Quantum Field Theory of Time

In canonical quantum gravity the Wheeler–DeWitt equation freezes evolution, while standard quantum theory treats time as an external parameter. The Weak Entanglement Symmetry Hypothesis (WESH) promotes entanglement as the carrier of statistical Lorentz-type symmetry and as an engine of endogenous dissipative dynamics. Lorentz symmetry is recovered in expectation over the Poissonian ensemble of Eigentime events (discrete stochastic localizations of the time-field operator $T(x)$ within its continuous spectrum, induced by the quadratic WESH dissipators D[T²(x)] and D[Lxy] — mean spacing τEig), whereas global conserved charges obey a stronger operator-level constraint (WESH–Noether, L^[Qₐ]=0). On this foundation, physical time becomes a local quantum field operator T̂(x), subject to superposition and objective collapse, with dynamics constructed from first principles. An open-system master equation in an auxiliary label s generates physical time through dt/ds=Γ[ρ]≥ 0. Complete positivity, no-signaling, and a pre-geometric WESH–Noether conservation principle single out a CPT-even Lindblad structure with quadratic local dissipators and a Rényi-2 weighted bilocal channel. In the infrared, spontaneous gradient alignment ∂_μ T = k·∂_μΦ defines an emergent metric and reproduces the Einstein equations with Newton constant fixed by the same matching; no background geometry is assumed. A near-horizon analysis of the T² channel and the emergent KMS structure yields SBH = A/(4LP²) + γBH·ln(A/LP²) + without thermal ansatz. The same eigentime statistics yields the cosmological constant as irreducible shot noise, with scaling δΛ ~ H². The framework predicts collective coherence scaling τcoh ∝ N² and a robust cos²θ angular law for parity decay. Collision-model simulations ($N=2$–$16$) and experiments on IBM Eagle and Rigetti Ankaa-3 show trends consistent with both signatures. The construction has no free dimensionless parameters; deviations from the $1/4$ prefactor, or the N² scaling would falsify the framework. This repository contains: The complete Manuscript (TEX, PDF). The Formal Verification source code in Lean 4 (6,700+ LOC). The Experimental Datasets (raw & processed).