Time as an Emergent Spectral Observable

Time is not assumed as a fundamental background parameter but emerges as an observable associated with the spectral structure of a universal substrate. Requiring finite physical response excludes continuous scale invariance and enforces discrete scale invariance, which in turn generates logarithmic phase modes that order physical events. Event times are thus understood as phase coordinates of substrate eigenmodes rather than as points along an intrinsic temporal flow. Statistical tests across independent physical systems—most notably solar wind magnetic turbulence—reveal highly significant logarithmic phase coherence that survives structure-preserving null hypotheses, ruling out chance, clustering, or rate effects. In this framework, relativistic time arises as a coarse-grained limit of densely populated spectral modes, while time itself is reinterpreted as an emergent ordering observable derived from measurable correlations rather than a primitive ingredient of physical law.