# 转发葛墨林院士：我同意杨振宁，中国不应建大加速器

##### 葛墨林院士：我同意杨振宁，中国不应建大加速器

https://mp.weixin.qq.com/s/dvjJQc5723QuMh6Y_FhO4g科技日报记者 高博

CEPC的造价，我听到的数字：一开始提的是300亿元。但这个数字不包括基建。挖那样大直径、那样深的一个隧道，单位成本高过地铁，可想这笔数目小不了。

# 杨振宁：盛宴已过

## 杨振宁：盛宴已过

https://mp.weixin.qq.com/s/pYjs2cb18XxguYyeGFMoBw

“我的看法完全没有改变。”

4月29日下午，北京雁栖湖畔，中国科学院大学（以下简称国科大）庞大的新礼堂座无虚席。端坐在台上白色沙发里的，是中国科学院院士、诺贝尔奖得主杨振宁先生，他很坚定地给台下一位研究生“泼了一瓢冷水”。

其二，中国仍然只是一个发展中国家，建造超大对撞机，费用奇大，对解决燃眉问题不利。其三，建造超大对撞机必将大大挤压其他基础科学的经费。其四，多数物理学家，包括杨振宁在内，认为超对称粒子的存在只是一个猜想，没有任何实验根据，希望用极大对撞机发现此猜想中的粒子更只是猜想加猜想。

“中国现在做大的对撞机，这个事情与我刚才讲的内容有密切的关系。”杨振宁此行是作为“明德讲堂”演讲嘉宾，来与国科大学子分享自己的学习和科研经历的。

“而现在，是大对撞机‘没落’的时候了。”

“可是多半人还不知道。”

“The party is over.”

“什么意思？盛宴已过。”坐在沙发里的杨先生挥挥手，补充翻译道。

The party is over.

“不幸的是很多年轻人没有听进去我这句话，或者是他们只知道跟随老师，那些老师没有懂我这句话。所以今天我才讲得更清楚一点。”

2012年科学家宣布发现了一个新粒子，与希格斯玻色子特征有吻合之处。2013年3月14日，欧洲核子研究组织发布新闻稿表示，先前探测到的新粒子是希格斯玻色子。

“这个贡献重不重要？当然重要。它证明了上世纪的那些理论是对的。”杨振宁说，“可是这重要的贡献的理论起头，不是现在，不是20年前，也不是30年以前，而是上世纪五六十年代了。”

“这个实验做完了以后，这个机器不能再做下去了，要造更大的对撞机，需要花更多的钱，至少要200亿美元。”杨振宁说，“别的国家没钱，大家说中国有钱。”

“我知道我的同行对我很不满意，说我（的反对）是要把他们这行给关闭掉。可是这个对撞机要花中国200亿美元，我没办法能够接受这个事情。”杨振宁说。

“我没办法能够接受这个事情”

“您讲到科研成功的第一步就是兴趣，我们对高能物理是有兴趣的。200亿美元的经费也是一个长期的投入，我们并不是一年就把它花完，与其分散做很多小项目，我们想的是做一个大项目。而且高能物理到底有没有前途，不是还得靠我们的努力吗？”

“20世纪后半世纪最红的物理学是高能物理。而上世纪非常红的东西，到这个世纪还继续红下去，是很少有的。你为什么不考虑21世纪将要发展的是什么呢？”他再次反问。

（文中图片均为杨天鹏摄）

5-3 新浪科技_新浪网 https://tech.sina.com.cn/2019-05-03/doc-ihvhiqax6392390.shtml

作者 | 倪思洁

4月29日下午，在中国科学院大学“明德讲堂”上，曾浩高举的手，被主持人注意到。

“我本科的时候就知道杨先生反对CEPC，但最近听说他好像改口，不反对这件事了，所以就来问一下，没想到他还是泼了一盆冷水。”曾浩告诉《中国科学报》。

“杨先生说科研成功的第一步是兴趣，我的科研兴趣就是高能物理，如果我对材料学之类的热门领域感兴趣，就不会来做高能物理的研究生了。既然选择了这个方向，我还会继续做这方面的研究。”曾浩说。

观点一：盛宴已过？盛宴正酣！

2008年前后，我在欧洲核子研究中心（CERN）已经做了五六年高能物理的研究工作。有一回，杨先生访问CERN，做完报告之后，他把我们这些年轻华人召集起来开了一个会，会上他谈到，加速器物理的前景很悲观，劝我们转去做其他方向。

观点二 ：200亿美元？没那么多！

CEPC的预研工作和核心技术攻关工作得到了中科院、科技部、国家自然科学基金委的支持。

观点三：人傻钱多？我们走在前面！

2012年7月4日，CERN宣布发现希格斯粒子。9月13日，中国高能物理学会在北京召开战略研讨会，会上我向大家汇报了调研进展。

观点四：追热点？不值得推崇！

# 第一张黑洞照片是否隐瞒了什么？

（1）福州原创物理研究所

（2）中国传媒大学信息工程学院

2019年4月10日，由多国天文学家合作的事件视界望远镜项目组（EHT），公布的一张黑洞照片，风靡全球。它被称为人类拍到的第一张证明黑洞真实存在的照片，并被认为再次证实了爱因斯坦引力理论。

EHT实验组的射电天文望远镜采用的是亚毫米波段，严格地说是1.3毫米无线电波。因此这次公布的黑洞照片，只针对波长为1.3毫米无线电波而言，图1中心区域的的无线电波发射能力很弱，我们只能在这种意义上说它是黑的。至于其他范围更广的波段上是否存在辐射，图片中心区域对其他波段的辐射是否也是黑的，EHT实验组并没有给出说明。因此我们有什么理由认为，图1是一张真正的黑洞照片呢？

