Characteristics of unification: exploring the tension between quantum and gravitational physics

Abstract

Ever since the bifurcation of classical physics into general relativity and quantum physics, physicists have sought a unified theory of quantum gravity. However, the profound mathematical and conceptual difference between the two theories has meant little success. Despite this, the partial unification achieved in quantum field theory in curved spacetime (QFTCS) has yielded novel phenomena such as Hawking radiation and raised conceptual questions such as the problem of time and the black hole information paradox. While proposed grand syntheses such as string theory and loop quantum gravity approach the problem from a top-down perspective, toy theories and in particular, the continued study of QFTCS—constituting the bottom-up approach—address problems of unification with a stronger empirical basis. Recently, a new field known as relativistic quantum information has applied techniques and concepts from quantum optics & computing to QFTCS and toy theories. In this thesis, I utilise relativistic quantum information as well as standard techniques from QFTCS to investigate four projects. In the first project, we consider the black hole information paradox and the associated firewall paradox and suggest a modification of the standard black hole theory. We propose that the vacuum state of a scalar field around a black hole is a modified Unruh vacuum. In (1+1) dimensions, we show that a free-faller close to an event horizon can be modelled as an inertial observer in a modified Minkowski vacuum. The modification allows for information-leaking correlations at high frequencies. Using a Gaussian detector centred at k0, we find that the expectation value of the number operator for a detector crossing the horizon is proportional to 1/|k0|, implying that the free-faller will observe unbounded numbers of high energy photons, i.e. a firewall. In the second project, we derive the theory of a scalar field in Minkowski spacetime and its coupling with gravitational waves. Using Feynman diagrammatic techniques, we identify the reason why particles are not created by linear plane gravitational waves up to arbitrary orders in Feynman diagrams. We then extend our theory to second order gravitational waves & diagrams and show how non-linear waves could create particles. Finally, we show how the gravitational quasinormal modes (QNMs) of a Schwarzschild black hole play the role of a multimode squeezer that can generate particles. For a minimally coupled scalar field, the QNMs “squeeze” the initial state of the scalar field and produce scalar particles. In the third project, we examine acausal quantum mechanics and causal inequalities. Processes with an indefinite causal structure may violate a causal inequality, which quantifies quantum correlations that arise from a lack of causal order. We show that when the inequalities are analysed with a Gaussian-localised field theoretic definition of particles and labs, the causal indeterminacy of the fields themselves allows a causal inequality to be violated within the causal structure of Minkowski spacetime. We also quantify the violation of the inequality and determine the optimal ordering of observers. Finally, in the fourth project, we derive the theory for the levitation of a mirror by a laser. Using a Fabry-Perot cavity oriented vertically, a laser maintains a circulating steady state ‘bed’ of photons that supports a freely floating upper mirror. The fluctuations of the mirror-cavity system around the steady state then act as a linearised quantum optomechanical system. We analyse the stability of the system and conclude that for experimentally accessible parameters, the mirror must be ‘blue detuned’ and would normally be considered in optomechanics as weakly coupled to the cavity. However, when we calculate the entanglement between the mirror and cavity using the covariance matrix and we find fairly strong entanglement (15 ebit peak) between them. Finally, we find that the mirror’s position is squeezed below shot noise.