The problem of time. Quantum mechanics versus general relativity (Q2362737)

From a very special perspective, this book presents a well-versed discussion of quantum gravity programs and, respectively, their problems. The starting point are the well-known difficulties on the way to a unification of Quantum Theory (QT) and General Relativity theory (GR) which, first of all, were intensively analyzed by Isham and Kuchař. This analysis shows that the difficulties are due to fundamentally different basic structures of non-general-relativistic theories (including QT) and GR. For, the transition to GR, which was necessary to arrive at a relativistic theory of gravitation, required a drastic change in physics thinking. One had to go over from theories, whose dynamics takes place in front of a given space-time structure, to theories, where this structure itself is a quantity dynamically changing together with the physical matter. The book's author characterizes this change as a transition to ``Background Independence''. In view of the difficulties for a unification of QT and GR in the spirit of Planck's Principle of \textit{Unit of Physics} (in the book represented in a diagram as \textit{Planck's cube of theories}), also alternative ways, if not of a unification then at least of a harmonization of QT and GR, are discussed. They are called ``different paths around Planck's cube''. The author stresses that ``this book mostly concerns Theoretical Physics rather than Philosophy of Physics''. But it is also true that the text of the book is strongly molded by his philosophical credo which bases on his understanding of Leibniz' and Mach's ideas of space and time and, respectively, Mach's empirio-pragmatic philosophy. In this spirit, the text begins with a ``largely theory-free conceptual outline of time and clock concepts, alongside notions of space, length-measuring devices, spacetime and frames''. Due to this mental background, a great deal of the book's discussion is guided by the conceptual framework of Relational Particle Mechanics theory (RPM) founded by Barbour and Bertotti. This mechanics (as one of the consistent realizations of Mach's principle) is insofar interesting in the current context as, at a non-relativistic level, it establishes a background-independent formalism. The comparison of this mechanics with GR and GR-like theories helps the author to identify those features of GR-like theories which are caused by Background Independence and to additionally demonstrate that problems like the Problem of Time that one meets at the quantum level can partly already be found in classical theories. Following Isham and Kuchař's Reviews of the Problem of Time, those nine facets of this problem are discussed which result from nine corresponding aspects of Background Independence. So, for instance, the \textit{Frozen Formalism Problem} that at the quantum level appears in form of the Wheeler-DeWitt equation is traced back to Temporal Relationalism. Part I outlines fundamental theories of physics from Newtonian Mechanics over Special Relativity Theory and Quantum Field Theory to general Relativity Theory, alongside explaining the notion of time in each. It follow conceptual outlines, both of Quantum Gravity and the nine aspects of Background Independence with the ensuing facets of the Problem of Time. Subsequently, different strategies that have been suggested to deal with these facets are outlined. Part I and its supported mathematical appendices additionally contain Exercises for students. Parts II (classical) and III (quantum) concern the rather more advanced material ``necessary for a more full and up to date an account of the Problem of Time'', again supported by mathematical appendices. ``Parts II and III reflect that the Devil is in the detail. For, as Isham and Kuchař argued, the Problem of Time Facets are heavily interlinked, and none of the strategies proposed to date work when examined insufficient detail.'' Since the material of Parts II and III is more advanced, these contain not Exercises but Research Projects. According to the author, this book has the following advances (here summarized in brief): (i) it has enough room to trace the Problem of Time facets back to more basic and well-known temporal concepts which reside within the non-general-relativistic fundamental theories of physics, by presenting the latter in prequel chapters, (ii) it presents many improvements in the conceptualization of Problem of Time facets and linking them to underlying notions of Background Independence, (iii) it updates Reviews being over 20 years old by involving Supergravity, String and M-theory, Loop Quantum Gravity, or other modern approaches to Quantum Gravity, (iv) it goes much further than previous authors in identifying the mathematics that modeling each facet requires, (v) it temporarily presents each facet's concepts and consequent mathematical modeling by itself, in full awareness that these approaches will subsequently need to be combined, and that the lion's share of the difficulty is in the latter, and (vi) it demonstrates that if the mathematics needed to model ach facet is taken far enough, then resolutions of different facets can be combined after all.