物理学+教程:Introduction to Loop Quantum Gravity (圈量子引力) by 韩慕辛【已结课】
物理学+教程:Introduction to Loop Quantum Gravity(圈量子引力导论) by Carlo Rovelli(英文字幕)
理论物理:拓扑场论和二维量子引力【转载】
全文转载自知乎:拓扑场论和二维量子引力 – 知乎 (zhihu.com)
1. 引言
过去几年见证了量子场论技术在研究各种数学问题上丰硕的应用。这个主要归功于Edward Witten的项目,已经找到了量子场论和拓扑与几何量间意想不到的关联。这点的精彩范例是,三维规范理论和二维共形场论中出现了像Jones多项式这样的纽结不变量[1]。直到最近,这些发展也主要是带给我们,要么是新的数学上的不变量,要么是对从量子场论的直觉得到的结果的更好理解。用在这些构造中的量子场论,虽然是更物理的场论的近亲,但没有直接的物理应用。
随着对矩阵模型和一般的二维量子引力的研究,意想不到的转机出现了。一个称为拓扑引力[2]的特殊场论,最初被构造来处理Riemann面模空间的问题,被证明与二维量子引力有密不可分的关联。可将它看成引力的另一个更简单的相,其中关联函数更容易计算。借助矩阵模型在二维引力中取得重大突破[3]后不久,Witten指出量子引力可能不过是拓扑引力的简单微扰[4]。这点现在已经有了坚实的证据,提供了从拓扑引力开始得到所有矩阵模型结果的相当直接的方法[4][5][6][7][8][9]。拓扑引力有个推广,称为拓扑弦论,其中引力与各种物质系统耦合[4]。拓扑弦论可用于描述和解与引力耦合的所有 极小模型,以及很多其它理论[10][11][12][13]。
这份讲义旨在对一般的拓扑场论,特别是拓扑引力进行初步介绍。我们的最终目标,是建立起与矩阵模型结果的关联,特别是可积的KdV型层次结构[14][15]的出现。不过,最后一节才会涉及这点。沿途我们将讨论几何,代数和量子场论间诸多优美的关联。
这份讲义中,描述与E. 和H. Verlinde,以及与E. Witten合作的工作的部分,将基本照着同一主题其它已出版的讲义[16],但有些地方可能更加友好。这份讲义会和在冬季学校讲的四节课高度一致,也是依此来组织的。在第2节,我们讨论拓扑场论的一些一般性质。我们强调因子化的概念,并应用于二维情形。在第3节,我们考虑拓扑共形场论,它们与 超对称模型密切相关,并为上节的抽象讨论提供一些例子。拓扑引力放在第4节,那里我们还将用递归关系讨论它的解。最后,在第5节,我们讨论与矩阵模型和可积KdV层次结构的关联。
物理学+深度学习:Interpretable Deep Learning for New Physics Discovery
TED演讲视频:The death of the universe — and what it means for life
物理学:图形化演示视频 Waves: Light, Sound, and the nature of Reality
物理学:An Epic Journey to a Black Hole to Give You Goosebumps
物理学:黑洞信息悖论进展——The Black Hole Information Paradox Comes to an End【转载】
原文来自:The Black Hole Information Paradox Comes to an End | Quanta Magazine
The Most Famous Paradox in Physics Nears Its End
In a landmark series of calculations, physicists have proved that black holes can shed information, which seems impossible by definition. The work appears to resolve a paradox that Stephen Hawking first described five decades ago.
In a series of breakthrough papers, theoretical physicists have come tantalizingly close to resolving the black hole information paradox that has entranced and bedeviled them for nearly 50 years. Information, they now say with confidence, does escape a black hole. If you jump into one, you will not be gone for good. Particle by particle, the information needed to reconstitute your body will reemerge. Most physicists have long assumed it would; that was the upshot of string theory, their leading candidate for a unified theory of nature. But the new calculations, though inspired by string theory, stand on their own, with nary a string in sight. Information gets out through the workings of gravity itself — just ordinary gravity with a single layer of quantum effects.
This is a peculiar role reversal for gravity. According to Einstein’s general theory of relativity, the gravity of a black hole is so intense that nothing can escape it. The more sophisticated understanding of black holes developed by Stephen Hawking and his colleagues in the 1970s did not question this principle. Hawking and others sought to describe matter in and around black holes using quantum theory, but they continued to describe gravity using Einstein’s classical theory — a hybrid approach that physicists call “semiclassical.” Although the approach predicted new effects at the perimeter of the hole, the interior remained strictly sealed off. Physicists figured that Hawking had nailed the semiclassical calculation. Any further progress would have to treat gravity, too, as quantum.
That is what the authors of the new studies dispute. They have found additional semiclassical effects — new gravitational configurations that Einstein’s theory permits, but that Hawking did not include. Muted at first, these effects come to dominate when the black hole gets to be extremely old. The hole transforms from a hermit kingdom to a vigorously open system. Not only does information spill out, anything new that falls in is regurgitated almost immediately. The revised semiclassical theory has yet to explain how exactly the information gets out, but such has been the pace of discovery in the past two years that theorists already have hints of the escape mechanism.
