Quantum Theory, Black Holes and Inflation

Abstract

Quantum Theory, Black Holes and Inflation is a succinct summary of the principles of several of the forefront areas where gravity and the quantum realm meet. We do not yet have a complete, consistent theory of quantum gravity, but we do know of various situations where gravitational effects should be analysed quantum mechanically, and we do have some interesting partial theories of how this should be done. Ian Moss has given a short but beautiful account of these situations and how they are handled by our current theoretical understanding, after starting with an introduction to quantum mechanics and path integrals, quantum field theory, gauge theories, quantum statistical mechanics and classical gravity. Perhaps the most remarkable situation in which quantum theory predicts new gravitational effects is the evaporation of a black hole, discovered by Stephen Hawking (Moss's PhD supervisor) in 1974. Strictly speaking, what Hawking derived is a flux of particles created by and emitted from a black hole, and Moss gives an excellent version of the derivation and a brief discussion of the thermodynamic consequences. Although it is not known precisely how to take into account the backreaction of these particles and how to treat the hole itself quantum mechanically, by all expectations the energy carried away from the black hole should cause it to shrink. Whether the hole eventually disappears completely is an open question that Moss mentions, but his treatment is too brief to get into the mystery of what happens to the information that apparently falls into a black hole that evaporates. The inflationary Universe is another situation in which quantum theory has a significant effect beyond what would be expected purely classically. In this case they may actually be responsible for the inhomogeneities we see in the Universe in the form of anisotropies in the cosmic microwave background, superclusters, clusters, galaxies, stars, planets and even ourselves. Moss gives a 14 page summary of inflation, which is a useful introduction to this subject that is covered in much more detail in other books. The third main situation that Moss treats is quantum cosmology, which is a quantum account of the entire Universe, especially in the earliest stages. One of the primary goals of quantum cosmology is to understand how the Universe began and what quantum state emerged for inflation or whatever followed the earliest stages. Theories of inflation typically make some strong assumptions about the quantum state, such as the assumption that all sufficiently high-frequency perturbation modes are very nearly in their ground states, but theories of quantum cosmology seek to derive these conditions from other more basic assumptions, such as the Hartle - Hawking no-boundary proposal. Quantum Theory, Black Holes and Inflation does not give an exhaustive treatment of the subjects it discusses, but it covers the basics of three exciting topics in quantum theory and gravitation, at a level suitable for graduate students or researchers from other areas of physics. It should certainly whet the appetite for delving deeper into the published literature on these topics and for pursuing original research in them.