标题： 论引力与不确定性原理 显示英文标题

标题： On Gravity and the Uncertainty Principle

摘要： 海森堡在量子理论的早期指出，不确定性原理是电磁辐射以光子形式量子化的直接结果。 正如我们在这里所展示的，光子与被观测粒子之间的引力相互作用以附加项的形式修改了不确定性原理。 从修正后的引力不确定性原理可以得出，任何粒子的位置都存在一个绝对最小的不确定性，大约为普朗克长度的量级。 这种形式的修正不确定性关系是超弦理论的一个标准结果，但这里给出的推导基于牛顿引力理论或广义相对论的更简单且相当普遍的考虑。 显示英文摘要

摘要： Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring theory, but the derivation given here is based on simpler and rather general considerations with either Newtonian gravitational theory or general relativity theory.