Firstly, most of the essays appearing in this book are available as preprints. However, it is still very handy to have all of these marvelous papers collected together in a single volume. So who should buy this book? (1) Philosophers of physics who are looking to get into this field - and are perhaps a little put off by the considerable technical hurdles one must leap over in order to understand the journal articles (and who are getting a little bored of doing the interpretation of quantum mechanics!). (2) Physicists who wish to understand the conceptual difficulties spawned by their work or the work of their collegues. Also, possibly physicsts who wish to get a quick n' easy fix. We could maybe add a third category: (3) Philosophers of space and time. This is because most of the difficulties of quantum gravity (certainly those discussed in these essays, e.g."Spacetime and the Philosophical Challenge of Quantum Gravity", by Isham & Butterfield) arise from the difference between the treatments of spacetime in general relativity and quantum mechanics: briefly, localization is relative in general relativity but not in quantum mechanics and quantum field theory. This problem could be a treasure trove for philosophers of space and time willing to spend a bit of time and effort learning the physics (but they do tend to be a lazy bunch on the whole, generally stopping at special relativity!). As regards category (1), there are three excellent articles which could serve as introductions to the various theories of quantum gravity: these are the papers by Isham & Butterfield, Baez, and Rovelli. They are quite remarkable achievements, understandable by those with only a meagre amount of maths and physics knowledge (the Baez paper is one of the most amazingly well written papers I've ever read). There are many unresolved problems mentioned for the philosophers to get stuck into - many would provide good research topics for ambitious MA and PhD students. I expect those in category (2) will find some of the primarily philosophical papers a little weak - particularly Weinstein's paper "Naive Quantum Gravity" in which he discusses a particular implementation of quantum gravity according to which a theory of quantum gravity entails a fluctuating gravitational field at each spacetime point - why bother? No one is today proposing such a view so who is this directed at? I would have liked to have seen a detailed introductory essay concentrating solely on the hole argument, diffeomorphism invariance, and their relation to the problem of quantum gravity. This would have set many of the later essays up nicely. This is my only serious criticism. In conclusion, this is a truly remarkable book and Huggett and Callender should be praised for having the gumption to get it done!
This book, edited by a physicist and a philosopher is described in five sections. The first section gives an introduction to the theories presented in the rest of four sections that deals with the unification of quantum physics and general relativity, i.e., quantization of spacetime. The second section reviews string theory that includes a chapter from the leading string theorist Ed Witten, and the third section discusses the advantages of topological quantum field theory (TQFT) in spacetime quantization. The last two chapters discuss quantum gravity by either using general relativity (minimizing quantum effects) or quantum physics (minimizing relativistic effects). Contributions from well known physicists like Roger Penrose, Carlo Rovelli, and William Unruh are included in this book. There are numerous quantum gravity theories, and one of the features of these theories is that they are highly mathematical, and largely unsupported by experimental evidence. The author's claim that this book is written for a general reader; this is not true because you need to know significant amount of physics and mathematics to clearly understand this book. Philosophical discussion of quantized spacetime and its relevance to physical reality is minimal. You will be disappointed if you are reading this book purely from philosophical interest.
The relevance of spacetime quantization in relation to existence and reality is summarized as follows: Newtonian mechanics, relativistic physics, and quantum mechanics provide us physical laws that are used to describe existence and physical reality. Newtonian physics is sufficient to describe reality of our normal daily experiences in this world. At the level of atomic and subatomic particles, the reality is described by the laws of quantum physics; the application of Newtonian physics under these circumstances is very limited. At the cosmic level, the physical reality of stars, galaxies, and black holes are described by the theory of relativity. At low velocities (or momentum), relativistic physics is simplified and Newtonian physics becomes relevant; but at high velocities (or momentum), effects of relativity dominate and spacetime gets distorted, and Newtonian physics is no longer applicable. Hence to explain existence and physical reality one needs unified laws of physics that can explain all phenomenon at all sizes; let it be momentum of an electron or an automobile or a galaxy.
Does spacetime exist in quantized state? If yes, then the energy-momentum will not be conserved or the superluminal (faster than speed of light) signaling will be allowed in quantum spacetime. How do we combine the quantum theory and relativistic physics into one theory that treats matter fields governed by quantum physics evolving on a curved spacetime that is governed by the theory of relativity? The main quantum gravity theories are; canonical quantum gravity and superstring theory. Alternative theories are twister theory, holographic hypothesis, non-commutative geometry, topological quantum field theory, and many others explore different avenues to the unification of spacetime. General relativity is a theory of gravity, hence a theory of space and time. Application of quantum physics into the concept of spacetime doesn't have to be like converting continuity to discreteness, the conception space and time could be still be held at the most fundamental level. One of the fundamental issues is that there are no phenomenon that is a result of interplay between general relativity and quantum physics. The lack of empirical data originates from a dimensional argument. The quantum scales; Planck's length, Planck's mass, Planck's time are extremely small and Plank's energy is extremely large. The theory of blackbody radiation gave the first indication that the field such as electromagnetic fields is quantized. Later developments showed that except gravity, all other three forces are unified in quantum field models. The values of these fields consequently are subjected to Heisenberg uncertainty which means that exact strengths at any given point are not specifiable. Hence any quantum theoretical description of gravity must provide for uncertainty in the value of gravity. One of the basic problems is that theory of relativity, the principle of equivalence, the equivalence of gravitational and inertial mass regard classical gravity as a theory of spacetime geometry. Quantum field treatment of a point results in quantization and no definable point is possible. If we use a massive object, the position is measurable with accuracy with respect to the classical background but it also amounts increasing gravitational charge and hence it interacts with the quantum gravitational background one is trying to measure. Thus the classical gravitational observables are diffeomorphism-invariant, which means we can not isolate a system gravitationally, and all matter and reference objects must be included in the description and these raise profound difficulties at the quantum level. One way to quantify the effects of gravity at a point is to make use of the relational properties but the downside of that is it fails to capture all observable gravitational phenomenons. In canonical quantum gravity the obvious part is the difficulty in finding any observable. The one that is expected to be found is highly non-local observable, yet the quantum gravity at a point corresponds to Planck's length. The second problem is the problem of time in quantum gravity. The fact that there is no definite quantum field strength at a point suggests that there is no adequate definition of local energy density.
The applications of quantum physics to field theory, the conventional quantum field theory, rely on the existence of stage or fixed non-dynamical background metric structure, the Minkowski metric and this can not be replaced with quantum fields. Hence one way is to disvalue general relativity concepts and define gravitational field (spacetime curvature) to include Minkowski metric and the quantum fluctuations. Quantize only the fluctuations and hope to recover general relativity later; this approach has been used in perturbative string theory. The second approach is to find a theory that does not use background space. Each theory has its advantages and disadvantages but none comes close to the description of reality.
This is the most comprehensive and fascinating review of today's phisicists struggle to find the 'theory of everything'. Very well written, clear but always up to the point, it contains essays by both philosophers and physicists along a very clear and well organized path. It is not for the fainthearted, since you need to know quite a lot of physics in order to take full advantage of it, but even for the occasional reader it's full of beatifully drawn insights. And it will change forever the way you look at the world around you.