Time and Spacetime from Open-System Boundary Persistence: Two Postulates

The author proposes two postulates for the foundation of time and spacetime in open quantum systems. Postulate P1 (Time): the proper time of an open quantum system is generated by the integral of its boundary structural-persistence functional Φ on the variationally selected autonomous boundary. Postulate P2 (Spacetime): spacetime is the synchronisation pattern of a network of open-system boundary Φ-clocks coupled through shared baths. From P1 the author derives (i) a thermodynamic clock τ_∂ = ∫ Φ ds, whose sign and magnitude classify structure-building, structure-maintaining, and structure-dissolving regimes, and (ii) two channels of local arrow-inversion windows (monitored feedback Φfb > 1; non-Markovian backflow ΦNM > 1), bounded in duration by the local entropy budget and consistent with the global second law (Sagawa–Ueda for feedback; memory-induced negative σᵢrr for backflow). From P2 the author derives (iii) a synchronisation functional Σᵢj between two Φ-clocks coupled through a shared bath, with the Connes–Rovelli thermal time hypothesis recovered in a triple limit (joint KMS state + Σ → 1 + Spohn-modular reduction), and (iv) an induced graph distance dᵢj = −log|⟨Xᵢ Xⱼ⟩|/N that satisfies the triangle inequality on a metric-compatibility regime operationally characterised by joint CP-divisibility and absence of BLP non-Markovianity witnesses on the relevant triangles. The two witness conditions are shown to be jointly necessary for the triangle inequality on this regime; their sufficiency is conjectured under qualifications stated in the manuscript and listed as an open problem. The author provides a complete epistemic-status audit of every quantitative claim and an explicit comparison with the principal existing programmes on time and emergent spacetime: Connes–Rovelli thermal time hypothesis, Page–Wootters conditional time, Van Raamsdonk / AdS-CFT entanglement-based emergence, causal set theory (Sorkin), Verlinde / Padmanabhan thermal gravity, and Wolfram hypergraph rewriting. The audit of falsifiable predictions, the experimental discriminators (3-qubit feedforward, directional asymmetry, triangle inequality), and the worked-case reanalysis of Micadei et al. (2019) are the subject of the companion Preprint II.