Emergent Spacetime from Projection-Induced Information Loss

Spacetime is typically assumed to be a fundamental structure underlying physical law. We propose instead that spacetime geometry, causal structure, and aspects of gravitational dynamics emerge from information loss under coarse-graining of an underlying quantum system. Modeling observables as completely positive trace-preserving (CPTP) maps, we construct an information-geometric description based on the Fisher metric. We show that irreversible entropy flow induces an effective deformation of this metric. Under well-defined conditions, this deformation leads to a transition in signature, providing a mechanism for the emergence of Lorentzian structure without imposing it a priori. Using a Gaussian model, we demonstrate how causal structure follows from monotonicity of distinguishability. We further derive a scaling relation for an emergent vacuum energy density tied to coarse-graining scale. The framework connects quantum information, spacetime geometry, and cosmology, and yields testable phenomenological consequences.