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Extra dimensions in space and time. Foreword by Lawrence M. Krauss. (English) Zbl 1207.83001
Multiversal Journeys. New York, NY: Springer (ISBN 978-0-387-77637-8/hbk). xiv, 217 p. (2010).
The origin of this book lies in two public lectures given by the authors for a general public, under the auspices of Multiversal Journeys, a non-profit organization dedicated to disseminating knowledge on current theoretical physics to the general public. It allows the authors to explore in greater depth the topics of their lectures and at places to go beyond a merely popular scientific description of their research.
Part I, written by Itzhak Bars, is titled ‘Two-time physics: the unified view from higher dimensional space and time’. The author first gives a general introduction to some basics of modern physics, in particular into the Einsteinian view on space-time. This is followed by a gentle primer on the concept of symmetry. The core of the presentation is concerned with two-time physics, a field of research initiated by the author himself. He expounds his approach to fundamental physics, based on two time and four space dimensions as a consequence of a new fundamental symmetry of the equations of motion in classical or quantum physics. Using a shadow-analogy the author argues that certain subtle effects of $$3+1$$ physics can be viewed as consequences of an underlying $$4+2$$ structure. He considers the standard model as a 2T field theory and describes the 2T approach to gravity. Finally, the current status of the theory is reviewed and references for further reading are given.
Part II, due to John Terning, is called ‘Extra dimensions of space’. Here the author, starting from scratch, gives a carefully thought out popular introduction to the concept of dimension and reviews some fundamental contributions of the theory of relativity to our understanding of the concept of dimension. He then introduces some basic ideas of string theory, with an emphasis on warped extra dimensions and on ways to experimentally gather evidence for the existence of such. In the final section, called ‘Extra material: the equations behind the words’, a more mathematical presentation of some important aspects of fundamental physics are explored: relativity, quantum mechanics, string theory, and the Maxwell equations.
In line with the mission of Multiversal Journeys, these contributions are mainly addressed at laypersons who want to gain insight into current developments of modern physics. The format of a book-length presentation offers the possibility of also including pointers to specialized literature and to add a more mathematical treatment of the subject at times. This is done using footnotes in the first article and in an extra section in the second.
It certainly is to be welcomed that leading theoretical physicists make an effort to communicate their research to the general public. This book demonstrates how to succeed in such an endeavour.

##### MSC:
 83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory 83F05 Cosmology 85A40 Cosmology 83-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational theory 81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory 97M50 Physics, astronomy, technology, engineering (aspects of mathematics education) 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories 83E15 Kaluza-Klein and other higher-dimensional theories 83E30 String and superstring theories in gravitational theory 81V05 Strong interaction, including quantum chromodynamics