1. 如果不是采用1.3毫米波段，而是采用其它频率做观测，比可见光波段，这张黑洞照片还是黑洞吗？

2. 照片中原来应当存在的那条无线电波射线哪里去了？

3. 在照片的什么地方看出物质被压缩到成奇点？从哪里看出黑洞视界内是真空？从哪里看出视界内时间和空间互换？如果都看不出来，凭什么认为这张照片证实了爱因斯坦黑洞理论？

2004年霍金公开承认自己30年前提出的黑洞理论的错误。十年后，他索性否認黑洞的存在，認爲黑洞和量子力學不相容。他在與《自然》雜誌的訪談中說：“在經典理論中物質無法從黑洞中逃脫，可是量子理論容許能量和信息從黑洞中脫逃。” “正確的答案仍然是個謎。” 2014年他在arXiv上貼出的文稿中说：“不存在黑洞边界（event horizon）就意味着没有黑洞”，说黑洞理論是他一生鑄成的“大錯”（biggest blunder）。

# 量子力学的困境与出路

——读温伯格的《量子力学的困境》一文有感

“20世纪头十年间量子力学的发展给许多物理学家带来冲击。时至今日，尽管量子力学已经取得巨大成功，关于它的意义与未来的争论却仍在继续。

——随着新实验与新科技的快速发展，对量子力学理论，我们确实需要“继续讨论”和深刻反思了！

1、电子波并非是电子物质的波，这和海浪是水波完全不同。电子波是概率波……概率通常被看作是那些还在研究中的不完美知识的反映，而不是反映了潜在物理学定律中的非决定性。

2、我也不像以前那样确信量子力学的未来。一个不好的信号是即使那些最适应量子力学的物理学家们也无法就它的意义达成共识。这种分歧主要产生于量子力学中测量的本质……如果我们忽略其他关于电子的一切而只考虑自旋，那它的波函数跟波动性其实没什么关系。

3、把概率引入物理学原理曾困扰物理学家，但是量子力学的真正困难不在于概率。困难在于量子力学波函数随时演化的方程，薛定谔方程，本身并不涉及概率……如果我们认定整个测量过程都是由量子力学方程来确定，而这些方程又是确定性的，那量子力学中的概率究竟是怎么来的呢？

4、对我来说似乎它的问题不仅仅在于放弃了自古以来科学的目标：寻求世界的终极奥义。它更是以一种令人遗憾的方式投降……有些物理学家采用工具主义的方法，他们声称我们从波函数中得到的概率是客观存在的概率，不依赖于人们究竟有没有做测量。我则不认为这观点是站得住脚的。

5、在现实主义者的观点中，这个世界的历史时时都在进行无穷无尽的分裂; 每当有宏观物体伴随量子状态的选择时历史就会分裂。这种不可思议的历史分裂为科幻小说提供了素材[12]，而且为多重宇宙提供了依据，众多宇宙之中某个特定宇宙历史中的我们发现自己被限定在条件优渥从而允许有意识生命存在的历史中的一个。但是展望这些平行历史令人深深不安，同其他很多物理学家一样，我倾向于单一存在的历史。

6、纠缠带给爱因斯坦对量子力学的不信任感甚至超过概率的出现。针对量子力学的缺点又应该做些什么呢？ 其实如何去用量子力学并无争议，有争议的是如何阐述它的意义。

7、可惜的是，这些对量子力学修正的想法不仅带有推测性质而且还很模糊，我们也不知道应该期待量子力学的修正究竟有多大。想到此处更是思及量子力学的未来，我唯有引用维奥拉在《第十二夜》中的话：

“O time, thou must untangle this, not I”[1]

……，……，……

1、光与电磁波问题

1.1、光是电磁波的确立基础问题

（1）、Fe=Fm，这说明他对“光也是一种电磁波”的推断是建立在库伦电荷力与磁荷力是同一种力基础之上的，即他首先将电、磁力作了“统一”假定。

（2）、H=B，由此得出qm=qv，这说明磁极是电荷运动产生的，即静止电荷并不产生磁极；静态电荷之间的力来自于电场，运动电荷之间的力来自于磁场。

1.2、赫兹实验问题

LC 振荡能够产生二种效应：（1）、电磁感应效应，这就是麦克斯韦所说的电磁波，（2）、激发辐射光子效应，它就不再是电磁感应现象，而是一种热效应现象。

2、黑体辐射问题

1900年，马克斯·普朗克将维恩定律加以改良，又将玻尔兹曼熵公式重新诠释，得出了一个与实验数据完全吻合普朗克公式来描述黑体辐射；但他在诠释这个公式时，通过将物体中原子看作是微小量子谐振子，为此他不得不假设这些量子谐振子的总能量不是连续的，即总能量只能是离散的数值（这与经典物理学观点相悖），即单个量子谐振子吸收和放射的辐射能是量子化的，即ε=hγ.

