Black Holes and Quantum Cosmology

黑洞和量子宇宙学

• 批准号: RGPIN-2014-06260
• 负责人: Page, Don
• 金额: $ 3.79万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=567697
• 关键词: Black; Holes; Quantum; Cosmology

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.

理论物理学的首要目标是找到（1）支配宇宙演化的完整动力学定律，（2）量子态作为这些动力学定律的特殊解，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，仅仅知道完整的动力学定律不足以给出宇宙的完整描述（即，量子态）。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获得各种可能观测的概率。我进一步证明了玻恩概率规则作为投影算子的期望值对大宇宙不起作用。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，我计划研究黑洞的量子引力动力学，它似乎需要非定域特征，超越了量子场论。我计划研究合适的非定域性，也许沿着我所谓的极端宇宙审查，可能允许黑洞的形成和蒸发，以保存信息，但又防止出现防火墙，已经被提议在旧黑洞内部形成。在（2）中，我计划寻找既简单又与我们的观察一致的量子态。其中一类似乎是服从我提出的极端宇宙审查的量子态，它们是在半经典极限下既没有大爆炸奇点也没有大紧缩奇点的量子态。我打算研究这种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，如何为宇宙中的观测给出定义明确的概率，这些宇宙膨胀到无限大，以至于似乎有许多不同类型的无穷多个观测。在这种情况下，不同类型的观测值的数量之比就变成了无限数的模糊比，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结果一致，但没有一个措施像我们所希望的那样优雅，因此还有改进的余地。人们寻求一个完整的理论，用于描述动力学定律、量子态以及从中提取观测概率的规则，这个理论既要尽可能简单，又要尽可能给出我们所观测到的概率。这两个要求通常有些不一致，但人们希望使这个产品尽可能大。因此，在简单性和可能性之间找到正确的权衡是形成完整的宇宙理论所面临的挑战。学生、PDF和我自己要研究的其他更小的问题包括物理常数的从头计算估计，爱因斯坦方程的可积性，两个螺旋形无质量粒子的临界度量，两个2球乘积的连接和的紧凑爱因斯坦度量，在不发射火箭排气的情况下逃离太阳系，牛顿和广义相对论均匀各向异性宇宙学的比较，极端Kerr视界度规的视界等距嵌入到三维平坦空间中，在穿过大气足够远的地方下落的球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Schwinger对产生。