  We study how local rearrangements alter droplet stresses within flowing dense
quasi-two-dimensional emulsions at area fractions $\phi \geq 0.88$. Using
microscopy, we measure droplet positions while simultaneously using their
deformed shape to measure droplet stresses. We find that rearrangements alter
nearby stresses in a quadrupolar pattern: stresses on neighboring droplets tend
to either decrease or increase depending on location. The stress redistribution
is more anisotropic with increasing $\phi$. The spatial character of the stress
redistribution influences where subsequent rearrangements occur. Our results
provide direct quantitative support for rheological theories of dense amorphous
materials that connect local rearrangements to changes in nearby stress.
