Since the very beginning of astronomy the location of objects on the sky has
been a fundamental observational quantity that has been taken for granted.
While precise two dimensional positional information is easy to obtain for
observations in the electromagnetic spectrum, the positional accuracy of
current and near future gravitational wave detectors is limited to between tens
and hundreds of square degrees, which makes it extremely challenging to
identify the host galaxies of gravitational wave events or to confidently
detect any electromagnetic counterparts. Gravitational wave observations
provide information on source properties and distances that is complementary to
the information in any associated electromagnetic emission and that is very
hard to obtain in any other way. Observing systems with multiple messengers
thus has scientific potential much greater than the sum of its parts. A
gravitational wave detector with higher angular resolution would significantly
increase the prospects for finding the hosts of gravitational wave sources and
triggering a multi-messenger follow-up campaign. An observatory with arcminute
precision or better could be realised within the Voyage 2050 programme by
creating a large baseline interferometer array in space and would have
transformative scientific potential. Precise positional information of standard
sirens would enable precision measurements of cosmological parameters and offer
new insights on structure formation; a high angular resolution gravitational
wave observatory would allow the detection of a stochastic background and
resolution of the anisotropies within it; it would also allow the study of
accretion processes around black holes; and it would have tremendous potential
for tests of modified gravity and the discovery of physics beyond the Standard
Model.