杨振宁写的一篇科普性综述:麦克斯韦方程和规范理论的观念起源(The conceptual origins of Maxwell’s equations and gauge theory)



以下是发表于 Physics Today 的原文:

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课程链接: 孙昌璞(中国科学院院士、第三世界科学院院士):高等量子力学


loading中国科学院院士、第三世界科学院院士、中物院研究生院院长。研究领域:量子物理、量子信息、数学物理、复杂系统的统计物理。 研究方向:量子测量、黑洞的信息丢失、量子热力学与非平衡量子开系统、生命系统的量子效应、量子传感和可靠性理论等。 国家自然科学二等奖(2008),美国ISI经典引文奖(2000),中国科学院青年科学家一等奖(1998),全国先进工作者(1995),中国科学院优秀导师(10次)。 培养的研究生2人获全国“百篇优秀博士学位论文”;8人获“中国科学院优秀博士论文”;1人获中国科学院院长特别奖。

孙昌璞的个人主页:The Sun Group (csrc.ac.cn)


量子物理的基本概念及相关研究 量子物理应用
1. 量子的概念 量子信息 原子 物质波 宏观量子态 1. 玻色-爱因斯坦凝聚
2. 经典与量子边界上的薛定谔猫 2. 量子绝热近似理论与Berry相因子
3. 量子力学测量问题与量子信息 3. 微腔量子电动力学的基本概念
4. 量子理论创建的科学启示 4. 宏观物体的退相干与量子宇宙的经典约化
5. 量子测量问题的研究及应用 5. 从参数“浸渐”的量子演化到热力学的绝热过程
6. 量子测量问题与量子力学诠释 6. 宏观人工原子相关的量子相干操纵
7. 量子力学若干基本问题研究的新进展 (I) (II) 7. 基于量子系综的准自旋波激发的量子存贮研究
8. 量子退相干问题 8. 量子态操纵的若干基础物理问题
9. 薜定愕猫与量子测量—兼谈量子信息的发展 9. 量子信息启发的固体系统量子态操纵的基本问题
10. 量子开系统理论及其应用 10. 量子信息启发的量子态操纵
11. 量子力学诠释问题 11. 信息处理的物理极限与量子热力学
File:Linear Halbach Array (Weak side up).png


File:Linear Halbach Array (Weak side up).png

百度百科:Halbach Array一般指海尔贝克阵列,见 海尔贝克阵列_百度百科 (baidu.com)

海尔贝克阵列(Halbach Array)是一种磁体结构,是工程上的近似理想结构,目标是用最少量的磁体产生最强的磁场。1979 年,美国学者Klaus Halbach做电子加速实验时,发现了这种特殊的永磁铁结构,并逐步完善这种结构,最终形成了所谓的“Halbach”磁铁。

维基百科:Halbach array – Wikipedia

Halbach array is a special arrangement of permanent magnets that augments the magnetic field on one side of the array while cancelling the field to near zero on the other side.[1][2] This is achieved by having a spatially rotating pattern of magnetisation.

The rotating pattern of permanent magnets (on the front face; on the left, up, right, down) can be continued indefinitely and have the same effect. The effect of this arrangement is roughly similar to many horseshoe magnets placed adjacent to each other, with similar poles touching.

The principle was first invented by James (Jim) M. Winey of Magnepan in 1970, for the ideal case of continuously rotating magnetization, induced by a one-sided stripe-shaped coil.[3]

The effect was also discovered by John C. Mallinson in 1973, and these “one-sided flux” structures were initially described by him as a “curiosity”, although at the time he recognized from this discovery the potential for significant improvements in magnetic tape technology.[4]

Physicist Klaus Halbach, while at the Lawrence Berkeley National Laboratory during the 1980s, independently invented the Halbach array to focus particle accelerator beams.[5]


The advantages of one-sided flux distributions are twofold:

  • The field is twice as large on the side on which the flux is confined (in the idealized case).
  • There is no stray field produced (in the ideal case) on the opposite side. This helps with field confinement, usually a problem in the design of magnetic structures.

Although one-sided flux distributions may seem somewhat abstract, they have a surprising number of applications ranging from the refrigerator magnet through industrial applications such as the brushless DC motorvoice coils,[7] magnetic drug targeting[8] to high-tech applications such as wiggler magnets used in particle accelerators and free-electron lasers.

This device is also a key component of the Inductrack Maglev train[9] and Inductrack rocket-launch system,[10] wherein the Halbach array repels loops of wire that form the track after the train has been accelerated to a speed able to lift.

The simplest example of a one-sided flux magnet is a refrigerator magnet. These are usually composed of powdered ferrite in a binder such as plastic or rubber. The extruded magnet is exposed to a rotating field giving the ferrite particles in the magnetic compound a magnetization resulting in a one-sided flux distribution. This distribution increases the holding force of the magnet when placed on a permeable surface, compared to the holding force from, say, a uniform magnetization of the magnetic compound.

Scaling up this design and adding a top sheet gives a wiggler magnet, used in synchrotrons and free-electron lasers. Wiggler magnets wiggle, or oscillate, an electron beam perpendicular to the magnetic field. As the electrons are undergoing acceleration, they radiate electromagnetic energy in their flight direction, and as they interact with the light already emitted, photons along its line are emitted in phase, resulting in a “laser-like” monochromatic and coherent beam.

