  Recent developments in space technology like micro-propulsion systems for
drag-free control, thermal shielding, ultra-stable laser sources and stable
optical cavities set an ideal platform for quantum optomechanical experiments
with optically trapped dielectric spheres. Here, we will provide an overview of
the results of recent studies aiming at the realization of the space mission
MAQRO to test the foundations of quantum physics in a parameter regime orders
of magnitude beyond existing experiments. In particular, we will discuss
DECIDE, which is an experiment to prepare and then study a
Schr\"odinger-cat-type state, where a dielectric nanosphere of around 100nm
radius is prepared in a superposition of being in two clearly distinct
positions at the same time. This superposition leads to double-slit-type
interference, and the visibility of the interference pattern will be compared
to the predictions of quantum theory. This approach allows for testing for
possible deviations from quantum theory as our test objects approach
macroscopic dimensions. With DECIDE, it will be possible to distinctly test
several prominent theoretical models that predict such deviations, for example:
the Di\'osi-Pensrose model, the continuous-spontaneous-localization model of
Ghirardi, Rimini, Weber and Pearle, and the model of K\'arolyh\'azy.
