Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime

A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known as "Causal Dynamical Triangulations" (CDT).

The development of quantum cosmology, in which Stephen Hawking played a crucial role, has frequently encountered substantial conceptual and technical difficulties related to the problem of time in quantum gravity and to general issues concerning the foundations of quantum theory. In this contribution to Stephen's 60th Birthday Conference, I describe some recent work in which the decoherent histories approach to quantum theory is used to quantize simple cosmological models and...

We report on joint work, past and in progress, with K.Fredenhagen and with J.E,Roberts, on the quantum structure of spacetime in the small which is dictated by the principles of Quantum Mechanics and of General Relativity; we comment on how these principles point to a deep link between coordinates and fields. This is an expanded version of a lecture delivered at the 37th Karpacz School in Theoretical Physics, February 2001.

Time in quantum gravity is not a well-defined notion, despite its central role in the very definition of dynamics. Using the formalism of quantum geometrodynamics, we shortly review the problem and illustrate it with two proposed solutions. Our main application is quantum cosmology -- the application of quantum gravity to the Universe as a whole.

In conventional path integral quantum mechanics, the integral variables are the canonical variables of Hamiltonian mechanics. We show that these integral variables can be transformed into the spacetime metric, leading to a new representation of quantum mechanics. We show that the wave-particle duality can be interpreted as the uncertainty of spacetime for the particle. Summarizing all possible trajectories in conventional path integral quantum mechanics can be transformed int...

The search for a consistent and empirically established quantum theory of gravity is among the biggest open problems of fundamental physics. The obstacles are of formal and of conceptual nature. Here, I address the main conceptual problems, discuss their present status and outline further directions of research. For this purpose, the main current approaches to quantum gravity are briefly reviewed and compared.

This is a contribution to a book on quantum gravity and philosophy. I discuss nature and origin of the problem of quantum gravity. I examine the knowledge that may guide us in addressing this problem, and the reliability of such knowledge. In particular, I discuss the subtle modification of the notions of space and time engendered by general relativity, and how these might merge into quantum theory. I also present some reflections on methodological questions, and on some gene...

This is an introductory set of lecture notes on quantum cosmology, given in 1995 to an audience with interests ranging from astronomy to particle physics. Topics covered: 1. Introduction: 1.1 Quantum cosmology and quantum gravity; 1.2 A brief history of quantum cosmology. 2. Hamiltonian formulation of general relativity: 2.1 The 3+1 decomposition; 2.2 The action. 3. Quantisation: 3.1 Superspace; 3.2 Canonical quantisation; 3.3 Path integral quantisation; 3.4 Minisuperspace; 3...

When quantum mechanics was developed in the '20s of the last century another revolution in physics was just starting. It began with the discovery that the universe is expanding. For a long time quantum mechanics and cosmology developed independently of one another. Yet the very discovery of the expansion would eventually draw the two subjects together because it implied the big bang where quantum mechanics wasimportant for cosmology and for understanding and predicting our ob...

We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities can be assigned only to sets of histories that approximately decohere. Decoherence is defined and ...