  The energy localization hypothesis of the author that energy is localized in
non-vanishing regions of the energy-momentum tensor implies that gravitational
waves do not carry energy in vacuum. If substantiated, this has significant
implications for current research. Support for the hypothesis is provided by a
re-examination of Eddington's classic calculation of energy loss by a spinning
rod. It is emphasized that Eddington did not monitor the entire Tolman energy
integral, concentrating solely upon the change of the 'kinetic' part of the
energy . The 'quadrupole formula' is thus seen to measure the kinetic energy
change. When the derivative of the missing stress-trace integral is computed,
it is seen to cancel the Eddington term and hence the energy of the rod is
conserved, in support of the localization hypothesis. The issue of initial and
final states is addressed.
