Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime

This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that some of the quantum histories must approximate (in a suitable sense) to classical histories, if the correct classical regime is to be recovered. This observation has significance for the formulation of new theories (such as quantum gravity theories) as it puts a constraint on the kinematics, if the quantum/classical correspondence p...

In the first part of this paper I propose the Construction Interpretation of the Quantum. The main point of this interpretation is that (unlike previous interpretations) it is not actually an interpretation but rather a methodology aimed to encourage a conceptually driven construction of a theory of Quantum Gravity. In so doing we will, I hope, resolve the ontological problems that come along with Quantum Theory. In the second part of this paper I offer a particular perspecti...

These are notes for a graduate course in quantum gravity planned at IFT-UAM/CSIC for the spring term of 2020, but delayed for an indefinite period of time (although a shortened version was given in the Escuela de Fisica (Institute of Physics) in the University of Costa Rica.). The aim of the course was to highlight the most important conceptual problems in the field and to summarize some of the most imaginative solutions to them that have been proposed in the literature. The ...

In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature of GR is at the forefront. However, the short distance dynamics in the quantum theory are quite different from those of GR and classical spacetimes and gravitons emerge only in a suitable limit. Our emphasis is on communicating the key strat...

This article will summarize selected aspects of the semiclassical theory of gravity, which involves a classical gravitational field coupled to quantum matter fields. Among the issues which will be discussed are the role of quantum effects in black hole physics and in cosmology, the effects of quantum violations of the classical energy conditions, and inequalities which constrain the extent of such violations. We will also examine the first steps beyond semiclassical gravity, ...

General lectures on quantum gravity.

Understanding quantum theory has been a subject of debate from its birth. Many different formulations and interpretations have been proposed. Here we examine a recent novel formulation, namely the coevents formulation. It is a histories formulation and has as starting point the Feynman path integral and the decoherence functional. The new ontology turns out to be that of a coarse-grained history. We start with a quantum measure defined on the space of histories, and the exist...

The literature on quantum-gravity-inspired scenarios for the quantization of spacetime has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum-gravity theories, but we here argue that valuable insight can be gained through semi-heuristic analyses of the implications for gravitational phenomena of some results obtained in the quantum-spacetime literature. In particular, we show that the types of d...

This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The quantization of gravity is discussed by analogy with the quantization of the electromagnetic field. The conceptual and technical problems of both approaches are discussed, and the paper concludes with a discussion of evidence for quantum gravit...

Condensed account of the Lectures delivered at the Meeting on {\it Noncommutative Geometry in Field and String Theory}, Corfu, September 18 - 20, 2005.