Quantum Phase Propagation, Light-Cone Invariance (∆τ = 0), and the Thermodynamic Emergence of Spacetime: A Vacuum Statistical Mechanics Mechanism for the Cosmological Constant Scale and Unitary Information Conservation

Abstract

The 120-orders-of-magnitude discrepancy in the estimation of the quantum vacuum energy densityreflects a fundamental disconnect between Quantum Field Theory in flat space and the holographicconstraints imposed by Emergent Gravity. In this paper, we reevaluate the zero-point energycalculation starting from the induced gravity formalism and the UV/IR coupling proposed byCohen, Kaplan, and Nelson. We demonstrate that requiring the total vacuum energy within avolume of cosmological radius L ∼ H−10 not to exceed the mass of the corresponding black holeestablishes a non-local link between the ultraviolet cutoff scale (kUV) and the infrared cosmologicallimit (kIR). We analyze the complementary role of the null proper time condition (∆τ = 0) as afilter of radiative observability on the mass shell and show how Newton’s constant G emerges fromvacuum dynamics via Sakharov induction. Finally, we extend the model to unitary informationpreservation in gravitational collapse horizons and refine the proposed Q-VLBI interferometricprotocol for experimental verification.