  Explaining the behavior of macroscopic objects from the point of view of the
quantum paradigm has challenged the scientific community for a century today. A
mechanism of gravitational self-interaction, governed by the so-called
Schroedinger-Newton equation, is among the proposals that aim to shed some
light on it. Despite all efforts, this mechanism has been proven difficult to
probe. Here, we consider a simple Stern-Gerlach-like experiment to try it out.
The Schroedinger-Newton equation can be analytically solved under certain
proper conditions, and a dephasing effect induced by the gravitational
self-interacting potential can be calculated.
