Pressure Tuned Modal Rank Reduction in Confined Electromagnetic Fields

Does stronger confinement drive a multimode electromagnetic field toward a lower-rank state? Existing laser, polariton, and photon-condensation experiments show macroscopic occupation and phase locking, while high-pressure photonics shows that stress can tune cavity spectra and polarization. These facts do not establish a pressure-driven reduction of modal entropy. We formulate that missing proposition as a falsifiable hypothesis. The state variable is the normalized first-order coherence matrix, whose eigenvalue spectrum defines modal entropy, effective mode number, purity, and a basis-independent majorization order. We prove a null result: lossless linear compression, including arbitrary pressure-dependent unitary mode mixing, cannot change that spectrum. Apparent rank reduction can also arise from calibrated mode-dependent attenuation. A genuine collective effect therefore requires a nonlinear, dissipative, thermalizing, or gain-mediated channel and must exceed a measured linear-filter baseline. We give a minimal multimode rate model that predicts a pressuredependent instability, a two-parameter phase map in pressure and intracavity photon number, and a downward shift of the critical photon number with pressure. We then specify a diamond-anvil microcavity experiment with bidirectional pressure sweeps, coherence tomography, energy accounting, cross-material controls, and preregistered majorization tests. The experiment is informative even if it yields a null result: it separates ordinary optical filtering from collective electromagnetic self-organization. Finally, we state the narrow conditions under which laboratory evidence could motivate, but not verify, an extrapolation to fields under gravitational collapse. The proposal converts a broad entropy-reduction intuition into an operational test with explicit failure conditions.