This book has three main goals. First, it
explores a selection of topics from the early period of the theory of
relativity, focusing on particular aspects that are interesting or
unusual. These include the twin paradox; relativistic mechanics and
its interaction with Maxwell's laws; the earliest triumphs of general
relativity relating to the orbit of Mercury and the deflection of
light passing near the sun; and the surprising bizarre metric of Kurt
Gödel, in which time travel is possible. Second, it provides an
exposition of the differential geometry needed to understand these
topics on a level that is intended to be accessible to those with just
two years of university-level mathematics as background. Third, it
reflects on the historical development of the subject and its
significance for our understanding of what reality is and how we can
know about the physical universe. The book also takes note of
historical prefigurations of relativity, such as Euler's 1744 result
that a particle moving on a surface and subject to no tangential
acceleration will move along a geodesic, and the work of Lorentz and
Poincaré on space-time coordinate transformations between two
observers in motion at constant relative velocity.
The book is aimed at advanced undergraduate mathematics, science,
and engineering majors (and, of course, at any interested person who
knows a little university-level mathematics). The reader is assumed to
know the rudiments of advanced calculus, a few techniques for solving
differential equations, some linear algebra, and basics of set theory
and groups.
Readership
Undergraduate and graduate students and general readers
interested in mathematical aspects of relativity.