“That is the most exciting thing that has happened in this subject, I think, since Hawking,” said one of the co-authors, Donald Marolf of the University of California, Santa Barbara.
“It’s a landmark calculation,” said Eva Silverstein of Stanford University, a leading theoretical physicist who was not directly involved.
You might expect the authors to celebrate, but they say they also feel let down. Had the calculation involved deep features of quantum gravity rather than a light dusting, it might have been even harder to pull off, but once that was accomplished, it would have illuminated those depths. So they worry they may have solved this one problem without achieving the broader closure they sought. “The hope was, if we could answer this question — if we could see the information coming out — in order to do that we would have had to learn about the microscopic theory,” said Geoff Penington of the University of California, Berkeley, alluding to a fully quantum theory of gravity.
What it all means is being intensely debated in Zoom calls and webinars. The work is highly mathematical and has a Rube Goldberg quality to it, stringing together one calculational trick after another in a way that is hard to interpret. Wormholes, the holographic principle, emergent space-time, quantum entanglement, quantum computers: Nearly every concept in fundamental physics these days makes an appearance, making the subject both captivating and confounding.
And not everyone is convinced. Some still think that Hawking got it right and that string theory or other novel physics has to come into play if information is to escape. “I’m very resistant to people who come in and say, ‘I’ve got a solution in just quantum mechanics and gravity,’” said Nick Warner of the University of Southern California. “Because it’s taken us around in circles before.”
But almost everyone appears to agree on one thing. In some way or other, space-time itself seems to fall apart at a black hole, implying that space-time is not the root level of reality, but an emergent structure from something deeper. Although Einstein conceived of gravity as the geometry of space-time, his theory also entails the dissolution of space-time, which is ultimately why information can escape its gravitational prison.
The Curve Becomes the Key
In 1992, Don Page and his family spent their Christmas vacation house-sitting in Pasadena, enjoying the swimming pool and watching the Rose Parade. Page, a physicist at the University of Alberta in Canada, also used the break to think about how paradoxical black holes really are. His first studies of black holes, when he was a graduate student in the ’70s, were key to his adviser Stephen Hawking’s realization that black holes emit radiation — the result of random quantum processes at the edge of the hole. Put simply, a black hole rots from the outside in.
物理学:Does Time Really Flow? New Clues Come From a Century-Old Approach to Math.
Strangely, although we feel as if we sweep through time on the knife-edge between the fixed past and the open future, that edge — the present — appears nowhere in the existing laws of physics.
理论物理:斯奈德-席尔德时空(Snyder-Schild spacetime)
物理学:一文读懂量子纠缠【转载】
本文转载自知乎:一文读懂量(xiang)子(ai)纠(xiang)缠(sha)
英文原文1:Entanglement Made Simple
英文原文2:Your Simple (Yes, Simple) Guide to Quantum Entanglement
量子纠缠及其“多世界”诠释都带有一种神秘而迷人的光环。然而,这些都是,或者都应该是科学观点,它们都有实实在在的具体含义。在下面这篇文章中,我们将尽可能简单明了地为大家解释一下量子纠缠和多世界的概念。
纠缠:从经典迈入量子
量子纠缠经常被看作量子力学才独有的现象,但事实并不是这样。实际上,我们可以首先通过思考一个简单的非量子(或者“经典”)现象来考察纠缠,这是一种比较反传统的做法。这样可以让我们绕开量子论中纠缠的怪异之处来体会量子纠缠的精妙。
一个系统由两个子系统组成,纠缠发生在我们对系统的状态有部分了解的情况下。我们将子系统称之为c-on。“c”的意思是“经典的”,为了便于理解,我们把c-on看作蛋糕。
这里我们的蛋糕有两种形状,正方形或者圆形。那么两个蛋糕的总状态就有4种,它们分别是(方,方)(方,圆)(圆,方)(圆,圆)。下面两个表格给出了在四个状态中找到某一个状态的概率。
当我们不能通过一个蛋糕的信息来判断另一个蛋糕的状态时,我们称这两个子系统是独立的。我们的第一个表格就具有这种特性。即使我们知道第一个蛋糕是方的,我们仍然不知道另一个的形状。类似的,第二个子系统的形状并不能告诉我们关于第一个子系统形状的任何有用信息。
另一方面,如果一个蛋糕的信息可以增加我们对另一个蛋糕的认识,我们就说这两个蛋糕是纠缠的。第二个表格中的情况就表现出高度的纠缠。在这种情况中,如果我们已经知道第一个蛋糕是圆的,那么我们就知道第二个蛋糕一定也是圆形的。如果第一个蛋糕是方形的,第二个也是。当我们知道了第一个蛋糕的形状我们就能确定另一个蛋糕的形状。