Semiclassical Pictures of Gravity: Investigating and Testing Non-Linear Theories of Quantum Gravity

Abstract

The question of how to unify quantum mechanics with general relativity is one of the most difficult, far-reaching questions of modern physics. This thesis investigates one potentinal answer to that question: semiclassical gravity, for the purpose of determining experimental parameters that can be used to test the theory. It examines two branches of semiclassical gravity theories: the Schrodinger-Newton equation, and a new formulation called Causal Conditional Collapse.

The Schrodinger-Newton Equation is a theory of semiclassical gravity that has recently been shown to provide testable, falsifiable predictions using optomechanical oscillators. This thesis derives and uses a Taylor expansion of the Schrodinger-Newton equation, and examines it in the mathematical context, then models it for a series of experimental devices - some extant, some in development - and compares the predictions of the model to the noise floor of the systems to determine whether the device in question could detect Schrodinger-Newton semiclassical gravity. It is shown that the prototype device for the Laser Interferometer Space Antenna; LISA Pathfinder, had sufficient sensitivity to detect the effects of Schrodinger-Newton semiclassical gravity, and so this data was used to rule the theory out, by comparing the empirical data to the modelled prediction.

Causal Conditional Collapse is a new formulation of semiclassical gravity developed in response to the LISA Pathfinder results, which draws on the Transactional Interpretation to restrict the propagation of wave function collapse to light cones. This formalism allows for the linearisation of the nonlinear gravitational self-interaction term common to all semiclassical gravity theories, and allows us to construct a Wiener-Hopf filter to treat the semiclassical gravitational potential as a feedback force. Using this linearised, feed-back equivalent formalism, we construct new models, comparing them to the LISA Pathfinder, and and other experimental systems, and find that the signal of Causal Conditional Collapse is much harder to detect than that of the Schr\"odinger-Newton equation - the semiclassical signature is sufficiently small that the theory cannot currently be ruled out given current experimental noise constraints.