Black Holes and Quantum Cosmology

我建议继续研究理论物理，主要是引力物理和宇宙学，特别关注量子方面。******一个主要的焦点是量子宇宙学，将量子理论应用于整个宇宙。理论宇宙学中最深奥的问题之一是测量问题，即如何在宇宙的量子模型中获得有限观察者观测的可测试概率。传统上，在量子理论中，人们使用所谓的玻恩法则，它说概率是由量子理论中称为振幅的平方给出的。然而，我发现玻恩法则在一个大到足以让两个几乎完全相同的观察者无法区分他们的宇宙中是不成立的。我提出了一个将量子振幅转换为观测概率的新框架，但有一些未知的细节。我想为这些细节找到更好的模型。******量子宇宙学中的一个相关问题是所谓的宇宙的量子态，这是量子理论中对宇宙的完整描述，直到如何确定观测概率的问题。哈特尔和霍金提出了他们称之为无边界波函数（NBWF）的绝妙建议。然而，萨斯金德对这个模型提出了反对意见，我将其具体化，当真空反引力时，就像在我们的宇宙中观察到的那样（所以遥远的星系正在加速分开），那么NBWF似乎由空的宇宙主导，显然与我们观察到的相反。然而，目前关于如何在NBWF中计算概率存在一些争议，因此我计划进一步研究这个问题，看看它是否可以与观测相一致，如果不一致，关于宇宙量子态（以及从量子态获得观测概率的规则）的其他建议是否可以与观测相一致。******我继续研究的另一个主要焦点是黑洞热力学和霍金蒸发，特别是关于落入黑洞的信息发生了什么。阿尔姆赫里、马罗夫、波尔钦斯基和萨利的观点使这个谜题变得更加复杂。他们认为，比所谓的Page时间更老的黑洞被他们所谓的“防火墙”包围着，它会立即摧毁掉任何掉进去的东西。我已经写了几篇论文来批评这个观点，我的研究生Kento Osuga和我已经建立了一个玩具模型来获取信息。我打算改进这个玩具模型。******我计划进行的较小的项目包括对蒸发黑洞几何形状的更好的近似，对巨大电荷黑洞的时间演化和最低温度的近似，以及通过碰撞激光束产生电子-正电子对的概率。

I propose to continue research in theoretical physics, primarily gravitational physics and cosmology, particularly focusing on the quantum aspects.******One main focus is on quantum cosmology, applying quantum theory to the universe as a whole. One of the deepest problems in theoretical cosmology is the measure problem, how to obtain testable probabilities for observations by finite observers in a quantum model for the universe. Traditionally in quantum theory one uses what is called Born's rule, which says that probabilities are given by the squares of what in quantum theory are called amplitudes. However, I have discovered that Born's rule does not work in a universe large enough for there to be two observers so nearly identical that their observations do not distinguish them. I have proposed a new framework for converting quantum amplitudes to the probabilities of observations, but there are are unknown details. I would like to find better models for these details.******A related issue in quantum cosmology is what is called the quantum state of the universe, which is a complete description of the universe in quantum theory, up to the question of how to determine observational probabilities from it. Hartle and Hawking have made the brilliant proposal of what they called the no-boundary wavefunction (NBWF). However, Susskind raised an objection to this model, which I fleshed out, that when empty space anti-gravitates, as it is observed to do in our universe (so that distant galaxies are accelerating apart), then the NBWF appears to be dominated by universes that are empty, obviously contrary to what we observe. Nevertheless, there is presently some controversy about how probabilities should be calculated in the NBWF, so I plan to examine this further to see whether it can be made consistent with observations, and, if not, what other proposals for the quantum state of the universe (and for the rules for getting the observational probabilities from the quantum state) could be consistent with observations.******Another main focus of my continuing research is on black hole thermodynamics and Hawking evaporation, particularly for the information puzzle of what happens to the information that falls into a black hole. This puzzle was heightened by the argument of Almheiri, Marolf, Polchinski, and Sully, which suggests that black holes older than the so-called Page time are surrounded by what they call a `firewall,' which would immediately destroy anything falling in. I have written several papers critiquing this argument, and my graduate student Kento Osuga and I have built a toy model for getting the information out. I plan to work on improvements of this toy model.******Smaller projects that I plan to pursue include better approximations for the geometry of an evaporating black hole, the time evolution and minimum temperature of a black hole of enormous electric charge, and the probabilities for the production of electron-positron pairs by colliding laser beams.