92 PART 1^ |^ EXPLORING THE SKY
the scope of this book, but you can have confi dence that these
strange eff ects have been confi rmed many times in experiments.
Einstein’s work is called the special theory of relativity because it meets
the scientifi c defi nition of a theory: it is very well understood, has
been checked many times in many ways, and is widely applicable.The General Theory of Relativity
In 1916, Einstein published a more general version of the theory of
relativity that dealt with accelerated as well as uniform motion. Th is
general theory of relativity contained a new description of gravity.
Einstein began by thinking about observers in accelerated
motion. Imagine an observer sitting in a windowless spaceship.
Such an observer cannot distinguish between the force of gravity
and the inertial forces produced by the acceleration of the space-
ship (■ Figure 5-13). Th is led Einstein to conclude that gravitythat the energy of a motionless particle is not zero. Rather, its
energy at rest is m 0 c^2. Th is is of course the famous equation:
E m 0 c^2Th e constant c is the speed of
light, and m 0 is the mass of the
particle when it is at rest. Th is
simple formula shows that
mass and energy are related,
and you will see in later chap-
ters how nature can convert
one into the other inside stars.
For example, suppose that
you convert 1 kg of matter
into energy. Th e speed of light
is 3 108 m/s, so your result
is 9 1016 joules ( J) (approxi-
mately equal to a 20-megaton
nuclear bomb). Recall that a
joule is a unit of energy roughly
equivalent to the energy given
up when an apple falls from a
table to the fl oor. Th is simple
calculation shows that the
energy equivalent of even a
small mass is very large.
Other relativistic eff ects
include the slowing of moving
clocks and the shrinkage of
lengths measured in the direc-
tion of motion. A detailed dis-
cussion of the major
consequences of the special
theory of relativity is beyond
High-velocity electrons
have higher masses.Constant massv
cm
m 0
1.81.61.41.21.00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9■ Figure 5-12
The observed mass of moving electrons depends on their velocity. As the
ratio of their velocity to the velocity of light, v/c, gets larger, the mass of
the electrons in terms of their mass at rest, m/m 0 , increases. Such relativistic
effects are quite evident in particle accelerators, which accelerate atomic
particles to very high velocities.
I feel gravity.
I must be on
the surface of
a planet.I feel gravity.
I must be on
the surface of
a planet.a b■ Figure 5-13
(a) An observer in a closed spaceship on the surface of a planet feels
gravity. (b) In space, with the rockets smoothly fi ring and accelerating the
spaceship, the observer feels inertial forces that are equivalent to gravita-
tional forces.