Time as a generated quantity: the ΔT differential-time model and its unification of relativistic, perceptual, and quantum temporal phenomena

Physical observation registers time not as an absolute quantity but as a structured comparison between two reference processes. We formalise this principle through the differential-time quantity ΔT(t) = S(t) − C(t), where S(t) represents the progression of an external reference structure and C(t) represents an internal reference structure maintained by the observer. Under a Post-Newtonian (1PN) approximation, ΔT(t) is shown to be grounded in the coordinate-invariant proper time difference, and its effective detuning Δωeff arises naturally from gravitational potential and peculiar-velocity differences between the two reference frames. Within this framework, we define cross as the local condition in which ΔT(t) enters a near-zero band with a simultaneous sign flip, and cross window as its maximal contiguous interval. From these definitions, we derive a temporal information weight W(t) that redistributes temporal contribution non-uniformly across otherwise identical physical events. We show that: (i) the cross-window width depends systematically on the frequency of the internal reference structure, providing a structural account of why higher-frequency internal references yield finer temporal resolution; (ii) relative velocity and gravitational potential each produce systematic deformations of ΔT(t), with integrated temporal support collapsing toward an operational near-loss threshold under extreme conditions; and (iii) a quantitative prediction for cross-window narrowing as a function of internal reference frequency is derived. The model connects, within a single formal language, relativistic time modulation (where ΔT arises from proper-time differences along distinct worldlines), perceptual time (where ΔT arises from the mismatch between neural oscillatory structure and external stimuli), and quantum-temporal difficulties (where the finite width of the cross window offers a conceptual reinterpretation of tunnelling time and quantum jump duration). All numerical figures are accompanied by exact reproducibility conditions. The causality constraint dΔT/dC > −1 is satisfied throughout.