Coherence Filtering and Phase Correction in Gravitational-Wave Detectors from the Universal Ψ Lagrangian

Current kilometer–scale interferometers such as LIGO and Virgo operate with 4kmarm lengths assumed to be optimal for 1064nm laser light in a purely classical spacetimemetric. However, when the interferometric phase evolution is analyzed within theUniversal Ψ Lagrangian framework, the gravitational channel and the optical referencearm appear detuned by a coherence factor F = 2/√3 ≃ 1.1547. This factor emergesdirectly from the informational constraint (Ψ†Ψ − 1)2 and quantifies the mismatch betweenthe physical metric fluctuations and their coherent representation in the Ψ field.The correct resonant condition requires an effective arm lengthLΨ =LexpF≈4.00 km1.1547= 3.46 km,which restores phase coherence between optical and gravitational degrees of freedomand maximizes the detector’s true sensitivity. This paper provides a rigorous derivationof the coherence factor from the Universal Ψ field and formulates the practical correctionrequired for current gravitational–wave observatories.