广义不确定原理：对黑洞互补性的启示
Generalized Uncertainty Principle: Implications for Black Hole Complementarity
摘要：
黑洞信息丢失悖论和防火墙争议的核心是量子力学和广义相对论之间的冲突。关于对广义相对论的量子修正已经说了很多，但在相反的方向上就少得多了。因此，研究引力对量子力学的可能修正是至关重要的。事实上，海森堡不确定原理是量子力学的一个深刻特征，然而当引力效应变得重要时，它可能会得到修正。这样的广义不确定原理[GUP]不仅来自于对量子力学和引力的一般考虑，而且也来自于弦理论的论证。我们研究的背景下，黑洞互补的GUP的作用。我们发现，虽然互补性可以违反大N重标度，如果只假设海森堡的不确定原理，GUP的应用可能会保存互补性，但只有当某些N-依赖性也被假定。这就提出了超出本工作范围的两个重要问题，即：GUP是否真的具有所提出的N依赖形式，以及黑洞互补性是否确实正确。
英文摘要：
At the heart of the black hole information loss paradox and the firewall controversy lies the conflict between quantum mechanics and general relativity. Much has been said about quantum corrections to general relativity, but much less in the opposite direction. It is therefore crucial to examine possible corrections to quantum mechanics due to gravity. Indeed, the Heisenberg Uncertainty Principle is one profound feature of quantum mechanics, which nevertheless may receive correction when gravitational effects become important. Such generalized uncertainty principle [GUP] has been motivated from not only quite general considerations of quantum mechanics and gravity, but also string theoretic arguments. We examine the role of GUP in the context of black hole complementarity. We find that while complementarity can be violated by large N rescaling if one assumes only the Heisenberg's Uncertainty Principle, the application of GUP may save complementarity, but only if certain N-dependence is also assumed. This raises two important questions beyond the scope of this work, i.e., whether GUP really has the proposed form of N-dependence, and whether black hole complementarity is indeed correct.
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