The relativistic character of the laws of physics began to be apparent very early
in the evolution of classical physics. Even before the time of Galileo and
Newton, Nicolaus Copernicus1 had shown that the complicated and imprecise
Aristotelian method of computing the motions of the planets, based on the assumption
that Earth was located at the center of the universe, could be made much simpler,
though no more accurate, if it were assumed that the planets move about the Sun
instead of Earth. Although Copernicus did not publish his work until very late in
life, it became widely known through correspondence with his contemporaries and
helped pave the way for acceptance a century later of the heliocentric theory of
planetary motion. While the Copernican theory led to a dramatic revolution in human
thought, the aspect that concerns us here is that it did not consider the location of
Earth to be special or favored in any way. Thus, the laws of physics discovered
on Earth could apply equally well with any point taken as the center—i.e., the
same equations would be obtained regardless of the origin of coordinates. This
invariance of the equations that express the laws of physics is what we mean by the
term relativity.
We will begin this chapter by investigating briefly the relativity of Newton’s
laws and then concentrate on the theory of relativity as developed by Albert Einstein
(1879–1955). The theory of relativity consists of two rather different theories, the
special theory and the general theory. The special theory, developed by Einstein and
others in 1905, concerns the comparison of measurements made in different frames
of reference moving with constant velocity relative to each other. Contrary to popu-
lar opinion, the special theory is not difficult to understand. Its consequences, which
can be derived with a minimum of mathematics, are applicable in a wide variety of
situations in physics and engineering. On the other hand, the general theory, also
developed by Einstein (around 1916), is concerned with accelerated reference frames
and gravity. Although a thorough understanding of the general theory requires more
sophisticated mathematics (e.g., tensor analysis), a number of its basic ideas and
important predictions can be discussed at the level of this book. The general theory
is of great importance in cosmology and in understanding events that occur in the
1-1 The Experimental
Basis of
Relativity 4
1-2 Einstein’s
Postulates 11
1-3 The Lorenz
Transformation 17
1-4 TimeDilation
and Length
Contraction 29
1-5 The Doppler
Effect 41
1-6 TheTwin
Paradox and
Other Surprises 45
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