Stochastic gravity

We give a summary of the status of current research in stochastic semiclass ical gravity and suggest directions for further investigations. This theory generalizes the semiclassical Einstein equation to an Einstein-Langevin eq uation with a stochastic source term arising from the fluctuations of the e nergy-momentum tensor of quantum fields. We mention recent efforts in apply ing this theory to the study of black hole fluctuation and backreaction pro blems, linear response of hot Oat space, and structure formation in inflati onary cosmology. To explore the physical meaning and implications of this s tochastic regime in relation to both classical and quantum gravity, we find it useful to take the view that semiclassical gravity is mesoscopic physic s and that general relativity is the hydrodynamic limit of:certain spacetim e quantum substructures. We view the classical spacetime depicted by genera l relativity as a collective state and the metric or connection functions a s collective variables. Three basic issues-stochasticity, collectivity, cor relations-and three processes-dissipation, fluctuations, decoherence-unders core the transformation from quantum microstructure and interaction to the emergence of: classical macrostructure and dynamics. We discuss ways to pro be into the high-energy activity from below and make two suggestions: via e ffective field theory and the correlation hierarchy. We discuss how stochas tic behavior at low energy in:an effective theory and how correlation noise associated with coarse-grained higher correlation functions in an interact ing quantum field could carry nontrivial information about the high-energy sector. Finally, we describe processes deemed important at the Planck scale , including tunneling and pair creation, wave scattering in random geometry , growth of fluctuations and forms, Planck-scale resonance states, and spac etime foams.