量子重力場三重奏: 從飛翔鏡、蟲洞橋、到黑洞蒸發

Abstract

本論文主要由三個與量子重力相關的篇章所組成。在第一部分，我們以平坦 時空中的相對論性飛翔鏡來類比彎曲時空中的黑洞所輻射出的半古典霍京輻射。 然而，要把傳統的相對論性飛翔鏡應用到現實的實驗中，有幾件事項需要新的擴 展。我們研究該如何把鏡子的反射率、幾何形狀、以及不同的時空維度納入考 量。這些考量對於未來的實驗設計至關重要。

在本論文的第二個部分，我們研究歐幾里德氏量子宇宙學。在歐氏量子宇宙 學中，我們所生存的宇宙的誕生可以藉由無中生有來解釋。此外，憑藉量子效應 而凝結出的多重宇宙可以藉由歐氏蟲洞建立起彼此的連結。我們研究了歐氏蟲洞 對於原初宇宙的起始條件的影響，以及蟲洞兩端的宇宙之間的量子糾纏對於觀測 天文學中的宇宙微波背景輻射所可能遺留的訊號特徵。

在本論文的最終章，我們將在歐氏量子宇宙學中學到的技巧應用到黑洞蒸發 來解決黑洞資訊悖論。我們將黑洞蒸發想像成一個衰變過程，而這衰變正是藉由 凝結時空泡膜所達成的。凝結出的時空泡膜不再具有黑洞，並且原本半古典霍京 輻射的量子糾纏對可以藉由時空泡膜的擴張而被原本黑洞外的觀察者所觀察到， 進而提供一種另類解決黑洞資訊悖論的方法。

This thesis mainly consists of three pieces related to quantum gravity. In the first part, we first investigate the semiclassical black hole Hawking radiation with the conventional relativistic flying mirror model in flat spacetime, which is one of the earliest analogue gravity models proposed right after the discovery of Hawking radiation. We subsequently make extension of the flying mirror model to incorporate the effects of the mirror’s non-trivial reflectivity and geometry in higher spacetime dimension, which are essential for laboratory experiments.

The second part of the thesis investigates quantum cosmology with the Euclidean approach, in which the cosmological singularity is resolved by considering the universe as a nucleation of something from nothing. In Euclidean quantum cosmology, nucleated multiverse can be bridged by a Euclidean wormhole. We investigate the effect of the wormhole on the initial condition of the perturbation of inflaton, and we search for the imprint of the quantum entanglement across the wormhole in the observed cosmic microwave background power spectrum.

In the final part of this thesis, we apply the Euclidean approach learned in quantum cosmology to the black hole information loss paradox. In particular, we consider a black hole to decay by nucleating a spacetime bubble without black holes. The entangled pair of the Hawking radiation will be released along with the expansion of the bubble, which provides an alternative scenario for resolving the long-standing information paradox.