THE NEW DYNAMICS 28lDo gravitational waves exist? Is the derivation of the quadrupole formula cor-
rect? If so, does the formula apply to those extreme circumstances mentioned
above, which may offer the most potent sources of gravitational radiation?
There exists an extensive and important literature on these questions, beginning
in 1922 with a remark by Eddington, who believed that the waves were spurious
and 'propagate... with the speed of thought' [E24]. In 1937, Einstein briefly
thought that gravitational waves do not exist (see Chapter 29). 'Among the present
day theoretical physicists there is a strong consensus that gravitational radiation
does exist,' one reads in [H8]. At GR9, the validity of the quadrupole formula
was the subject of a plenary lecture and a discussion session. In the closing months
of 1980, there appeared in the literature 'a contribution to the debate concerning
the validity of Einstein's quadrupole formula' [W16].
The difficulties in answering the above questions stem, of course, from the non-
linear nature of gravitation, an aspect not incorporated in Einstein's linearized
approximation. No one doubts that Eq. 15.15 holds true (in the long-wavelength,
slow-motion approximation) for nongravitational sources of gravitational waves,
such as elastically vibrating bars. The hard question is what happens if both
material sources and the gravitational field itself are included as sources of grav-
itational waves. The difficult questions which arise are related in part to the def-
inition of energy localization referred to in the previous section. For a recent
assessment of these difficulties see especially [E25] and [R2]. For a less severe
judgment, see [T5]. I myself have not struggled enough with these problems to
dare take sides.*
Finally, as a gift from the heavens, there comes to us the binary pulsar
PSR1913 + 16, 'the first known system in which relativistic gravity can be used
as a practical tool for the determination of astrophysical parameters' [W17]. This
system offers the possibility of testing whether the quantitative general relativistic
prediction of a change in period due to energy loss arising from gravitational quad-
rupole radiation holds true. At GR9, this loss was reported to be 1.04 + 0.13
times the quadrupole prediction. This result does, of course, not prove the validity
of the quadrupole formula, nor does it diminish the urge to observe gravitational
waves directly. It seems more than fair to note, however, that this binary pulsar
result strengthens the belief that the quadrupole formula cannot be far off the
mark and that the experimental relativists' search for gravitational waves will not
be in vain.
15e. Cosmology
Die Unbegrenztheit des Raumes besitzt... eine groszere empir-
ische Gewiszheit als irgend eine aiiszere Erfahrung. Hieraus folgt
aber die Unendlichkeit keineswegs....
Bernhard Riemann, Habilitationsvortrag, 1854.
* I am grateful to J. Ehlers and P. Havas for enlightening discussions on this group of problems.