3、波粒二象性问题

4、薛定谔方程物理意义问题

.这与质点柱螺旋方程组中的y值描述形式是一致的，这不得不说，从立体空间上看机械波方程应可以视为柱螺旋方程的一个侧投影形式。

5、几率波问题

“几率”通常被看作是那些还在研究中的不完美知识的反映，而不是反映了潜在物理学定律中的非决定性，是一个宏观次（个）的统计概念，这对于单个事件则是不适用的，如温度就是一个统计意义上的概念，只有几个分子的系统，定义温度概念是没有太大意义的，只有当我们需要在统计意义上研究系统时，温度概念才有必要性。

6、测量与波函数崩塌问题

“上个世纪二十年代，海森堡发现，所有客体，主要是微观粒子如电子，如果你不去观测它，它的状态是不确定的。比如，当我们用确定电子位置的仪器去看电子之前，电子的位置是不确定的，根本不知道它在哪里。一旦我们去看它，它瞬间就出现在某个位置，海森堡说，这是因为电子本来不确定位置的“波函数”因为人的观测瞬间塌缩成某个确定位置的“波函数”了。

7、量子纠缠问题

8、电子轨道磁矩与自旋问题

8.1、电子轨道磁矩

（1）、开普勒三定律，其中角动量守恒最重要；

（2）、牛顿万有引力定律。

7.2、电子1/2自旋

9、量子力学研究对象及范围问题

（1）、自旋磁粒子在磁场中作平面“转弯”运动（即磁场洛伦兹运动）；

（2）、自旋磁粒子自旋磁轴方向受磁场磁极影响而产生的磁场梯度力运动（即施特恩实验中所描述的F=μdB/dz）。

（1）、能量不连续性，即普朗克所描述的传递能量的粒子是“一份一份进行的”；

（2）、角动量不连续性，比如电子在核外分别时，其轨道角动量是不连续的，具有量化“跳跃性”；

（3）、运动的自旋性和自旋磁矩性，量子描述的世界是一个带有自旋和自旋磁矩性运动的物质世界，这与经典力学中的粒子概念不同。

“自旋生磁”是我的“自旋场理论”的重要组成部分，当然，磁的产生还包括“公转生磁”，这说明磁的产生应有二种形式，即“自旋生磁”和“公转生磁”；但目前电磁学和量子力学只研究了“公转生磁”，却忽略了“自旋生磁”性，这是当今物理学存在严重“疏漏”的地方，值得去大家关注！

10、量子力学出路问题

“波粒二象性”不是研究微观世界的真正出路，把握微观世界粒子的自旋与自旋磁场性及微观空间的磁场性才是我们真正打开微观世界大门的一把金鈅匙。

11、结束语

【注】

[1] 温伯格《量子力学的困境》：http://chuansong.me/n/1473016951311

[2] 张天蓉《拿什么拯救你量子力学》：http://blog.sciencenet.cn/blog-677221-1054026.html

[3] 李淼在头条：量子坍塌到底是个什现象？

https://wenda.toutiao.com/question/6402115736763891969/

[4] 赵凯华，罗蔚茵/著《量子物理》，高等教育出版社2008年1月第2版，P51～53页。

[5]司今/《从磁陀螺运动谈粒子衍射形成的物理机制》：

【参考文献】

〔1〕赵凯华/著《光学》，高等教育出版社2004年11月第1版。

〔2〕赵凯华，陈熙谋/著《电磁学》，高等教育出版社2003年4月第1版。

〔3〕【美】Richard P.Olenick,Tom M.Apostol David L.Goodstein/著/李椿，陶如玉 译《力学世界》，北京大学出版社2002年2月第1版。

〔4〕赵凯华，罗蔚茵/著《量子物理》，高等教育出版社2008年1月第2版。

〔5〕费恩曼/物理学讲义（2），上海科学技术出版社，2013年4月第1版。

〔6〕徐龙道等/著《物理学词典》，科学出版社2004年5月第1版。

〔7〕百度图片及「百度百科」相关内容。

# 爱因斯坦：机遇与眼光 | 杨振宁

## 爱因斯坦：机遇与眼光 | 杨振宁

杨振宁_网易订阅  http://dy.163.com/v2/article/detail/DUSH03LJ05322F8R.html

1

1905 年通常称为阿尔伯特爱因斯坦的“奇迹年” (Annus Mirabilis)。在那一年，爱因斯坦引发了人类关于物理世界的基本概念 (时间、空间、能量、光和物质) 的三大革命。一个 26 岁、默默无闻的专利局职员如何能引起如此深远的观念变革，因而打开了通往现代科技时代之门？当然没有人能够绝对完满地回答这个问题。可是，我们也许可以分析他成为这一历史性人物的一些必要因素。

“虽然牛顿确实是杰出的天才，但是我们必须承认他也是最幸运的人：人类只有一次机会去建立世界的体系。”

‘Newton’, William Blake, 1795-1805

“幸运的牛顿，幸福的科学童年……他既融合实验者、理论家、机械师为一体，又是阐释的艺术家。他屹立在我们面前，坚强、自信、独一无二。”

“与其他人保持距离；单独地、孤立地、独自地。(《牛津英文词典》)”

1905 年爱因斯坦另一个具有历史意义的成果是他于 3 月间写的论文《关于光的产生和转化的一个启发性观点》(On A Heuristic Point of View Concerning the Generation and Conversion of Light )。这篇文章首次提出了光是带分立能量 hν 的量子。常数 h 由普朗克于 1900 年在其大胆的关于黑体辐射的理论研究中提出。然而，在接下来的几年里，普朗克变得胆怯，开始退缩。1905 年爱因斯坦不仅没有退缩，还勇敢地提出关于光量子的“启发性观点” 。这一大胆的观点当时完全没有受到人们的赞赏，从以下的几句话就可以看出这一点：八年后，当普朗克、能斯特 (W. H. Nernst)、鲁本斯 (Heinrich Rubens)、瓦尔堡 (O. H. Warburg) 提名爱因斯坦为普鲁士科学院院士时，推荐书上说：

“总之，我们可以说几乎没有一个现代物理学的重要问题是爱因斯坦没有做过巨大贡献的。当然他有时在创新思维中会错过目标，例如，他对光―量子的假设。可是我们不应该过分批评他，因为即使在最准确的科学里，要提出真正新的观点而不冒任何风险是不可能的。 (参见前引 A. Pais 的著作，p.382)”

