66 Tests of General Relativity
many-body problem of the Solar System, a task which one can readily characterize
as impossible. Already the relativistic two-body problem presents extreme mathemat-
ical difficulties. Therefore, all the classical tests of general relativity treated only the
one-body problem of the massive Sun influencing its surroundings, and only in the
weak field limit.
Note that the expansion of the Universe and Hubble’s linear law [Equation (4.15)]
are not tests of general relativity. Objects observed at wavelengths ranging from radio
to gamma rays are close to isotropically distributed over the sky. Either we are close to
a center of spherical symmetry—an anthropocentric view—or the Universe is close to
homogeneous. In the latter case, and if the distribution of objects is expanding so as
to preserve homogeneity and isotropy (this is local Lorentz invariance), the recession
velocities satisfy Hubble’s law.
Mercury’s Perihelion Shift. The earliest phenomenon requiring general relativity
for its explanation was noted in 1859, 20 years before Einstein’s birth. The French
astronomerUrban Le Verrier(1811–1877) found that something was wrong with the
planet Mercury’s elongated elliptical orbit. As the innermost planet it feels the solar
gravitation very strongly, but the orbit is also perturbed by the other planets. The total
effect is that the elliptical orbit is nonstationary: it precesses slowly around the Sun.
The locus of Mercury’s orbit nearest the Sun, theperihelion, advances 574
′′
(seconds of
arc) per century. This is calculable using Newtonian mechanics and Newtonian grav-
ity, but the result is only 531
′′
which is 43
′′
too little. Le Verrier, who had already suc-
cessfully predicted the existence of Neptune from perturbations in the orbit of Uranus,
suspected that the discrepancy was caused by a small undetected planet inside Mer-
cury’s orbit, which he named Vulcan. That prediction was, however, never confirmed.
With the advent of general relativity the calculations could be remade. This time the
discrepant 43′′were successfully explained by the new theory, which thereby gained
credibility. This counts as the first one of three ‘classical’ tests of general relativity. For
details on this test as well as on most of the subsequent tests see, for example, [1]
and [2].
Also, the precessions of Venus and Earth have been put to similar use, and within
the Solar System many more consistency tests have been done, based on measure-
ments of distances and other orbital parameters.
Deflection of Star Light. The second classical test was the predicted deflection of
a ray of light passing near the Sun. A consequence of the relativistic phenomenon
of light rays bending around gravitating masses is that masses can serve asgravi-
tational lensesif the distances are right and the gravitational potential is sufficient.
Newton discussed the possibility that celestial bodies could deflect light (in 1704),
and the astronomer Soldner published a paper (in 1804) in which he obtained the
correct Newtonian deflection angle by the Sun, assuming that light was corpuscu-
lar in nature. Einstein published the general relativistic calculation of this deflection
only in 1936, and it was not until 1979 that a suitable solar eclipse occurred which
permitted astronomers to see the effect.
We shall return to a fuller presentation of gravitational lensing in Section 4.3.