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Wavefunction collapse models modify Schr\"odinger's equation so that itdescribes the collapse of a superposition of macroscopically distinguishablestates as a dynamical process. This provides a basis for the resolution of thequantum measurement problem. An additional generic consequence of the collapsemechanism is that it causes particles to exhibit a tiny random diffusivemotion. Here it is shown that for the continuous spontaneous localization (CSL)model---one of the most well developed collapse models---the diffusions of twosufficiently nearby particles are positively correlated. An experimental testof this effect is proposed in which random displacements of pairs of freenanoparticles are measured after they have been simultaneously released fromnearby traps. The experiment must be carried out at sufficiently lowtemperature and pressure in order for the collapse effects to dominate over theambient environmental noise. It is argued that these constraints can besatisfied by current technologies for a large region of the viable parameterspace of the CSL model. The effect disappears as the separation betweenparticles exceeds the CSL length scale. The test therefore provides a means ofbounding this length scale.

Correlated random walks caused by dynamical wavefunction collapse