1 、1905 年 爱因斯坦关于 E = hν 的论文

2 、1916 年 爱因斯坦关于 P = E/c 的论文

3 、1924 年 康普顿效应

2

3

“……理论物理的公理基础不可能从经验中提取，而是必须自由地创造出来……经验可能提示适当的数学观念，可是它们绝对不能从经验中演绎而出……

“……我作为一个学生并不懂得获取物理学基本原理的深奥知识的方法是与最复杂的数学方法紧密相连的。在许多年独立的科学工作以后，我才渐渐明白了这一点。”

* 本文来自《我的世界观》（阿尔伯特 · 爱因斯坦著，方在庆编译）中杨振宁所作序言
*

# 孙昌璞：理论物理的六个趋势

❖孙昌璞院士

1、理论物理研究纵深且广泛，其理论立足于全部实验的总和之上。由于物质结构是分层次的，每个层次上都有自己的基本规律，不同层次上的规律又是互相联系的。物质层次结构及其运动规律的基础性、多样性和复杂性不仅为理论物理学提供了丰富的研究对象，而且对理论物理学家提出巨大的智力挑战，激发出人类探索自然的强大动力。因此，理论物理这种高度概括的综合性研究，具有显著的多学科交叉与知识原创的特点。在理论物理中，有的学科（诸如粒子物理、凝聚态物理等），与实验研究关系十分密切，但还有一些更加基础的领域（如统计物理、引力理论和量子基础理论），它们一时并不直接涉及实验。虽然物理学本身是一门实验科学，但物理理论是立足于长时间全部实验总和之上，而不是只针对个别实验。虽然理论正确与否必须落实到实验检验上，但在物理学发展过程中间，有的阶段性理论研究和纯理论探索性研究，开始不必过分强调具体的实验检验。其实，导致重大科学突破甚至科学革命的广义相对论、规范场论和玻色-爱因斯坦凝聚就是这方面的典型例证，它们从纯理论出发，实验验证却等待几十年、甚至近百年。近百年前爱因斯坦广义相对论预言了一种以光速传播的时空波动——引力波。直到2016年2月，美国科学家才宣布人类首次直接探测到引力波。引力波的预言是理论物理发展的里程碑，它的观察发现将开创一个崭新的引力波天文学研究领域，更深刻地揭示宇宙奥秘。

2、面对当代实验科学日趋复杂的技术挑战和巨大经费需求，理论物理对物理学的引领作用必不可少。第二次世界大战后，基于大型加速器的粒子物理学开创了大科学工程的新时代，也使得物理学发展面临经费需求的巨大挑战。因此，伴随着实验和理论对物理学发展发挥的作用有了明显的差异变化，理论物理高屋建瓴的指导作用日趋重要。在高能物理领域，轻子和夸克只能有三代是纯理论的结果，顶夸克和最近在大型强子对撞机（LHC）发现的Higgs粒子首先来自理论预言。当今高能物理实验基本上都是在理论指导下设计进行的，没有理论上的动机和指导，高能物理实验如同大海捞针、无从下手。可以说，每一个大型粒子对撞机和其它大型实验装置，都与一个具体理论密切相关。天体宇宙学的观测更是如此。天文观测只会给出一些初步的宇宙信息，但其物理解释必依赖于具体的理论模型。宇宙的演化只有一次，其初态和末态迄今都是未知的。宇宙学的研究不能像通常的物理实验那样，不可能为获得其演化的信息任意调整其初末态。因此，仅仅基于观测，不可能构造完全合理的宇宙模型。要对宇宙的演化有真正的了解、建立自洽的宇宙学模型和理论，就必须立足于粒子物理和广义相对论等物理理论。

3、理论物理学本质上是一门交叉综合科学。大家知道，量子力学20世纪的奠基性科学理论之一，是人们理解微观世界运动规律的现代物理基础。它的建立，导致了以激光、半导体和核能为代表的新技术革命，深刻地影响了人类的物质、精神生活，已成为社会经济发展的原动力之一。然而，量子力学基础却存在诸多的争议，哥本哈根学派对量子力学的“标准”诠释遭遇诸多挑战。不过这些学术争论不仅促进了量子理论自身发展，而且促使量子力学走向交叉科学领域，使得量子物理从观测解释阶段进入自主调控的新时代，从此量子世界从自在之物变成为我之物。近二十年来，理论物理学在综合交叉方面的重要进展是量子物理与信息计算科学的交叉，由此形成了以量子计算、量子通信和量子精密测量为主体的量子信息科学：它充分利用量子力学基本原理，基于独特的量子相干进行计算、编码、信息传输和精密测量，探索突破芯片极限、保证信息安全的新概念和新思路。统计物理学为理论物理研究开拓了跨度更大的交叉综合领域，如生物物理和软凝聚态物理。统计物理的思想和方法不断地被应用到各种新的领域，对其基本理论和自身发展提出了更高的要求。由于软物质是在自然界中存在的最广泛的复杂凝聚态物质，它处于固体和理想流体之间，与人们的日常生活及工业技术密切相关。例如，水是一种软凝聚态物质，其研究涉及的基础科学问题关乎人类社会今天面对的水源危机。

