Non-linear coupling of quantum theory and classical gravity

Abstract

Discusses the possibility that the non-linear evolution proposed earlier for a relativistic quantum field theory may be related to its coupling to a classical gravitational field. Formally, in the Schrodinger picture, it is shown how both the Schrodinger equation and Einstein's equations (with the expectation value of the energy-momentum tensor on the right) can be derived from a variational principle. This yields a non-linear quantum evolution. Other terms can be added to the action integral to incorporate explicit nonlinearities of the type discussed previously. The authors discuss briefly the possibility of giving a meaning to the resulting equation in a Heisenberg or interaction-like picture.