  Erik Verlinde's theory of entropic gravity [arXiv:1001.0785], postulating
that gravity is not a fundamental force but rather emerges thermodynamically,
has garnered much attention as a possible resolution to the quantum gravity
problem. Some have ruled this theory out on grounds that entropic forces are by
nature noisy and entropic gravity would therefore display far more decoherence
than is observed in ultra-cold neutron experiments. We address this criticism
by modeling linear gravity acting on small objects as an open quantum system.
In the strong coupling limit, when the model's unitless free parameter $\sigma$
goes to infinity, the entropic master equation recovers conservative gravity.
We show that the proposed master equation is fully compatible with the qBOUNCE
experiment for ultra-cold neutrons as long as $\sigma\gtrsim 250$ at $90\%$
confidence. Furthermore, the entropic master equation predicts energy increase
and decoherence on long time scales and for large masses, phenomena which
tabletop experiments could test. In addition, comparing entropic gravity's
energy increase to that of the Di\'{o}si-Penrose model for gravity induced
decoherence indicates that the two theories are incompatible. These findings
support the theory of entropic gravity, motivating future experimental and
theoretical research.
