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It's About Time - Elementary Mathematical Aspects of Relativity (Hardcover)
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It's About Time - Elementary Mathematical Aspects of Relativity (Hardcover)
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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 Goedel, 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 Poincare 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.
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