Binary Pulsars 67Timekeeping in Gravitational Fields. The third classical test was the gravitational
shift of atomic spectra, first observed byJohn Evershedin 1927. The frequency of
emitted radiation makes atoms into clocks. In a strong gravitational field these clocks
run slower, so the atomic spectra shift towards lower frequencies. This is an effect
which we already met in Equation (3.1): light emerging from a star with mass푀
is gravitationally redshifted in proportion to푀. Evershed observed the line shifts
in a cloud of plasma ejected by the Sun to an elevation of about 72000km above
the photosphere and found an effect only slightly larger than that predicted by gen-
eral relativity. Modern observations of atoms radiating above the photosphere of the
Sun have improved on this result, finding agreement with theory at the level of about
2. 1 × 10 −^6. Similar measurements have been made in the vicinity of more massive
starssuchasSirius.
Thus time passes faster at higher elevations above the ground so that the biological
time of an astronaut in a space craft passes faster than on the ground—the famous
twin paradox.
TheGlobal Positioning Systemwas originally proposed as a test of general relativ-
ity using accurate atomic clocks in orbit inside space satellites. Position determina-
tions with radio signals from GPS satellites in well-known orbits are based on the
Doppler effect which is not relativistic. However, calculations based on general rela-
tivity showed that the clocks in the satellites would be seen by terrestrial observers to
run 38 microseconds faster per day, which had to be corrected for.
The most accurate timekeeping devices built today are atomic clocks with a preci-
sion of the order of 10−^18 s and can measure a vertical separation of 33 cm.
Radio Signal Delay. Many experiments have studied the effects of changes in a
gravitational potential on the rate of a clock or on the frequency of an electromag-
netic signal. The so-called ‘fourth’ test of general relativity, which was conceived by
I. I. Shapiroin 1964 and carried out successfully in 1971 and later, deserves a special
mention. This is based on the prediction that an electromagnetic wave suffers a time
delay when traversing an increased gravitational potential.
The fourth test was carried out with the radio telescopes at the Haystack and
Arecibo observatories by emitting radar signals towards Mercury, Mars and, notably,
Venus, through the gravitational potential of the Sun. The round-trip time delay of
the reflected signal was compared with theoretical calculations. Further refinement
was achieved later by posing the Viking Lander on the Martian surface and having it
participate in the experiment by receiving and retransmitting the radio signal from
Earth. This experiment found the ratio of the delay observed to the delay predicted
by general relativity to be 1. 000 ± 0 .002.
4.2 Binary Pulsars
The most important tests have been carried out on the radio observations of pul-
sars that are members of binary pairs of two neutron stars or one neutron star spin-
ning around a white dwarf. The PSR 1913+16 discovered in 1974 byR. A. Hulseand