Lorentzian Wormholes: From Einstein to Hawking (AIP Series in Computational and Applied Mathematical Physics)

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Summary: Not a joke
Review: Research into non trivial topologies in space time is an old subject that attracted such names as Einstein, Feynman and Wheeler. But there are a host of problems associated with `wormholes'. First, there is no single theory that describes them. Wormholes can arise in one of many theories of quantum gravity, or they can arise in a classical theory of gravity. In the former case there is no over-arching theory which makes researching wormholes themselves is problematic (but not impossible). While in the later case, implications of non-trivial topologies are truly exotic: Materials needed to support the wormhole are rare if not non-existent, and non-trivial topologies lead inevitably to causality violation.

Matt Visser's monograph lucidly and humorously details what is known and unknown about wormholes. Visser himself has contributed significantly to our understanding of these unusual creatures and he does an excellent job at detailing a truly unusual subject. Readers who are not adept at general relativity might have great difficulty with this text. Many formalisms and results from GR -- including local and global --- are invoked in this text. There is also some QFT and some results from quantum gravity. But overall this monograph tells the story and does so in a truly refreshing manner.

Rating:
Summary: Buy a used copy
Review: Some of the words in this book have appeared in movies and science fiction stories, but in this book they take on a mathematical/scientific meaning, thanks to the efforts of the author. Although the concepts in the book are still far-removed from experimental verification, one must credit the author with writing of a book that may be standard reading in centuries to come. When reading the book, one can only hope that its ideas, or some similar to them, will eventually allow humans to traverse time and space routinely. The reader will need a strong background in general relativity and quantum field theory to really appreciate the book, but after reading it will obtain a solid understanding of what might be calle, in the words of the author, "non-boring" physics.

After a brief overview of general relativity and quantum field theory, the author devotes the first part of the book to the history of wormhole physics. I was surprised to learn that the study of wormholes goes as far back as 1916 in paper by the physicist L.Flamm. But it was the desire of A. Einstein and N. Rosen to build a geometrical model of an elementary particle that is finite and singularity-free that set the tone for the research that continues to this day. Their ideas are reviewed in detail, and the author shows that viewing elementary particles as they did predicts they have internal structure, contrary to experiment. The contributions of J.A. Wheeler, namely his interest in topological issues in general relativity, and his geon/spacetime foam ideas are discussed also. The role of wormhole physics in developing a quantum theory of gravity, via the quantization of weak field gravity and the subsequent appearance of gravitons is treated also. The author lists the things that be done with quantized linearized gravity and gives references for research that counters the idea of spacetime foam. "Back-of-the-envelope" calculations are given for the importance of quantum fluctuations in the gravitational field at Planckian scales. A very interesting, and critical discussion is given of topology changes of spacetime via quantum fluctuations. The author states (but does not prove) various theorems regarding the topology of spacetime if a Lorentz metric is put on it. These results are pretty restrictive in limiting the existence of certain topology changes, but as the author remarks, one can abandon the idea of spacetime being everywhere-Lorentzian if one gives up the strong equivalence principle, an idea he clearly is not comfortable with. Given his remarks, it is interesting to ask whether quantum fluctuations could force a violation of the strong equivalence principle. The author does consider the role of quantum tunneling in changing spacetime topology, but concludes that it is not a meaningful question. However, he does devote a brief paragraph to the consideration of an energy-dependent effective topology which is the one of relevance to physics. Based on the "quantum claustrophobia" effect arising from the tendency of a particle to avoid small regions (i.e Heisenberg uncertainty), some regions of spacetime may thus not be visible from a quantum point of view. The author gives one example of this, but this idea has far-reaching consequences: not just for physics but for mathematics. If viewed from a quantum perspective, many of the usual mathematical structures in topology and other areas of mathematics are changed considerably. One can then perform a kind of interpolation between "quantum" and "classical" mathematical constructions.

The author switches to more modern developments in part 3, with the idea of a traversable wormhole due to M. S. Morris and K.S. Thorne leading off the discussion. These wormholes are shown to violate the weak, strong, and dominant energy conditions, implying the existence of negative energy density near the throat of the wormhole. The existence of this energy will remind the reader of the Casimir effect, and the author does discuss this effect in detail. In addition, the thin shell formalism is discussed as a tool to analyze traversable wormholes without spherical geometry. Global techniques and the topological censorship are used to give a mathematically precise definition of a traversable wormhole, although the censorship theorem is not proven.

Part 4 attempts to remove the idea of time travel from pure fantasy science fiction and give it more of a scientific foundation. The author is convincing in his efforts, via his thorough analysis of causality conditions in spacetime, and the explicit constructions of simple time machines, which in the author's words are a consequence of general relativity being "infested" with geometries that produce them. The van Stockum, Godel, Kerr, and Gott tiem machines are discussed in detail, and the author shows explicitly how to construct time machines via wormholes. He also addresses the problems that arise in the actual construction of these time machines, such as the possibility of a non-Hausdorff topology, the problem of unique histories (Novikov conjecture), the breakdown of unitarity in the quantum realm, and the Hawking chronology protection conjecture.

Section 5 is an overview of the quantum field theory needed for a study of wormhole physics. The author shows that time- and space-orientable spacetimes are incompatible with the Standard model. He discusses in detail the result that the ANEC condition can be violated by scale anomalies. Readers will have to have a very detailed knowledge of quantum field theory in curved spacetime to follow the discussion. The calculation of van Vleck determinants, familiar as Green function techniques, are done also. The stress-energy tensor is calculated explictly for traversable wormhole spacetimes. The Wheeler-DeWitt minisuperspace formalism is used to shed light on the quantum aspects of Lorentzian wormholes, and the Wheeler-DeWitt equation for Einstein gravity on minisuperspace is solved exactly.

The last part of the book is more of a send off to the reader and an encouragement for further reading on the issues in the book A list of research problems in given for the ambitious and curious reader.