9.3 Deflection of Light
137
For starlight just grazing the edge of the sun this angle is about 1.75
of arc. This was
measured for the first time during an eclipse in 1919, and the observed deflection was
found to be in agreement with the relativity prediction to about 30% (Von Kluber
1960). It was a major triumph for general relativity because the observation came
after the theoretical prediction. It signaled the end of the long era in which Newtonian
gravitational theory was considered essentially perfect. We will discuss this further
in the next section.
9.4 Observational Tests of General Relativity
Some brief comments on observational tests of general relativity are in order at this
point. The literature on this subject is now vast so we will mention only a few useful
sources: the book of Will is a standard reference, and has a wealth of detail, including
an update chapter (Will 1993). See also the useful “living review” by Will available
on the internet (Will 2014). Also on the internet the Wikipedia article is useful and
generally up to date (Wiki TGR).
Much of the work on testing weak gravity now uses the isotropic coordinates and
the parametrized post Newtonian (PPN) system discussed in Appendix 1.
There are three classic tests of general relativity proposed by Einstein. The first
classic test is the gravitational redshift which we discussed in connection with the
equivalence principle. Since the gravitational redshift can be derived from the equivalence principle it cannot serve as a test of the field equations and the full theory,
but is nevertheless important since the equivalence is a conceptual cornerstone of
general relativity.
Early attempts to measure the redshift using stars such as white dwarfs were not
accurate enough to be satisfactory and the effect was not well-verified for stars until
the 1950s (Hetherington 1980). However terrestrial tests by Pound et al. in the 1950s
and 1960s using the Mossbauer effect definitively agreed with the theory to about
1% (Pound 2000). A later experiment, called Gravity Probe A, used a clock in a
rocket boosted to about 10
4 km, and yielded a result in agreement with theory to
about one part in 10
4 (Vessot 1980). Finally it is interesting to note that the GPS
(Global Positioning System) must be corrected for red shift effects or it would be
in error by many meters (Ashby 2003); thus the red shift is now continually being
tested and verified by everyone using the GPS!
The perihelion shift of Mercury is the second classic test (Adler 1975; Will 2014).
The anomalous precession of Mercury’s perihelion was well-known as early as 1859,
long before general relativity (Leverrier 1859; Newcomb 1895). One early proposed
solution to the problem was to postulate a new planet orbiting very close to the
sun, called Vulcan, which was never detected. Because this anomaly was already
known the calculation by Einstein was not a prediction, but was a very strong indication that general relativity was correct. There was once some dispute about the
amount of precession contributed by the quadrupole moment of the sun, but this
has largely been resolved, with the quadrupole contribution now believed to be only
137
For starlight just grazing the edge of the sun this angle is about 1.75
of arc. This was
measured for the first time during an eclipse in 1919, and the observed deflection was
found to be in agreement with the relativity prediction to about 30% (Von Kluber
1960). It was a major triumph for general relativity because the observation came
after the theoretical prediction. It signaled the end of the long era in which Newtonian
gravitational theory was considered essentially perfect. We will discuss this further
in the next section.
9.4 Observational Tests of General Relativity
Some brief comments on observational tests of general relativity are in order at this
point. The literature on this subject is now vast so we will mention only a few useful
sources: the book of Will is a standard reference, and has a wealth of detail, including
an update chapter (Will 1993). See also the useful “living review” by Will available
on the internet (Will 2014). Also on the internet the Wikipedia article is useful and
generally up to date (Wiki TGR).
Much of the work on testing weak gravity now uses the isotropic coordinates and
the parametrized post Newtonian (PPN) system discussed in Appendix 1.
There are three classic tests of general relativity proposed by Einstein. The first
classic test is the gravitational redshift which we discussed in connection with the
equivalence principle. Since the gravitational redshift can be derived from the equivalence principle it cannot serve as a test of the field equations and the full theory,
but is nevertheless important since the equivalence is a conceptual cornerstone of
general relativity.
Early attempts to measure the redshift using stars such as white dwarfs were not
accurate enough to be satisfactory and the effect was not well-verified for stars until
the 1950s (Hetherington 1980). However terrestrial tests by Pound et al. in the 1950s
and 1960s using the Mossbauer effect definitively agreed with the theory to about
1% (Pound 2000). A later experiment, called Gravity Probe A, used a clock in a
rocket boosted to about 10
4 km, and yielded a result in agreement with theory to
about one part in 10
4 (Vessot 1980). Finally it is interesting to note that the GPS
(Global Positioning System) must be corrected for red shift effects or it would be
in error by many meters (Ashby 2003); thus the red shift is now continually being
tested and verified by everyone using the GPS!
The perihelion shift of Mercury is the second classic test (Adler 1975; Will 2014).
The anomalous precession of Mercury’s perihelion was well-known as early as 1859,
long before general relativity (Leverrier 1859; Newcomb 1895). One early proposed
solution to the problem was to postulate a new planet orbiting very close to the
sun, called Vulcan, which was never detected. Because this anomaly was already
known the calculation by Einstein was not a prediction, but was a very strong indication that general relativity was correct. There was once some dispute about the
amount of precession contributed by the quadrupole moment of the sun, but this
has largely been resolved, with the quadrupole contribution now believed to be only