4、理论物理学在对具体系统应用中实现创新发展，并在基本的层次上回馈自身。从量子力学和统计物理对固体系统的具体应用开始，近半个世纪以来凝聚态物理学业已发展成当代物理学最大的一个分支。它不仅是材料、信息和能源科学的基础，也与化学和生物等学科交叉与融合，而其中发现的新现象、新效应，都有可能导致凝聚态物理一个新的学科方向或领域的诞生，为理论物理研究展现了更加广阔的前景。一方面，凝聚态物理自身理论发展异常迅猛和广泛，描述半导体和金属的能带论和费米液体理论为电子学、计算机和信息等学科发展的奠定了理论基础；另一方面，从凝聚态理论研究提炼出来的普适的概念和方法，对包括高能物理其它物理学科的发展也起到了重要的推动作用。BCS超导理论中的自发对称破缺概念，被应用到描述电弱相互作用统一的Yang-Mills 规范场论，导致了中间玻色子质量演生的Higgs机制，这是理论物理学发展的又一个重要里程碑。近二十年来，在凝聚态物理领域，有大量新型低维材料的合成和发现，有特殊功能的量子器件的设计和实现，有高温超导和拓扑绝缘体等大量新奇量子现象的展示。这些现象不能在以单体近似为前提的费米液体理论框架下得到解释，新的理论框架建立已迫在眉睫，如果成功将使凝聚态物理的基础及应用研究跨上一个新的历史台阶，也会为理论物理的引领作用发挥到极致。

5、理论物理的一个重要发展趋势是理论模型与强大的现代计算手段相结合。面对纷繁复杂的物质世界（如强关联物质和复杂系统），简单可解析求解的理论物理模型不足以涵盖复杂物质结构的全部特征，如非微扰和高度非线性。现代计算机的发明和快速发展提供了解决这些复杂问题的强大工具。辅以面向对象的科学计算方法（如第一原理计算、蒙特卡罗方法和精确对角化技术），复杂理论模型的近似求解将达到极高的精度，可以逐渐逼近真实的物质运动规律。因此，在解析手段无法胜任解决复杂问题任务时，理论物理必须通过数值分析和模拟的办法，使得理论预言进一步定量化和精密化。这方面的研究导致了计算物理这一重要学科分支的形成，成为连接物理实验和理论模型必不可少的纽带。

6、理论物理学将在国防安全等国家重大需求上发挥更多作用。大家知道，无论决胜第二次世界大战、冷战时代的战略平衡，还是中国国家战略地位提升，理论物理学在满足国家重大战略需求方面发挥了不可替代的作用。理论物理学家爱因斯坦、奥本海默、费米、彭桓武、于敏、周光召等人也因此彪炳史册。与战略武器发展息息相关，二战后开启了物理学大科学工程的新时代，基于大型加速器的重大科学发现反过来为理论物理学提供广阔的用武之地，如标准模型的建立。国防安全方面等国家重大需求往往会提出自由探索不易提出的基础科学问题，在对理论物理提出新挑战的同时，也为理论物理研究提供了源头创新的平台。因此，理论物理也要针对国民经济发展和国防安全方面等国家重大需求，凝练和发掘自己能够发挥关键作用的科学问题，在实践应用和理论原始创新方面取得重大突破。

《21世纪理论物理及其交叉学科前沿丛书》包括中英文的专著和基础理论，以相关专业领域的研究生为起点。主要内容有（包括但不限于）：

（1）最深层次物质结构和动力学规律的前沿：量子场论及与宇宙学；粒子物理及与宇宙学；高能重离子碰撞和强子物理中动力学规律。

（2）凝聚态理论：强关联多电子系统的理论研究；受限小量子系统。

（3）跨学科理论研究新领域：理论物理与生命科学；有机固体和聚合物的理论物理研究；纳米材料设计的基础理论；量子信息。

# 这些是科学探索中最重大的问题！

The biggest questions in science https://www.nature.com/collections/mnwshvsswk

INNOVATIONS IN

What Is Spacetime?
https://www.nature.com/articles/d41586-018-05095-z
Physicists believe that at the tiniest scales, space emerges from quanta. What might these building blocks look like?
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What Is Dark Matter? https://www.nature.com/articles/d41586-018-05096-y

INNOVATIONS IN，09 MAY 2018
An elusive substance that permeates the universe exerts many detectable gravitational influences yet eludes direct detection.
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INNOVATIONS IN

What Is Consciousness?
https://www.nature.com/articles/d41586-018-05097-x

# What Is Consciousness?

Scientists are beginning to unravel a mystery that has long vexed philosophers.

INNOVATIONS IN

How Did Life Begin? https://www.nature.com/articles/d41586-018-05098-w

# How Did Life Begin?

Untangling the origins of organisms will require experiments at the tiniest scales and observations at the vastest.

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INNOVATIONS IN

### What Are the Limits of Manipulating Nature?

By reaching down into the quantum world, scientists are hoping to gain more control over matter and energy.
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How Much Can We Know? https://www.nature.com/articles/d41586-018-05100-5

INNOVATIONS IN

# How Much Can We Know?

The reach of the scientific method is constrained by the limitations of our tools and the intrinsic impenetrability of some of nature’s deepest questions.
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# 《21世纪100个交叉科学难题》

《21世纪100个交叉科学难题》_百度文库 https://wenku.baidu.com/view/cd8dc465f12d2af90242e6da.html
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##### 龚学创新物理学理论方法论
1.新物理必须要有新的整体架构，新的方法论和认识论，新物理学必须具有统一性、一致性、完备性、终极性和完美性；
2.新的物理必须基于严格的数学和逻辑，如理论计算出精细结构常数、宇宙学常数、暗物质暗能量、希格斯粒子机制及质量等；
3.所有的结果及自然演绎要与自然客观观测一致及符合实验检验。

www.pptv1.com

# 究竟什么是物质，哲学上又指什么？

###### 原道童子 作答：

①物质的认知必须以绝对时空作为参照系。

②物质是基于真空漩涡场的(色空亦空)。

③物质来自既有自旋又有绕旋的基本粒子。

④物质是或独立自由或叠加约束的。

⑤物质是既有质量又有能量的。

⑥或直接测量或间接测量。

⑦物质是客观存在形式，而非数学臆断。

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DS =（i^n1，i^n2，i^n3）* C * DT =N * C * DT……（方程0)

i是虚数，i^n1是i 的n1幂次，同样i^ n2和i^n3；

{n1, n2, n3}自然数取值范围（0,1,2,3）或（1,2,3,4）；

DS是一个空间单元，DT一个时间单元；C是光速。

N是一个虚-实数域，而N方有四个可能的值。

N^ 2 = { + / – 1 ，+ / – 3 } ………….（方程0’）

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INNOVATIONS IN

doi: 10.1038/d41586-018-05096-y

# What Is Dark Matter?

An elusive substance that permeates the universe exerts many detectable gravitational influences yet eludes direct detection.

