Beginning from the standard Arnowitt–Deser–Misner (ADM) formulation of general relativity we construct a tentative model of quantum gravity from the point of view of an observer with constant proper acceleration, just outside of a horizon of spacetime. In addition of producing the standard results of black-hole thermodynamics, our model makes an entirely new prediction that there is a certain upper bound for the energies of massive particles. For protons, for instance, this upper bound is around \(1.1\times 10^{21}\) eV. The result is interesting, because this energy is roughly of the same order of magnitude as are the highest energies ever measured for protons in cosmic rays.

从广义相对论的标准 Arnowitt-Deser-Misner (ADM) 表述开始，我们从时空视界之外具有恒定适当加速度的观察者的角度构建了一个暂定的量子引力模型。除了产生黑洞热力学的标准结果之外，我们的模型还做出了全新的预测，即大质量粒子的能量存在一定的上限。例如，对于质子，这个上限约为 \(1.1\times 10^{21}\) eV。结果很有趣，因为这种能量与宇宙射线中质子的最高能量大致处于同一数量级。