Black Holes and Quantum Cosmology

理论物理学的首要目标是找到(1)控制宇宙演化的一整套动力学定律，(2)作为这些动力学定律的特解的量子态，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，如果不知道动力学定律的实际解（即量子态），仅仅知道完整的动力学定律是不足以给出宇宙的完整描述的。我最近强调，即使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中获得各种可能观测的概率。我已经进一步证明玻恩的概率规则作为投影算子的期望值并不适用于大的宇宙。我建议继续并扩展我在这三个关键领域以及更多次要领域的研究。在(1)中，我打算研究黑洞的量子引力动力学，它似乎需要非局部特征，超越量子场论。我计划研究如何适当地利用非定域性，或许连同我所称的“极端宇宙审查”（Extreme Cosmic Censorship），让黑洞的形成和蒸发既能保存信息，又能防止防火墙的发生。有人曾提出，防火墙就在老黑洞内部形成。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服从我提出的极端宇宙审查制度的人，这些量子态在半经典极限下既没有大爆炸奇点，也没有大压缩奇点。我建议研究对这些状态的更精确的量子描述可能是什么。在(3)中，我计划寻找解决永恒暴胀宇宙学的测量问题的规则，即如何为膨胀到无限大的宇宙中的观测给出定义良好的概率，这样就会出现许多不同类型的无限多的观测。在这种情况下，不同类型的观测值的数量之比变成了无限数的模糊比例，因此需要一个更好的公式来给出概率。我已经提出了一些似乎在统计上与我们的观察相一致的措施，但它们都不像我们期望的那样优雅，因此还有改进的余地。人们寻求一个完整的动力学定律理论，量子态，以及从中提取观测概率的规则，它既要尽可能简单，又要为我们观察到的东西提供尽可能高的概率。这两个要求通常是相互矛盾的，但一个人想让这个产品尽可能大。因此，在简单性和可能性之间找到正确的取舍是形成完整宇宙理论所面临的挑战。其他更小的问题需要学生、pdf和我自己研究，包括物理常数的从头算估计、爱因斯坦方程的可积性、两个吸气无质量粒子的临界度规、两个2球乘积的连通和上的紧致爱因斯坦度规、在不排放火箭废气的情况下逃离太阳系、牛顿和广义相对论齐次各向异性宇宙学的比较、极端克尔视界度量的视界等距嵌入三维平面空间，球在大气层中坠落足够远的速度之间的两个最大值和一个最小值，以及聚焦碰撞激光束脉冲中的施温格对产生。

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.