We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null infinity. Moreover, all information about the state that can be obtained through observations near a cut of future null infinity can also be obtained from observations near any earlier cut although the converse is not true. We provide independent arguments for these two assertions. Similar statements hold for past null infinity. These statements have immediate implications for the information paradox since they suggest that the fine-grained von Neumann entropy of the state defined on a segment $(-\infty,u)$ of future null infinity is independent of u. This is very different from the oft-discussed Page curve that this entropy is sometimes expected to obey. We contrast our results with recent discussions of the Page curve in the context of black hole evaporation, and also discuss the relation of our results to other proposals for holography in flat space.

中文翻译：

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空无穷大的全息性质

我们认为，在四维渐近平坦时空中的量子引力理论中，关于无质量激发的所有信息都可以从未来零无限大过去边界的无穷小邻域中获得，并且不需要对所有未来零无限大进行观测。此外，尽管反事实并非成立，但也可以从任何更早的切割点附近的观测值中获取通过将来的空无穷大的切口附近的观测值可获得的有关状态的所有信息。我们为这两个断言提供了独立的论据。类似的语句适用于过去的空无穷大。这些陈述对信息悖论具有直接的含义，因为它们表明在未来零无穷大的段$（-\ infty，u）$上定义的状态的细粒度冯·诺伊曼熵与u无关。这与经常讨论的佩吉曲线非常不同，后者有时需要遵守这一熵。我们将我们的结果与最近在黑洞蒸发的背景下对Page曲线的讨论进行对比，并讨论了我们的结果与平面空间全息术其他建议之间的关系。