Mathematics – Logic
Scientific paper
Jun 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007cqgra..24.3526.&link_type=abstract
Classical and Quantum Gravity, Volume 24, Issue 13, pp. 3526 (2007).
Mathematics
Logic
Scientific paper
All the physics we observe in our world is underlain by special relativity, a theory that has survived for more than a hundred years, in many respects completely intact. Yet despite its status as the most stringently tested theory in all of physics, special relativity is still frequently questioned. In the last decade and a half, many scientists have come to believe that special relativity, as Einstein formulated it, will need to be modified to accommodate a quantum theory of gravity. {\it Special Relativity: Will it Survive the Next 101 Years?} is a volume intended to introduce the reader to this new and still slightly controversial area of research.
The book is divided into four parts. The first part is essentially historical. It consists of an essay discussing Einstein's work in the context of contemporary technological developments and a amusing note by R W P Drever on a precision Lorentz test that he performed literally in his backyard. These set the stage for the more modern material that follows.
Part II discusses the theory of relativity and its mathematical foundations, from completely modern perspectives. There is much here that may be new even for experts on special relativity, and a significant level of mathematical sophistication on the part of the reader is assumed. A number of the lectures delve into the crucial question of how special relativity and its generalizations can be combined with quantum mechanics.
The third part discusses theoretical models of Lorentz violation, and all the important paradigms that appear in the current literature are considered. These include the standard model extension (an effective field theory), modified dispersion relations and 'double special relativity', and noncommutative geometry. These lectures generally delve into less detail than those in part II; the focus is on helping the reader digest the new principles that must arise in theories without Lorentz symmetry.
The final part of the volume covers current experimental tests of special relativity, especially state-of-the-art versions of 'classic' tests of rotation and boost invariance. These include Michelson-Morley experiments with high-finesse optical resonators, two-species atomic clock comparisons, and direct measurements of Doppler shifts in the radiation of moving atoms.
If there is a weakness in the overall presentation, it lies in the selection of material covered. {\it Special Relativity} is more of a volume of conference proceedings than a truly cohesive set of lecture notes. This is most evident in the section on experimental tests of Lorentz invariance, which includes contributions from three different experimental groups working on optical resonator measurements. Impressive as these experiments are, this repetitive coverage is not necessary. And at the same time, there is no detailed coverage of astrophysical tests of Lorentz invariance, even though the tightest absolute bounds on deviations from relativity come from astrophysical polarimetry.
However, taken as a whole, the volume presents an excellent survey of current research on Lorentz symmetry. Most of the book should be accessible to graduate students and researchers who are interested in the field but with little previous exposure to it. However, the mathematical level does vary quite a bit from one article to the next; especially in part II, facility with a fair number of mathematical physics concepts may be required. The coverage is broad enough that even an active researcher working on special relativity and possible modifications thereto will almost certainly find new material in this volume, and most of the authors provide abundant references, which should be quite valuable in a field with as many counterintuitive features as Lorentz violation research.
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