### Lisa Randall

Physicists and astronomers have determined that most of the material in the universe is “dark matter”—whose existence we infer from its gravitational effects but not through electromagnetic influences such as we find with ordinary, familiar matter. One of the simplest concepts in physics, dark matter can nonetheless be mystifying because of our human perspective. Each of us has five senses, all of which originate in electromagnetic interactions. Vision, for example, is based on our sensitivity to light: electromagnetic waves that lie within a specific range of frequencies. We can see the matter with which we are familiar because the atoms that make it up emit or absorb light. The electric charges carried by the electrons and protons in atoms are the reason we can see.

Matter is not necessarily composed of atoms, however. Most of it can be made of something entirely distinct. Matter is any material that interacts with gravity as normal matter does—becoming clumped into galaxies and galaxy clusters, for example.

There is no reason that matter must always consist of charged particles. But matter that has no electromagnetic interactions will be invisible to our eyes. So-called dark matter carries no (or as yet undetectably little) electromagnetic charge. No one has seen it directly with his or her eyes or even with sensitive optical instruments. Yet we believe it is out there because of its manifold gravitational influences. These include dark matter’s impact on the stars in our galaxy (which revolve at speeds too great for ordinary matter’s gravitational force to rein in) and the motions of galaxies in galaxy clusters (again, too fast to be accounted for only by matter that we see); its imprint on the cosmic microwave background radiation left over from the time of the big bang; its influence on the trajectories of visible matter from supernova expansions; the bending of light known as gravitational lensing; and the observation that the visible and invisible matter gets separated in merged galaxy clusters.

Perhaps the most significant sign of the existence of dark matter, however, is our very existence. Despite its invisibility, dark matter has been critical to the evolution of our universe and to the emergence of stars, planets and even life. That is because dark matter carries five times the mass of ordinary matter and, furthermore, does not directly interact with light. Both these properties were critical to the creation of structures such as galaxies—within the (relatively short) time span we know to be a typical galaxy lifetime—and, in particular, to the formation of a galaxy the size of the Milky Way. Without dark matter, radiation would have prevented clumping of the galactic structure for too long, in essence wiping it out and keeping the universe smooth and homogeneous. The galaxy essential to our solar system and our life was formed in the time since the big bang only because of the existence of dark matter.

Some people, on first hearing about dark matter, feel dismayed. How can something we do not see exist? At least since the Copernican revolution, humans should be prepared to admit their noncentrality to the makeup of the universe. Yet each time people learn about it in a new context, many get confused or surprised. There is no reason that the matter we see should be the only type of matter there is. The existence of dark matter might be expected and is compatible with everything we know.

Perhaps some confusion lies in the name. Dark matter should really be called transparent matter because, as with all transparent things, light just passes through it. Nevertheless, its nature is far from transparent. Physicists and astronomers would like to understand, at a more fundamental level, what exactly dark matter is. Is it made up of a new type of fundamental particle, or does it consist of some invisible, compact object, such as a black hole? If it is a particle, does it have any (albeit very weak) interaction with familiar matter, aside from gravity? Does that particle have any interactions with itself that would be invisible to our senses? Is there more than one type of such a particle? Do any of these particles have interactions of any sort?

My theoretical colleagues and I have thought about a number of interesting possibilities. Ultimately, however, we will learn about the true nature of dark matter only with the help of further observations to guide us. Those observations might consist of more detailed measurements of dark matter’s gravitational influence. Or—if we are very lucky and dark matter does have some tiny, nongravitational interaction with ordinary matter we have so far failed to observe—big underground detectors, satellites in space or the Large Hadron Collider at CERN near Geneva might in the future detect dark matter particles. Even without such interactions with ordinary matter, dark matter’s self-interactions might have observable consequences. For example, the internal structure of galaxies at small scales will be different if dark matter’s interactions with itself rearrange matter at galactic centers. Compact or other structures akin to the Milky Way, such as the bright gas clouds and stars we see when we look at the night sky, could indicate one or more distinct species of dark matter particles that interact with one another. Or hypothesized particles called axions that interact with magnetic fields might be detected in laboratories or in space.

For a theorist, an observer or an experimentalist, dark matter is a promising target for research. We know it exists, but we do not yet know what it is at a fundamental level. The reason we do not know might be obvious by now: it is just not interacting enough to tell us, at least so far. As humans, we can only do so much if ordinary matter is essentially oblivious to anything but dark matter’s very existence. But if dark matter has some more interesting properties, researchers are poised to find them—and, in the process, to help us more completely address this wonderful mystery.

Nature 557, S6-S7 (2018)

doi: 10.1038/d41586-018-05096-y

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INNOVATIONS IN

# What Is Spacetime?

Physicists believe that at the tiniest scales, space emerges from quanta. What might these building blocks look like?

### George Musser

People have always taken space for granted. It is just emptiness, after all—a backdrop to everything else. Time, likewise, simply ticks on incessantly. But if physicists have learned anything from the long slog to unify their theories, it is that space and time form a system of such staggering complexity that it may defy our most ardent efforts to understand.

