Relational Emergent Time for Quantum System: A Multi-Observer, Gravitational, and Cosmological Framework

Abstract: We present a relational framework in which temporal structure is not fundamental but emerges from correlations within a globally stationary quantum state. Each subsystem includes an internal clock, and conditional states evolve effectively with respect to these internal readings. The construction naturally extends to relativistic motion, gravitational redshift, and cosmological expansion, leading to a unified emergent-time functional valid across diverse physical regimes. The theory reproduces classical time dilation, predicts correlation-dependent deviations from standard evolution, and suggests that non-interacting or massless particles exhibit negligible internal time. These consequences open directions for conceptual and experimental investigations in the foundations of temporal physics, from multi-clock quantum systems to precision metrology and cosmological settings. In particular, the framework suggests measurable deviation from standard quantum evolution for highly entangled systems and predicts negligible internal time for massless particles.