Decoherence-free entropic gravity: Model and experimental tests

Erik Verlinde's theory of entropic gravity [E. Verlinde, J. High Energy Phys. 04 (2011) 029], 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 ultracold 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 s 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 ultracold neutrons as long as sigma greater than or similar to 250 at 90% confidence. Furthermore, the entropic master equation predicts energy increase and decoherence on long time scales and for large masses, phenomena that tabletop experiments could test. In addition, comparing entropic gravity's energy increase to that of the Diosi-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.