Albert Einstein saw what was coming as early as November 1916. A year earlier he had formulated his general theory of relativity, which postulates that gravity is not a force that propagates through space but a feature of spacetime itself. When you throw a ball high into the air, it arcs back to the ground because Earth distorts the spacetime around it, so that the paths of the ball and the ground intersect again. In a letter to a friend, Einstein contemplated the challenge of merging general relativity with his other brainchild, the nascent theory of quantum mechanics. That would not merely distort space but dismantle it. Mathematically, he hardly knew where to begin. “How much have I already plagued myself in this way!” he wrote.

Einstein never got very far. Even today there are almost as many contending ideas for a quantum theory of gravity as scientists working on the topic. The disputes obscure an important truth: the competing approaches all say space is derived from something deeper—an idea that breaks with 2,500 years of scientific and philosophical understanding.

Down the Black Hole

A kitchen magnet neatly demonstrates the problem that physicists face. It can grip a paper clip against the gravity of the entire Earth. Gravity is weaker than magnetism or than electric or nuclear forces. Whatever quantum effects it has are weaker still. The only tangible evidence that these processes occur at all is the mottled pattern of matter in the very early universe—thought to be caused, in part, by quantum fluctuations of the gravitational field.

Black holes are the best test case for quantum gravity. “It’s the closest thing we have to experiments,” says Ted Jacobson of the University of Maryland, College Park. He and other theorists study black holes as theoretical fulcrums. What happens when you take equations that work perfectly well under laboratory conditions and extrapolate them to the most extreme conceivable situation? Will some subtle flaw manifest itself?

General relativity predicts that matter falling into a black hole becomes compressed without limit as it approaches the center—a mathematical cul-de-sac called a singularity. Theorists cannot extrapolate the trajectory of an object beyond the singularity; its time line ends there. Even to speak of “there” is problematic because the very spacetime that would define the location of the singularity ceases to exist. Researchers hope that quantum theory could focus a microscope on that point and track what becomes of the material that falls in.

Out at the boundary of the hole, matter is not so compressed, gravity is weaker and, by all rights, the known laws of physics should still hold. Thus, it is all the more perplexing that they do not. The black hole is demarcated by an event horizon, a point of no return: matter that falls in cannot get back out. The descent is irreversible. That is a problem because all known laws of fundamental physics, including those of quantum mechanics as generally understood, are reversible. At least in principle, you should be able to reverse the motion of all the particles and recover what you had.

A very similar conundrum confronted physicists in the late 1800s, when they contemplated the mathematics of a “black body,” idealized as a cavity full of electromagnetic radiation. James Clerk Maxwell’s theory of electromagnetism predicted that such an object would absorb all the radiation that impinges on it and that it could never come to equilibrium with surrounding matter. “It would absorb an infinite amount of heat from a reservoir maintained at a fixed temperature,” explains Rafael Sorkin of the Perimeter Institute for Theoretical Physics in Ontario. In thermal terms, it would effectively have a temperature of absolute zero. This conclusion contradicted observations of real-life black bodies (such as an oven). Following up on work by Max Planck, Einstein showed that a black body can reach thermal equilibrium if radiative energy comes in discrete units, or quanta.

Theoretical physicists have been trying for nearly half a century to achieve an equivalent resolution for black holes. The late Stephen Hawking of the University of Cambridge took a huge step in the mid-1970s, when he applied quantum theory to the radiation field around black holes and showed they have a nonzero temperature. As such, they can not only absorb but also emit energy. Although his analysis brought black holes within the fold of thermodynamics, it deepened the problem of irreversibility. The outgoing radiation emerges from just outside the boundary of the hole and carries no information about the interior. It is random heat energy. If you reversed the process and fed the energy back in, the stuff that had fallen in would not pop out; you would just get more heat. And you cannot imagine that the original stuff is still there, merely trapped inside the hole, because as the hole emits radiation, it shrinks and, according to Hawking’s analysis, ultimately disappears.

This problem is called the information paradox because the black hole destroys the information about the infalling particles that would let you rewind their motion. If black hole physics really is reversible, something must carry information back out, and our conception of spacetime may need to change to allow for that.

Atoms of Spacetime

Heat is the random motion of microscopic parts, such as the molecules of a gas. Because black holes can warm up and cool down, it stands to reason that they have parts—or, more generally, a microscopic structure. And because a black hole is just empty space (according to general relativity, infalling matter passes through the horizon but cannot linger), the parts of the black hole must be the parts of space itself. As plain as an expanse of empty space may look, it has enormous latent complexity.

Even theories that set out to preserve a conventional notion of spacetime end up concluding that something lurks behind the featureless facade. For instance, in the late 1970s Steven Weinberg, now at the University of Texas at Austin, sought to describe gravity in much the same way as the other forces of nature. He still found that spacetime is radically modified on its finest scales.

Physicists initially visualized microscopic space as a mosaic of little chunks of space. If you zoomed in to the Planck scale, an almost inconceivably small size of 10–35 meter, they thought you would see something like a chessboard. But that cannot be quite right. For one thing, the grid lines of a chessboard space would privilege some directions over others, creating asymmetries that contradict the special theory of relativity. For example, light of different colors might travel at different speeds—just as in a glass prism, which refracts light into its constituent colors. Whereas effects on small scales are usually hard to see, violations of relativity would actually be fairly obvious.

The thermodynamics of black holes casts further doubt on picturing space as a simple mosaic. By measuring the thermal behavior of any system, you can count its parts, at least in principle. Dump in energy and watch the thermometer. If it shoots up, that energy must be spread out over comparatively few molecules. In effect, you are measuring the entropy of the system, which represents its microscopic complexity.

