Gravity-related collapse of the wave function and spontaneous heating: revisiting the experimental bounds

The possibility that the collapse of the wave function in quantum mechanics is a real and ultimately connected to (classical) gravity has been debated for decades, with main contributions by Diósi and Penrose. In particular, Diósi proposed a noise-based dynamical reduction model, which captures the same orders of magnitude for the collapse time suggested by Penrose based on heuristic arguments. This is known in literature as the DP model (Diósi-Penrose). A peculiarity of the DP model is the prediction of spontaneous heating of matter, which can be tested without the need for massive quantum superpositions. Notably, a very similar effect is predicted by recent theoretical approaches to gravity as a classical-only information channel. Here, we reconsider the current constraints on the DP model from spontaneous heating, by analyzing experimental situations not properly considered before. We argue that the the parameter-free version of the DP model is close to be ruled out by standard heat leak measurements at ultralow temperature, with a conclusive exclusion likely within reach with existing technology. This result would strengthen a recent claim of exclusion inferred by spontaneous x-ray emission experiments, which relies on the somewhat stronger assumption that the DP noise field is white up to x-ray frequencies.