Sequential Time Theory, Volume 2: Quantum Metrology and the Relativity of Observation Scale

This paper extends the temporal concept of Sequential Time Theory (STT) to the problem of metrology in the quantum domain. In STT, a time interval Δt is constructed by a counter n representing the number of realizations of a standard displacement ΔQᵤnit, while time t serves as a coordinate label assigned to this sequence. STT explicitly posits that "time is a scaling of physical change" and that "time is constructed solely by clock phenomena subject to the same conditions within a local system. " Consequently, in regimes where ΔQ is indistinguishable, time does not "cease to exist" but becomes "unconstructible (undefined). " Based on these definitions and axioms, this paper (i) organizes criteria for distinguishing between science and metaphysics, (ii) identifies conceptual confusions arising from the implicit assumption of an external classical clock in quantum theory, and (iii) proposes a relativity principle regarding differences in observation scale (e. g. , macroscopic observation of microscopic systems). We demonstrate that issues such as measurement, classicality, and tunneling time can be unifiedly organized as problems of "choice of clock (ΔQ) " and "recording (event-token) protocols. "Furthermore, we provide a mathematical derivation (Appendix A) showing that the intrinsic uncertainty of a physical clock (σ) naturally leads to the suppression of quantum interference terms (e^-²²), thereby identifying the metrological origin of decoherence and the phenomenological arrow of time. Version 4 Update: Major revision including Appendix A (Mathematical Proof of Intrinsic Decoherence) and Appendix B (Definition of Phenomenon Arrow). This version provides the quantitative foundation for the theory.