Gravitation and the
General Theory of Relativity
As we have discussed in an
the theoretical physicist
Special Theory of Relativity in 1905 and
General Theory of Relativity in 1915.
The first showed that Newton's
Laws of Motion were only approximately correct, breaking down when velocities
approached that of light. The second showed that Newton's Law of
Gravitation was also only approximately
correct, breaking down when
gravitation becames very strong.
Einstein's Special Theory of Relativity is valid for systems that are not
accelerating. Since from
Newton's second law
an acceleration implies a force, special
relativity is valid only when no forces act. Thus, it cannot be used
generally when there is a
gravitational field present (as we shall see below in conjunction with the
Principle of Equivalence, it can be used over a sufficiently
localized region of spacetime).
We have already discussed some of the important implications of the Special Theory
of Relativity. For example, the most famous is probably the
mass and energy. Other striking consequences
are associated with the dependence of space and time on velocity: at speeds near
that of light, space itself
becomes contracted in the direction of motion and the passage of time slows.
Although these seem bizarre ideas (because our everyday experience typically does
not include speeds near that of light), many experiments indicate that the Special
Theory of Relativity is correct and our "common sense" (and Newton's laws) are
incorrect near the speed of light.
The General Theory of Relativity was Einstein's stupendous effort to remove the
restriction on Special Relativity that no accelerations (and therefore no forces)
be present, so that he could apply his ideas to the gravitational force. It is a
measure of the difficulty of the problem that it took even the great Einstein
approximately 10 years to fully understand how to do this. Thus, the General
Theory of Relativity is a new theory of gravitation proposed in place of
Tests of the Theory of General Relativity
General Relativity and Newton's gravitational theory
make essentially identical predictions as long as the strength of the
gravitational field is weak, which is our usual experience. However, there are
several crucial predictions where the two theories diverge, and thus can be
tested with careful experiments.
The orientation of Mercury's orbit is found to precess in space over time,
as indicated in the adjacent figure (the magnitude of the effect is greatly
exaggerated for purposes of illustration). This is commonly called the
"precession of the perihelion", because it causes the position of the
perihelion to move around the center of mass.
Only part of this can be accounted for by
perturbations in Newton's theory. There is an extra 43 seconds of arc per
century in this precession that is predicted by the Theory of General
Relativity and observed to occur (recall that
a second of arc is 1/3600 of an angular
degree). This effect is extremely small, but the measurements are very precise
and can detect such small effects very well.
Einstein's theory predicts that the direction of light propagation should be
in a gravitational field. Precise
observations indicate that Einstein is right, both about the effect and its
magnitude. We have already seen a spectacular consequence of the deflection of
light in a gravitational field:
The General Theory of Relativity predicts that light coming from a strong
gravitational field should have its wavelength shifted to larger values
(a redshift). Once again,
detailed observations indicate such a redshift, and that its magnitude is
correctly given by Einstein's theory.
The electromagnetic field can have
in it that carry energy and that we
Likewise, the gravitational field can have waves that carry energy and are called
These may be thought of as ripples in the
spacetime that travel at the speed of light.
Just as accelerating
charges can emit electromagnetic waves,
accelerating masses can emit gravitational waves. However gravitational waves are
difficult to detect because they are very weak and no conclusive evidence has yet
reported for their direct observation. They have been observed indirectly
Because the arrival time of pulses from the
pulsar can be measured very
precisely, it can be determined that the period of the binary
system is gradually decreasing.
It is found that the rate of period change (about 75 millionths of a second
year) is what would be expected
for energy being lost to gravitational radiation,
as predicted by the Theory of General Relativity.
The Modern Theory of Gravitation
Our best current theory of gravitation
is the General Theory of Relativity. However, only if velocities are
comparable to that of light, or gravitational fields are much larger than those
encountered on the Earth, do the Relativity theory and Newton's theories differ
in their predictions. Under most conditions Newton's three
laws and his theory of
gravitation are adequate.
For a more comprehensive introduction to both
Special and General Relativity, see
the links at
Relativity on the WWW and
The Light Cone (An Illuminating Introduction to Relativity).