标题： 经典与量子物理几何 显示英文标题

标题： Classical and Quantum Physical Geometry

摘要： 将量子化引力的任务与爱因斯坦对引力的相对化进行比较。 广义相对论的哲学和物理基础被简要回顾。 利用自由下落的经典粒子轨迹来操作性地确定时空几何的Ehlers-Pirani-Schild方案是在每个点的无限小邻域内进行操作的。 研究量子波的自由下落暗示了一个量子等效原理。 广义协变原理得到澄清。 当费米子场旋转$2\pi$弧度时，其符号发生变化，这被用来论证对时空的量子力学修改，这自然导致了超对称性。 作者提出的一种量子引力中的新效应被用来将爱因斯坦的洞论证扩展到量子引力。 这表明了一个量子广义协变原理，根据该原理，物理学的基本定律应在“量子微分同胚”下协变。 这一启发式原理意味着在量子引力中，时空点没有不变的意义。 显示英文摘要

摘要： The task of quantizing gravity is compared with Einstein's relativization of gravity. The philosophical and physical foundations of general relativity are briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining the geometry of space-time, using freely falling classical particle trajectories, is done using operations in an infinitesimal neighborhood around each point. The study of the free fall of a quantum wave suggests a quantum principle of equivalence. The principle of general covariance is clarified. The sign change of a Fermion field when rotated by $2\pi$ radians is used to argue for a quantum mechanical modification of space-time, which leads naturally to supersymmetry. A novel effect in quantum gravity due to the author is used to extend Einstein's hole argument to quantum gravity. This suggests a quantum principle of general covariance, according to which the fundamental laws of physics should be covariant under `quantum diffeomorphisms'. This heuristic principle implies that space-time points have no invariant meaning in quantum gravity.