The design shown above is usually known as a Halbach wiggler. The magnetization vectors in the magnetized sheets rotate in the opposite senses to each other; above, the top sheet\\’s magnetization vector rotates clockwise, and the bottom sheet\\’s magnetization vector rotates counter-clockwise. This design is chosen so that the x components of the magnetic fields from the sheets cancel, and the y components reinforce, so that the field is given by

where k is the wavenumber of the magnetic sheet given by the spacing between magnetic blocks with the same magnetization vector.

These cylindrical structures are used in devices such as brushless AC motors, magnetic couplings and high-field cylinders. Both brushless motors and coupling devices use multipole field arrangements:

  • Brushless motors typically use cylindrical designs in which all the flux is confined to the centre of the bore (such as k = 4 above, a 6-pole rotor) with the AC coils also contained within the bore. Such self-shielding motors designs are more efficient and produce higher torque than conventional motor designs.
  • Magnetic-coupling devices transmit torque through magnetically transparent barriers (that is, the barrier is non-magnetic or is magnetic but not affected by an applied magnetic field), for instance, between sealed containers or pressurised vessels. The optimal torque couplings consists of a pair of coaxially nested cylinders with opposite k and −k flux magnetization patterns, as this configuration is the only system for infinitely long cylinders that produces a torque.[14] In the lowest-energy state, the outer flux of the inner cylinder exactly matches the internal flux of the outer cylinder. Rotating one cylinder relative to the other from this state results in a restoring torque.

Halbach array.svg


海尔贝克阵列(Halbach Array)_上海骏材_新浪博客 (sina.com.cn)

海尔贝克阵列(Halbach <wbr>Array)

Klaus Halbach(左)在探讨永磁阵列模型。

海尔贝克阵列(Halbach <wbr>Array) 海尔贝克阵列有哪些形式?海尔贝克阵列(Halbach <wbr>Array)
海尔贝克阵列(Halbach <wbr>Array)
海尔贝克阵列(Halbach <wbr>Array)
海尔贝克阵列(Halbach <wbr>Array)
海尔贝克阵列(Halbach <wbr>Array)


海尔贝克阵列(Halbach <wbr>Array)海尔贝克阵列(Halbach <wbr>Array)

海尔贝克阵列(Halbach <wbr>Array)海尔贝克阵列(Halbach <wbr>Array)

海尔贝克阵列(Halbach <wbr>Array)海尔贝克阵列(Halbach <wbr>Array)

海尔贝克阵列 Halbach Array_磁体 (sohu.com)


  • 直线阵列



  • 环形阵列








以下内容摘录自维基百科:引力波 – 维基百科,自由的百科全书 (wikipedia.org)








这里被称作迹反转度规微扰(trace-reverse metric perturbation)。











第一个条件表示引力波张量中所有与时间t有关的分量都为零,第二个条件表示引力波张量矩阵的为零。因此这组规范条件叫做横向无迹规范(transverse traceless gauge),简称TT规范。在TT规范下,。 由洛伦茨规范和TT规范共同决定下的引力波张量只有两个分量是独立的,它们实际对应着引力波的两种偏振态。对于在z方向传播的波矢,这两个振动分量垂直于传播方向,这表明引力波和电磁波一样是横波,其张量形式写作
















这里Q是张量矩阵的迹。 引力波的能量通量(单位面积的辐射功率)近似为






  • 宇宙学常数,\(\Lambda\)
  • Quintessence,物态方程的参数 \(\omega\) 在 0 到 -1 之间变化,是一个变量
  • Phantom,物态方程的参数 \(\omega\) 可以小于 -1,是一个变量
  • Quintom,物态方程的参数 \(\omega\) 可以等于 -1
  • 修改引力模型?

(238) An Epic Journey to a Black Hole to Give You Goosebumps – YouTube

A black hole is a mysterious place where the laws of physics people are familiar with stop working. Black holes appear when massive stars collapse under their own weight. The gravitational field of the newly formed object is so powerful that even light, including X-rays, can’t escape it. Every black hole has an invisible line-in-the-sand. Cross it – and you won’t be able to escape, even if you’re a beam of light. Beyond the point of no return, the gravity is just too strong. It’s called the event horizon.

There’s a black hole about 1,000 light-years away from the Earth. That’s almost 6 thousand, million, million miles. On the scale of the Universe, it’s right next door. More than four times the mass of our Sun, this medium-sized monster is surrounded by streams of gas. There are two stars nearby. Scientists think this newly discovered black hole might be the nearest to Earth. It’s also the only system with a black hole visible to the unaided eye. Good news – you’re going to visit it right now!


  • Nearest black hole to Earth 0:01
  • International Space Station 0:53 🛰
  • The Moon 1:20 🌙
  • Mars 1:36
  • Jupiter 2:02
  • Saturn 2:17
  • The Kuiper Belt 2:43
  • The Oort Cloud 3:14
  • ⚫ You reach your destination! ⚫ 3:50
  • How to see the back of your head 5:01
  • What’s behind the event horizon ❓6:24
  • What happens after spaghettification 🥡 7:16

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.