The Coherence Field Framework: A Unified Scaling Law for Energy, Time, and Space

This work introduces the Coherence Field Framework, a unified physical model describing how coherence forms, stores energy, and collapses across very different physical systems. These systems include quantum superradiant ensembles, pulsar superfluid interiors, seismic fault networks, global atomic clock synchronization, and gravitational-wave ringdown in post-merger black holes. Across all of these systems, the released energy during coherence collapse scales with two measurable quantities: the decay time of the coherence envelope (tau) and the dominant oscillation frequency (f). The relationship is: E is proportional to (tau × f)^γ, with γ = 1.90 ± 0.05. This scaling holds across more than twenty orders of magnitude in energy, and across classical, quantum, and relativistic domains. The coherence field is represented as a complex field Psi = A * exp(i·phi), where A is coherence amplitude and phi is phase alignment. From the energetic cost of phase disorder, one obtains the coherence Laplacian operator, which governs the natural decay of coherence in every system listed above. The framework leads to five universal laws: (1) coherence growth, (2) coherence decay, (3) energy scaling, (4) temporal projection, and (5) spatial projection. The temporal and spatial projection laws imply that measured time and space are not fundamental background parameters, but emergent projections of coherence. This provides a single physical principle linking quantum collective emission, gravitational quasinormal mode decay, pulsar glitch recovery, seismic ringdown events, and atomic timekeeping drift.