This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs.
This book shows moreover that eight of the nine facets of the
Problem of Time already occur upon entertaining background
independence in classical (rather than quantum) physics. By this
development, and interpreting shape theory as modelling
background independence, this book further establishes background
independence as a field of study. Background independent
mechanics, as well as minisuperspace (spatially homogeneous)
models of GR and perturbations thereabout are used to illustrate
these points. As hitherto formulated, the different facets of the
Problem of Time greatly interfere with each others'
attempted resolutions. This book explains how, none the less, a
local resolution of the Problem of Time can be arrived at after
various reconceptualizations of the facets and reformulations
of their mathematical implementation. Self-contained
appendices on mathematical methods for basic and foundational
quantum gravity are included. Finally, this book outlines how
supergravity is refreshingly different from GR as a realization
of background independence, and what background independence
entails at the topological level and beyond.