Band-Limited Relational Time in Constrained Quantum Gravity

We present a Lorentz-consistent, observer-relational construction of time for constrained
quantum gravity in which “time” is the phase advance of an internal clock subsystem restricted
to an observer’s finite spectral band. The construction—implemented via band-limited
POVMs1, modular-flow filters, or path-integral kernels—yields effective Schrödinger/Lindblad
dynamics for conditioned subsystem states, defines diffeomorphism-invariant band-relational
observables, and makes inter-observer consensus a function of spectral overlap and environmental redundancy. It preserves constraints, the Born rule, and no-signaling, while offering
regularization in path integrals and computable operational times in minisuperspace. This
provides a practical, testable bridge between canonical, relational, and algebraic approaches
to the problem of time.