hole evaporation, all parametrically controlled by the effective couplings η 1 , η 2 , and the imprint-gradient scale λ . • We provide an explicit parameter map connecting cosmological dark-sector fits within QMM to independent bounds from CMB polarization, FRB/GRB timing, laboratory cavity experiments, and primordial black-hole evaporation, thereby establishing observational testability of the framework.