论文标题
信息内容和最小长度度量：一滴光
Information content and minimum-length metric: A drop of light
论文作者
论文摘要
在将重力与热力学，统计和信息联系起来的大量结果中，描述了一条路径，该路径试图从重力场（非）位置的角度探索这种联系。首先，重点是与无效的曲面相关的众所周知的热力学结果（即灯表和广义的协变熵结合）可以解释为暗示着不可减少的重力内在性非局部性。即使可能在普通尺度上隐藏了这种非局部性（取决于重力场的来源，以及我们用来探测后者的重要性），不可避免地会以最小的尺度出现，请阅读Planck长度$ L_P $，无论是我们所考虑的哪种情况。然后，当在时空本身中体现出最小长度的$ l $，尤其是众所周知且有趣的事实，即这使得获得现场方程式以及与之相关的全部重力，从而探索了这种非销售的后果。这是在此处完成的，探讨了通过灯书（与其他帐户一样）通过灯显示（而不是固定型或及时的地理位置一致性）的邻居（在普通的时空中）的附近。这些派生的工具是非静态数量的，其中最小长度的RICCI标量均备受争议，这两者都在统计帐户中提供了微型自由度的重力，并且因为在$ l \ f \ 0 $ limit中无法从$ l \ licci scalar中恢复RICCI的奇异或“古典”标量。重点是，对于$ \ hbar \ ne 0 $，通常以这种方式获得了经典的重力，但在$ \ hbar \ to 0 $ limit中却不是（统计衍生的字段方程在此限制中变得单数），从而增加了以前的结果。 （截断的摘要；请参阅论文以获取完整的摘要）
In the vast amount of results linking gravity with thermodynamics, statistics, information, a path is described which tries to explore this connection from the point of view of (non)locality of the gravitational field. First the emphasis is put on that well-known thermodynamic results related to null hypersurfaces (i.e. to lightsheets and to generalized covariant entropy bound) can be interpreted as implying an irreducible intrinsic nonlocality of gravity. This nonlocality even if possibly concealed at ordinary scales(depending on which matter is source of the gravitational field, and which matter we use to probe the latter) unavoidably shows up at the smallest scales, read the Planck length $l_p$, whichever are the circumstances we are considering. Some consequences are then explored of this nonlocality when embodied in the fabric itself of spacetime by endowing the latter with a minimum length $L$, in particular the well-known and intriguing fact that this brings to get the field equations, and all of gravity with it, as a statistical-mechanical result. This is done here probing the neighborhood of a would-be (in ordinary spacetime) generic event through lightsheets (instead of spacelike or timelike geodesic congruences as in other accounts) from it. The tools for these derivations are nonlocal quantities, and among them the minimum-length Ricci scalar stands out both for providing micro degrees of freedom for gravity in the statistical account and for the fact that intriguingly the ordinary, or `classical', Ricci scalar can not be recovered from it in the $L\to 0$ limit. Emphasis is put on that classical gravity is generically obtained this way for $\hbar\ne 0$, but not in the $\hbar\to 0$ limit (the statistically derived field equations become singular in this limit), adding to previous results in this sense. (truncated Abstract; see the paper for full Abstract)
