Marine cloud brightening (MCB) is the deliberate injection of aerosol particles into shallow marine clouds to increase their reflection of solar radiation and reduce the amount of energy absorbed by the climate system. From the physical science perspective, the consensus of a broad international group of scientists is that the viability of MCB will ultimately depend on whether observations and models can robustly assess the scale-up of local-to-global brightening in today's climate and identify strategies that will ensure an equitable geographical distribution of the benefits and risks associated with projected regional changes in temperature and precipitation. To address the physical science knowledge gaps required to assess the societal implications of MCB, we propose a substantial and targeted program of research-field and laboratory experiments, monitoring, and numerical modeling across a range of scales.