Configuration Capacity: An Operational Measure of Distinguishability in Quantum Fields and Gravity

Quantum field theory assigns infinite-dimensional Hilbert spaces to finite spatial regions, while gravitational physics implies strict bounds on physically distinguishable states. This work introduces configuration capacity, a resolution-dependent operational measure of distinguishability defined using completely positive, trace-preserving coarse-graining channels and the trace distance. Configuration capacity quantifies the maximum number of operationally distinguishable configurations accessible to a physical system at finite resolution. It provides a conservative framework for reconciling infinite Hilbert-space structure with finite physical information without introducing new degrees of freedom or speculative microscopic assumptions. The concept is illustrated explicitly for harmonic oscillator systems, where finite experimental resolution enforces finiteness despite infinite Hilbert-space dimension. Standard entropy measures—including thermodynamic entropy, entanglement entropy, and Bekenstein–Hawking entropy—emerge as limiting cases or upper bounds under appropriate coarse-grainings. The framework further clarifies that gravitational interaction modifies unitary evolution through spacetime geometry but does not constitute a measurement, and that gravitational entropy bounds can be interpreted as ceilings on operational distinguishability rather than microscopic state multiplicity. This manuscript is intended for journal submission; the present version serves as an openly accessible preprint.