论文标题
来自非本地引力不确定性原理的彩虹时空
Rainbow Spacetime from a Nonlocal Gravitational Uncertainty Principle
论文作者
论文摘要
时空奇点的出现是爱因斯坦重力的特征之一，是探测时空短距离的信号限制。这暗示了本质上基本长度规模的存在。相反，海森堡量子不确定性关系似乎允许探测任意较小的长度尺度。为了根据众所周知的量子引力框架调和这两个矛盾的想法，已经提出了对海森堡代数的几种修改。但是，已经广泛认为，如此最小的长度将在量子重力理论中引入非局部性。在这封信中，我们分析了先前提出的Heisenberg代数的变形（即$ p \ rightarrow p（1 +λp^{ - 1}）$），以限制在受重力场的盒子中的粒子。对于手头的问题，这种变形似乎以与重力彩虹一致的方式产生了时空的能量依赖性行为，因此证明了非局部性与重力彩虹之间的联系。
Occurrence of spacetime singularities is one of the peculiar features of Einstein gravity, signalling limitation on probing short distances in spacetime. This alludes to the existence of a fundamental length scale in nature. On contrary, Heisenberg quantum uncertainty relation seems to allow for probing arbitrarily small length scales. To reconcile these two conflicting ideas in line with a well known framework of quantum gravity, several modifications of Heisenberg algebra have been proposed. However, it has been extensively argued that such a minimum length would introduce nonlocality in theories of quantum gravity. In this Letter, we analyze a previously proposed deformation of the Heisenberg algebra (i.e. $p \rightarrow p (1 + λp^{-1})$) for a particle confined in a box subjected to a gravitational field. For the problem in hand, such deformation seems to yield an energy-dependent behavior of spacetime in a way consistent with gravity's rainbow, hence demonstrating a connection between non-locality and gravity's rainbow.
