Quantum weak measurements with states both pre- and post-selected offer a window into a hitherto neglected sector of quantum mechanics. A class of such systems involves time dependent evolution with transitions possible. In this paper we explore two very simple systems in this class. The first is a toy model representing the decay of an excited atom. The second is the tunneling of a particle through a barrier. The post-selection criteria are chosen as follows: at the final time, the atom remains in its initial excited state for the first example and the particle remains behind the barrier for the second. We then ask what weak values are predicted in the physical environment of the atom (to which no net energy has been transferred) and in the region beyond the barrier (to which the particle has not tunneled). Thus, just as the dog that didn't bark in Arthur Conan Doyle's story Silver Blaze gave Sherlock Holmes meaningful information about the dog's non-canine environment, here we probe whether the particle that has not decayed or has not tunneled can provide measurable information about physical changes in the environment. Previous work suggests that very large weak values might arise in these regions for long durations between pre- and post-selection times. Our calculations reveal some distinct differences between the two model systems.

This thesis addresses certain quantum aspects of the event horizon using the AdS/CFT correspondence. This correspondence is profound since it describes a quantum theory of gravity in d + 1 dimensions from the perspective of a dual quantum field theory living in d dimensions. We begin by considering Rindler space which is the part of Minkowski space seen by an observer with a constant proper acceleration. Because it has an event horizon, Rindler space has been studied in great detail within the context of quantum field theory. However, a quantum gravitational treatment of Rindler space is handicapped by the fact that quantum gravity in flat space is poorly understood. By contrast, quantum gravity in anti-de Sitter space (AdS), is relatively well understood via the AdS/CFT correspondence. Taking this cue, we construct Rindler coordinates for AdS (Rindler-AdS space) in d + 1 spacetime dimensions. In three spacetime dimensions, we find novel one-parameter families of stationary vacua labeled by a rotation parameter β. The interesting thing about these rotating Rindler-AdS spaces is that they possess an observer-dependent ergoregion in addition to having an event horizon. Turning next to the application of AdS/CFT correspondence to Rindler-AdS space, we posit that the two Rindler wedges in AdSd+1 are dual to an entangled conformal field theory (CFT) that lives on two boundaries with geometry R × Hd-1. Specializing to three spacetime dimensions, we derive the thermodynamics of Rindler-AdS space using the boundary CFT. We then probe the causal structure of the spacetime by sending in a time-like source and observe that the CFT “knows” when the source has fallen past the Rindler horizon. We conclude by proposing an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space. Towards the end, we consider the concept of weak measurements in quantum mechanics, wherein the measuring instrument is weakly coupled to the system being measured. We consider such measurements in the context of two examples, viz. the decay of an excited atom, and the tunneling of a particle trapped in a well, and discuss the salient features of such measurements.