Quantum Jitter in the Refractive Index: Fundamental Limits in Casimir Force Measurements

The Casimir force has traditionally been modeled as a macroscopic manifestation of quantum vacuum fluctuations between perfectly conducting surfaces. However, recent advances in high-precision optical and nanomechanical measurements reveal that the refractive index of materials is not a static quantity, but exhibits quantum-scale fluctuations — a phenomenon we refer to as quantum jitter in the refractive index. This work introduces a theoretical framework for describing such fluctuations and derives their impact on measurable Casimir forces at submicron separations. The analysis establishes lower bounds for the detectability of Casimir forces in media with fluctuating dielectric response, showing that the apparent deviations from the standard Lifshitz theory can arise from refractive index noise intrinsic to the quantum vacuum itself.