  The Schrodinger-Newton equation has frequently been studied as a nonlinear
modification of the Schrodinger equation incorporating gravitational
self-interaction. However, there is no evidence yet as to whether nature
actually behaves this way. This work investigates a possible way to
experimentally test gravitational self-interaction. The effect of self-gravity
on interference of massive particles is studied by numerically solving the
Schrodinger-Newton equation for a particle passing through a double-slit. The
results show that the presence of gravitational self-interaction has an effect
on the fringe width of the interference that can be tested in matter-wave
interferometry experiments. Notably, this approach can distinguish between
gravitational self-interaction and environment induced decoherence, as the
latter does not affect the fringe width. This result will also provide a way to
test if gravity requires to be quantized on the scale of ordinary quantum
mechanics.
