This book offers a presentation of the special theory of
relativity that is mathematically rigorous and yet spells out in
considerable detail the physical significance of the mathematics.
It treats, in addition to the usual menu of topics one is
accustomed to finding in introductions to special relativity, a
wide variety of results of more contemporary origin. These include
Zeeman's characterization of the causal automorphisms of Minkowski
spacetime, the Penrose theorem on the apparent shape of a
relativistically moving sphere, a detailed introduction to the
theory of spinors, a Petrov-type classification of electromagnetic
fields in both tensor and spinor form, a topology for Minkowski
spacetime whose homeomorphism group is essentially the Lorentz
group, and a careful discussion of Dirac's famous Scissors Problem
and its relation to the notion of a two-valued representation of
the Lorentz group. This second edition includes a new chapter on
the de Sitter universe which is intended to serve two purposes. The
first is to provide a gentle prologue to the steps one must take to
move beyond special relativity and adapt to the presence of
gravitational fields that cannot be considered negligible. The
second is to understand some of the basic features of a model of
the empty universe that differs markedly from Minkowski spacetime,
but may be recommended by recent astronomical observations
suggesting that the expansion of our own universe is accelerating
rather than slowing down. The treatment presumes only a knowledge
of linear algebra in the first three chapters, a bit of real
analysis in the fourth and, in two appendices, some elementary
point-set topology.
The first edition of the book received the 1993 CHOICE award for
Outstanding Academic Title.
Reviews of first edition:
..". a valuable contribution to the pedagogical literature which
will be enjoyed by all who delight in precise mathematics and
physics." (American Mathematical Society, 1993)
"Where many physics texts explain physical phenomena by means of
mathematical models, here a rigorous and detailed mathematical
development is accompanied by precise physical interpretations."
(CHOICE, 1993)
..". his talent in choosing the most significant results and
ordering them within the book can't be denied. The reading of the
book is, really, a pleasure." (Dutch Mathematical Society,
1993)
"
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