Mathematics – Logic
Scientific paper
Oct 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008cqgra..25t9003.&link_type=abstract
Classical and Quantum Gravity, Volume 25, Issue 20, pp. 209003 (2008).
Mathematics
Logic
Scientific paper
This is the fifth edition of H Dieter Zeh's classic text on the physical foundations of time-irreversibility in the phenomena. A forerunner of this book was the 1984 German text 'Die Physik der Zeitrichtung' of about 80 pages, which appeared as volume 200 in the Springer series Lecture Notes in Physics. It was soon followed by a largely revised and extended English edition of about twice the length. Since then each new edition has been thoroughly revised and, edition by edition, new topics and chapters have been added.
As the author says in the introduction: 'The prime intention of this book is to discuss the relations between various arrows of time, and to search for a universal master arrow'. Correspondingly, after a short chapter on 'the physical concept of time', the author systematically discusses in the remaining five chapters the time arrows in electromagnetic radiation theory, in thermodynamics, in quantum mechanics, in black-hole physics and cosmology, and in quantum cosmology. The chapters on thermodynamics and quantum mechanics slightly outweigh the others in terms of length. The fifth edition now includes two new section on 'cosmic probabilities and history' and 'quantum computers', and the section on the 'expansion of the universe' has been restructured and extended. Other changes concentrate on the sections on radiation damping, decoherence, interpretation of quantum theory, and quantum cosmology. It should also be mentioned that the author maintains a regularly updated website for the book at www.time-direction.de.
The reading is always highly stimulating and uses results and ideas from a very broad range of physics, with interspersed historical and philosophical comments. Somehow outstanding and of particular interest is the chapter on quantum cosmology, which raises novel interpretational issues that cannot be found in any other textbook I know of on time asymmetry. As regards the mathematical prerequisites, the reader is assumed to have some knowledge on Green functions, special-relativistic electrodynamics, Hamiltonian mechanics, the formalisms of phenomenological and statistical thermodynamics, quantum mechanics, and general relativity. At some rare places the author avowedly shows a certain impatience with mathematical details, in particular if they do not fit with his expectations based on personal intuition. This stands in peculiar contrast to the conceptual depth and thoroughness that otherwise characterizes most of the book. Quite generally, the reader should be prepared to encounter provoking and partially controversial statements, but this should not be too surprising in such a complex and partially highly speculative field. All this certainly sets high standards for the reader's intellectual independence and maturity, but this is definitely in accord with the philosophy of Springer's 'Frontiers Collection'.
On the other hand, from personal experience I can say that already the original German text has been very popular with beginning graduate students who had a serious interest in foundational issues. (I obtained my first personal copy as a birthday present from a fellow student.) This is essentially due to the fact that the author's genuine urge to understand, rather than just describe, gives the text a characteristic flair of freshness and authenticity to which beginning researchers are particularly susceptible. Being provocative at places is just part of that. This spirit has essentially survived the various editions, thanks to the author's constant efforts to improve the existing presentation, and also by adding modern topics. However, the negative side of this constant streamlining of presentation according to the author's evolving understanding is that it tends to amplify the already existing idiosyncratic tendencies, sometimes resulting in cryptic remarks which fail their intended clarifying purpose.
This already applies to the fairly steep introduction, where the author attempts to clarify in a few lines the central issue of what it means (structurally) to say that a particular dynamical law is (a)symmetric under time reversal. Here I think it would definitely be necessary to give more detailed explanations, e.g., by elaborating on the author's own discussion in 'Note on the time reversal asymmetry of equations of motion' (1999 Found. Phys. Lett. 12 193 96). Also, the structural relations between the operation of time reversal and other space-time symmetries are hardly mentioned. This may be excused insofar as T symmetry in quantum-field theory is not generally addressed in this book (which itself may be regretted), but as part of a structural characterization of the operation of time reversal it would certainly have been useful.
The books provides an extensive bibliography which seems (as far as I can tell) fairly complete, though sometimes and for no obvious reason, preprints posted on web-archives are cited instead of the corresponding journal articles. Each reference comes with the page numbers of where it is cited in the text, which is very useful indeed.
The positive aspects by far outweigh the critical ones. The new edition of H Dieter Zeh's classic text is highly recommended to anybody interested in foundational issues and ready to take the challenge to follow the sometimes intuitive approach of someone who has spent much time and effort to understand the conceptual intricacies and variations of this indisputably difficult and demanding subject.
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