Switching internal times and a new perspective on the 'wave function of the universe'
Philipp A Hoehn
备注：
14+7 pages. Invited contribution to the special issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms", Eds. S. Carrozza, S. Gielen and D. Oriti. Minor clarifications, updated references, matches published version
Despite its importance in general relativity, a quantum notion of general covariance has not yet been established in quantum gravity and cosmology, where, given the a priori absence of coordinates, it is necessary to replace classical frames with dynamical quantum reference systems. As such, quantum general covariance bears on the ability to consistently switch between the descriptions of the same physics relative to arbitrary choices of quantum reference system. Recently, a systematic approach for such switches has been developed (arXiv:1809.00556, 1809.05093, 1810.04153). It links the descriptions relative to different choices of quantum reference system, identified as the correspondingly reduced quantum theories, via the reference-system-neutral Dirac quantization, in analogy to coordinate changes on a manifold. In this work, we apply this method to a simple cosmological model to demonstrate how to consistently switch between different internal time choices in quantum cosmology. We substantiate the argument that the conjunction of Dirac and reduced quantized versions of the theory defines a complete relational quantum theory that not only admits a quantum general covariance, but, we argue, also suggests a new perspective on the 'wave function of the universe'. It assumes the role of a perspective-neutral global state, without immediate physical interpretation, that, however, encodes all the descriptions of the universe relative to all possible choices of reference system at once and constitutes the crucial link between these internal perspectives. While, for simplicity, we use the Wheeler-DeWitt formulation, the method and arguments might be also adaptable to loop quantum cosmology.
The Internal Geometry of an Evaporating Black Hole
我们提出了一个四维黑洞形成和蒸发的半经典模型。我们数值求解方程，得到描述从坍缩到蒸发结束的整个时空几何的解。这些解满足蒸发定律：$\dot M \propto -M^{-2}$，它动态地证实了黑洞确实是热蒸发的。我们发现，蒸发过程实际上是连接宏观内部“宇宙”和渐近平坦外部的咽喉的收缩。它的结局要么是捏断喉咙，留下一个封闭的宇宙和闵可夫斯基的外表，要么是当喉咙的半径接近普朗克尺寸时冻结。在这两种情况下，宏观的内部宇宙是蒸发过程中丢失的信息被隐藏的区域。
