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We describe and implement a technique for extracting forces from therelaxation of an overdamped thermal system with normal modes. At sufficientlyshort time intervals, the evolution of a normal mode is well described by aone-dimensional Smoluchowski equation with constant drift velocity, v, anddiffusion coefficient, D. By virtue of fluctuation-dissipation, these transportcoefficients are simply related to conservative forces, F, acting on the normalmode: F = k_BT v/D. This relationship implicitly accounts for hydrodynamicinteractions, requires no mechanical calibration, makes no assumptions aboutthe form of conservative forces, and requires no prior knowledge of materialproperties. We apply this method to measure the electrostatic interactions ofpolymer microspheres suspended in nonpolar microemulsions.Comment: 4 pages, 3 figure

Statistics of Particle Trajectories at Short Time Intervals Reveal fN-Scale Colloidal Forces