Description
Title: A nonlinear gravitisation of quantum field theory?
Abstract: We develop a relativistically causal generally covariant gravitisation of quantum field theory. The resulting model is similar to Møller-Rosenfeld semiclassical gravity: the classical gravitational field is sourced by the expectation value of the quantum stress-energy tensor, though now taken with respect to the local quantum state at each point of spacetime. We derive the weak-field limit which exhibits the explicitly causal dynamical structure of the theory, and recover the Schrödinger-Newton system in the nonrelativistic limit. This model can thus be understood as a causal completion of the Schrödinger-Newton equation. We then explore relativistic quantum measurements in this nonlinear setup, showing that these need not lead to superluminal signalling should quantum states update in the future light-cone of the measurement region. This aligns with detector-based quantum measurements in quantum field theory. We show that the discontinuities in the expectation value of the stress-energy tensor caused by quantum measurements need not violate the distributional gravitational field equations. We also highlight that the theory presents non-standard measurements -- namely readout devices -- from its nonlinearities, which allows one to approximately determine a quantum state without affecting it through the state's influence on the
classical gravitational field. This allows for quantum state cloning, though in a way consistent with no-superluminal signaling. If time permits, we will discuss the black-hole information paradox within this model, and explore some routes towards the falsifiability of the theory.