Roger Penrose proposed that a spatial quantum superposition collapses as a back-reaction from spacetime, which is curved in different ways by each branch of the superposition. In this sense, one speaks of gravity-related wave function collapse. He also provided a heuristic formula to compute the decay time of the superposition—similar to that suggested earlier by Lajos Diósi, hence the name Diósi–Penrose model. The collapse depends on the effective size of the mass density of particles in the superposition, and is random: this randomness shows up as a diffusion of the particles’ motion, resulting, if charged, in the emission of radiation. Here, we compute the radiation emission rate, which is faint but detectable. We then report the results of a dedicated experiment at the Gran Sasso underground laboratory to measure this radiation emission rate. Our result sets a lower bound on the effective size of the mass density of nuclei, which is about three orders of magnitude larger than previous bounds. This rules out the natural parameter-free version of the Diósi–Penrose model.

罗杰·彭罗斯（Roger Penrose）提出，空间量子叠加作为时空的反向反应而崩溃，叠加的每个分支以不同的方式弯曲。从这个意义上讲，人们可以说与重力有关的波动函数崩溃。他还提供了一个启发式公式来计算叠加的衰减时间，类似于LajosDiósi先前提出的公式，因此命名为Diósi-Penrose模型。塌陷取决于叠加中粒子质量密度的有效大小，并且是随机的：这种随机性表现为粒子运动的扩散，如果带电，则会导致辐射的发射。在这里，我们计算出的辐射发射率微弱但可检测。然后，我们报告在Gran Sasso地下实验室进行的一项专门实验的结果，以测量该辐射发射率。我们的结果为核的质量密度的有效大小设定了一个下限，比先前的界限大了三个数量级。这排除了Diósi–Penrose模型的自然无参数版本。