通过欧几里得路径积分解决信息丢失悖论
Solving information loss paradox via Euclidean path integral
AI总结：
本文通过欧几里得路径积分中分支的半经典历史重新研究黑洞信息丢失悖论，提出信息丢失与信息保持两类历史在不同时期主导，从而恢复佩奇曲线和幺正性，但佩奇时间显著后移并可能违反熵界。
摘要：
与黑洞霍金蒸发相关的信息丢失悖论是现代理论物理学中一个悬而未决的问题。在本文中，我们通过量子态的欧几里得路径积分（EPI）重新审视纠缠熵，并允许半经典历史沿洛伦兹演化发生分支。我们假定至少存在两个对EPI有贡献的历史，其中一个是信息丢失的历史，另一个是信息保持的历史。在早期，前者主导EPI，而在晚期，后者变得占主导地位。通过这样做，我们恢复了佩奇曲线的本质，从而恢复了幺正性，尽管转折点，即佩奇时间，大大向晚期偏移。这一修正后的佩奇曲线的一个含义是，熵界可能因此被违反。我们评论了我们的方法与副本虫洞和岛屿猜想之间的相似性和差异。
英文摘要：
The information loss paradox associated with black hole Hawking evaporation is an unresolved problem in modern theoretical physics. In this paper, we revisit the entanglement entropy via the Euclidean path integral (EPI) of the quantum state and allow for the branching of semi-classical histories along the Lorentzian evolution. We posit that there exist at least two histories that contribute to EPI, where one is an information-losing history while the other is information-preserving. At early times, the former dominates EPI, while at late times the latter becomes dominant. By so doing we recover the essence of the Page curve and thus the unitarity, albeit with the turning point, i.e., the Page time, much shifted toward the late time. One implication of this modified Page curve is that the entropy bound may thus be violated. We comment on the similarity and difference between our approach and that of the replica wormholes and the island conjecture.
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