  We summarize how future measurements of electromagnetic (e.m.) probes at the
Relativistic Heavy Ion Collider (RHIC), in connection with theoretical
analysis, can advance our understanding of strongly interacting matter at high
energy densities and temperatures. After a brief survey of the important role
that e.m. probes data have played at the Super Proton Synchrotron (SPS, CERN)
and RHIC to date, we identify key physics objectives and observables that
remain to be addressed to characterize the (strongly interacting) Quark-Gluon
Plasma (sQGP) and associated transition properties at RHIC. These include
medium modifications of vector mesons via low-mass dileptons, a temperature
measurement of the hot phases via continuum radiation, as well as gamma-gamma
correlations to characterize early source sizes. We outline strategies to
establish microscopic matter and transition properties such as the number of
degrees of freedom in the sQGP, the origin of the hadron masses and
manifestations of chiral symmetry restoration, which will require accompanying
but rather well-defined advances in theory. Increased experimental precision,
order of magnitude higher statistics than currently achievable, as well as a
detailed scan of colliding species and energies are then mandatory to achieve
sufficient discrimination power in theoretical interpretations. This increased
precision can be achieved with hardware upgrades to the large RHIC detectors
(PHENIX and STAR) along with at least a factor of ten as increase in luminosity
over the next few years as envisioned for RHIC-II.
