We present a modification of quantum mechanics in which a specific class of state-dependent term is added to the Schroedinger Equation. We show that this term produces non-trivial effects which amount to the ‘wave function talking to itself’. We show that these effects are nevertheless causal (don’t violate relativity) while having profound experimental consequences. We also show that this modification has a simple embedding in local quantum field theory. While the physical effects are dramatic, they are also fickle, in that their strength depends on the cosmological history of the wave function of the universe. We will present proposals for laboratory (e.g., AMO), astrophysical, and cosmological tests that could be done to discover such an effect.