278 RELATIVITY, THE GENERAL THEORY
The discovery of Eq. 15.9 marks the beginning of a new chapter in general
relativity. New problems arise. Since t\ is not a general tensor density, to what
extent are the definitions of energy and momentum independent of the choice of
coordinate system? During the next two years, this question was discussed by
Felix Klein, Levi-Civita, Lorentz, Pauli, Schroedinger, and others,* as well as by
Einstein himself, who in 1918 came back to this issue one more time. 'The sig-
nificance of [Eq. 15.9] is rather generally doubted,' he wrote. He noted that the
quantity ff can be given arbitrary values at any given point but that nevertheless
the energy and momentum integrated over all space have a definite meaning
[E19b]. Later investigations have shown that /*„ is well defined provided that the
metric suitably approaches the Minkowski metric at spatial infinity.
Many related questions continue to be studied intensely in the era of renewed
activity following Einstein's death. Examples: Can one calculate the energy in a
finite domain? Can one separate the energy into a gravitational and a nongravi-
tational part? Does purely gravitational energy exist? Is the total energy of a grav-
itating system always positive? A status report on these questions (many of them
not yet fully answered) is found in an article by Trautman [T2]. The last-men-
tioned question was the subject of a plenary lecture at GR9. This difficult problem
(known for years as the positive energy program) arises because ^ by itself is not
positive definite. It was found in 1979 that positive definiteness of the total energy
can nevertheless be demonstrated [S10]. After my return from GR9,1 learned that
the original proof can be simplified considerably [W13].15d. Gravitational Waves
At no time during GR9 did I sense more strongly how much general relativity
belongs to the future than when I listened to the plenary lectures by Kip Thorne
from Pasadena and Vladimir Braginsky from Moscow on the present state of
experiments designed to detect gravitational waves. So far such waves have not
been found, but perhaps, Thorne said, they will be observed in this century. Fif-
teen experimental groups, some of them multinational, are preparing for this
event.
None of these groups is planning to emulate Hertz's discovery of electromag-
netic waves by terrestrial means. The probability of an atomic transition accom-
panied by gravitational radiation is some fifty powers of 10 less than for photon
emission. We have to look to the heavens for the best sources of gravitational
radiation, most particularly to exotic, violent, and rare stellar phenomena such as
the collapse of star cores into neutron stars or supernovas; or the formation of
black holes. Sources like these may produce intensities some fifty powers of 10
higher than what can be attained on earth. Gravitational antennas need to be built
which are sensitive enough to overcome stupendous background problems. Work"This early work is described in Pauli [P5]. See also [E19a],