ENTANGLEMENT AS METRIC (VIII v4)

Abstract

We present a rigorous pregeometric formulation of space-time emergence by emb edding Ted Jacobson ’ s thermo dynamic gravity (1995) and Mark Van Raamsdonk ’ s entanglement-metric corresp ondence (2010) into the FCD-RB (Folded Crunch Dip ole – Reversed Big Bang) braneworld framework. In FCD-RB, the quantum entanglement b etween the parallel branes is mediated by a dense, discrete network of non-traversable Einstein-Rosen (ER) bridges (transbrane dip oles), acting as the microscopic carrier of the entanglement entropy. We show that the continuous metric of our 4D space-time is an emergent coarse-grained description of this network, governed by a scalar connectivity fi eld d(x , t). By identifying the lo cal Killing horizon area with the ER throat area, we derive the Einstein- fi eld equations from the Clausius relation Q = T S , while resolving Jacobson ’ s long-standing asymptotic vacuum b oundary paradox. Speci fi cally, the relaxation of the connectivity fi eld to a basal background value d0 > 0 ensures space-time connectivity and metric coherence even in deep cosmic voids where heat flows vanish( Q ->0).