Black Holes and Quantum Cosmology

理论物理的首要目标是找到(1)支配宇宙演化的完整的动力学定律，(2)作为这些动力学定律的特定解的量子态，以及(3)从量子态中提取观测概率的规则。哈特尔和霍金强调，在不知道动力学定律(即量子态)的实际解的情况下，仅仅知道完整的动力学定律并不足以给出对宇宙的完整描述。我最近强调，即使同时知道完整的动力学定律和量子态，仍然是不够的，因为人们还需要知道如何从量子态获得各种可能的观测概率。我已经进一步证明，伯恩关于概率作为投影算子的期望值的规则在大宇宙中不起作用。我建议继续并扩大我在这三个关键领域以及更多次要领域的研究。在(1)中，我计划研究黑洞的量子引力动力学，这似乎需要非局域特征，超越了量子场论。我计划研究合适的非局域性--或许还有我所说的极端宇宙审查--如何允许黑洞的形成和蒸发，以保存信息，同时防止防火墙的发生，这些防火墙被提议只在旧黑洞内部形成。在(2)中，我计划寻找既简单又与我们的观察一致的量子态类别。其中一类似乎是那些遵守我提出的极端宇宙审查制度的人，这些极端宇宙审查制度是在半经典极限下既没有大爆炸也没有大压缩奇点的量子态。我建议研究如何更准确地描述这种状态。在(3)中，我计划寻找规则来解决永恒膨胀宇宙学的测量问题，如何为宇宙中的观测提供明确定义的概率，使其变得无限大，从而出现无限多的许多不同类型的观测。在这种情况下，不同类型观测的数量比变成了无限数量的模糊比，因此需要一个更好的处方来给出概率。我已经提出了一些措施，这些措施在统计上似乎与我们的观察一致，但没有一个像我们希望的那样优雅，因此还有改进的空间。人们为动力学定律、量子态和从中提取观测概率的规则寻求一个完整的理论，既要尽可能简单，又要给出我们观察到的尽可能高的概率。这两个要求通常有些不一致，但人们希望将此产品做得尽可能大。因此，在简单性和可能性之间找到正确的权衡，是形成一个完整的宇宙理论所面临的挑战。学生、PDF和我自己要学习的其他更小的问题包括：物理常数的从头估计，爱因斯坦方程的可积性，两个鼓舞人心的无质量粒子的临界度规，两个两球积的连通和上的紧致爱因斯坦度规，在不发射火箭尾气的情况下逃离太阳系，牛顿和一般相对论齐次各向异性宇宙的比较，极端克尔视界度规的视界在三维平面空间的等距嵌入，球落入大气层足够远的速度之间的两个最大值和一个最小值，以及聚焦碰撞激光脉冲中的薛温格对产生。

An overarching goal of theoretical physics is to find (1) the complete set of dynamical laws governing the evolution of the universe, (2) the quantum state as a particular solution of those dynamical laws, and (3) the rules for extracting observational probabilities from the quantum state. Hartle and Hawking have emphasized that just knowing the complete dynamical laws would not be enough to give a complete description of the universe without also knowing the actual solution of the dynamical laws (i.e., the quantum state). I have more recently emphasized that even knowing both the complete dynamical laws and the quantum state would still not be enough, as one also needs to know how to get the probabilities for the various possible observations from the quantum state. I have further shown that Born's rule for probabilities as expectation values of projection operators does not work for a large universe. I am proposing to continue and extend my research in all three of these key areas, as well as in more minor areas. In (1), I plan to look at the quantum gravity dynamics of black holes, which appears to require nonlocal features, going beyond quantum field theory. I plan to investigate how suitable nonlocality, perhaps along with what I have called Extreme Cosmic Censorship, may allow black hole formation and evaporation to preserve information and yet prevent the occurrence of firewalls that have been proposed to form just inside old black holes. In (2), I plan to look for classes of quantum states that would be both simple and also consistent with our observations. One such class appears to be those obeying my proposed Extreme Cosmic Censorship, which are quantum states that in the semiclassical limit have neither big bang nor big crunch singularities. I propose to investigate what a more precise quantum description of such states might be. In (3), I plan to look for rules that solve the measure problem of eternal inflationary cosmology, how to give well-defined probabilities for observations in universes that expand to become indefinitely large so that there appears to be infinitely many observations of many different types. In such cases, the ratios of the numbers of different types of observations become the ambiguous ratios of infinite numbers, so that a better prescription is needed for giving the probabilities. I have already proposed measures that seem to be statistically consistent with our observations, but none of them are so elegant as desired, so there is room for improvement. One seeks a complete theory for the dynamical laws, quantum state, and rules for extracting observational probabilities from it that is both as simple as possible and that gives as high a probability as possible for what we observe. These two requirements are generally somewhat at odds with each other, but one wants to make this product as large as possible. Therefore, finding the right trade-off between simplicity and likelihood is the challenge facing the formation of a complete theory of the universe. Other more minor problems for students, PDFs, and myself to study include ab initio estimates of constants of physics, integrability of the Einstein equations, the critical metric for two inspiralling massless particles, compact Einstein metrics on connected sums of the products of two 2-spheres, escaping the Solar System without emitting rocket exhaust, a comparison of Newtonian and general relativistic homogeneous anisotropic cosmologies, an isometric embedding of the horizon of the extreme Kerr horizon metric into 3-dimensional flat space, the two maxima and one minimum in between of the speed of a ball falling far enough through the atmosphere, and Schwinger pair production in focused colliding laser beam pulses.