If you go through this exercise for an ordinary substance, the number of molecules increases with the volume of material. That is as it should be: If you increase the radius of a beach ball by a factor of 10, you will have 1,000 times as many molecules inside it. But if you increase the radius of a black hole by a factor of 10, the inferred number of molecules goes up by only a factor of 100. The number of “molecules” that it is made up of must be proportional not to its volume but to its surface area. The black hole may look three-dimensional, but it behaves as if it were two-dimensional.

This weird effect goes under the name of the holographic principle because it is reminiscent of a hologram, which presents itself to us as a three-dimensional object. On closer examination, however, it turns out to be an image produced by a two-dimensional sheet of film. If the holographic principle counts the microscopic constituents of space and its contents—as physicists widely, though not universally, accept—it must take more to build space than splicing together little pieces of it.

The relation of part to whole is seldom so straightforward, anyway. An H2O molecule is not just a little piece of water. Consider what liquid water does: it flows, forms droplets, carries ripples and waves, and freezes and boils. An individual H2O molecule does none of that: those are collective behaviors. Likewise, the building blocks of space need not be spatial. “The atoms of space are not the smallest portions of space,” says Daniele Oriti of the Max Planck Institute for Gravitational Physics in Potsdam, Germany. “They are the constituents of space. The geometric properties of space are new, collective, approximate properties of a system made of many such atoms.”

What exactly those building blocks are depends on the theory. In loop quantum gravity, they are quanta of volume aggregated by applying quantum principles. In string theory, they are fields akin to those of electromagnetism that live on the surface traced out by a moving strand or loop of energy—the namesake string. In M-theory, which is related to string theory and may underlie it, they are a special type of particle: a membrane shrunk to a point. In causal set theory, they are events related by a web of cause and effect. In the amplituhedron theory and some other approaches, there are no building blocks at all—at least not in any conventional sense.

Although the organizing principles of these theories vary, all strive to uphold some version of the so-called relationalism of 17th- and 18th-century German philosopher Gottfried Leibniz. In broad terms, relationalism holds that space arises from a certain pattern of correlations among objects. In this view, space is a jigsaw puzzle. You start with a big pile of pieces, see how they connect and place them accordingly. If two pieces have similar properties, such as color, they are likely to be nearby; if they differ strongly, you tentatively put them far apart. Physicists commonly express these relations as a network with a certain pattern of connectivity. The relations are dictated by quantum theory or other principles, and the spatial arrangement follows.

Phase transitions are another common theme. If space is assembled, it might be disassembled, too; then its building blocks could organize into something that looks nothing like space. “Just like you have different phases of matter, like ice, water and water vapor, the atoms of space can also reconfigure themselves in different phases,” says Thanu Padmanabhan of the Inter-University Center for Astronomy and Astrophysics in India. In this view, black holes may be places where space melts. Known theories break down, but a more general theory would describe what happens in the new phase. Even when space reaches its end, physics carries on.

Entangled Webs

The big realization of recent years—and one that has crossed old disciplinary boundaries—is that the relevant relations involve quantum entanglement. An extrapowerful type of correlation, intrinsic to quantum mechanics, entanglement seems to be more primitive than space. For instance, an experimentalist might create two particles that fly off in opposing directions. If they are entangled, they remain coordinated no matter how far apart they may be.

Traditionally when people talked about “quantum” gravity, they were referring to quantum discreteness, quantum fluctuations and almost every other quantum effect in the book—but never quantum entanglement. That changed when black holes forced the issue. Over the lifetime of a black hole, entangled particles fall in, but after the hole evaporates fully, their partners on the outside are left entangled with—nothing. “Hawking should have called it the entanglement problem,” says Samir Mathur of Ohio State University.

Even in a vacuum, with no particles around, the electromagnetic and other fields are internally entangled. If you measure a field at two different spots, your readings will jiggle in a random but coordinated way. And if you divide a region in two, the pieces will be correlated, with the degree of correlation depending on the only geometric quantity they have in common: the area of their interface. In 1995 Jacobson argued that entanglement provides a link between the presence of matter and the geometry of spacetime—which is to say, it might explain the law of gravity. “More entanglement implies weaker gravity—that is, stiffer spacetime,” he says.

Several approaches to quantum gravity—most of all, string theory—now see entanglement as crucial. String theory applies the holographic principle not just to black holes but also to the universe at large, providing a recipe for how to create space—or at least some of it. For instance, a two-dimensional space could be threaded by fields that, when structured in the right way, generate an additional dimension of space. The original two-dimensional space would serve as the boundary of a more expansive realm, known as the bulk space. And entanglement is what knits the bulk space into a contiguous whole.

In 2009 Mark Van Raamsdonk of the University of British Columbia gave an elegant argument for this process. Suppose the fields at the boundary are not entangled—they form a pair of uncorrelated systems. They correspond to two separate universes, with no way to travel between them. When the systems become entangled, it is as if a tunnel, or wormhole, opens up between those universes, and a spaceship can go from one to the other. As the degree of entanglement increases, the wormhole shrinks in length, drawing the universes together until you would not even speak of them as two universes anymore. “The emergence of a big spacetime is directly tied into the entangling of these field theory degrees of freedom,” Van Raamsdonk says. When we observe correlations in the electromagnetic and other fields, they are a residue of the entanglement that binds space together.

Many other features of space, besides its contiguity, may also reflect entanglement. Van Raamsdonk and Brian Swingle, now at the University of Maryland, College Park, argue that the ubiquity of entanglement explains the universality of gravity—that it affects all objects and cannot be screened out. As for black holes, Leonard Susskind of Stanford University and Juan Maldacena of the Institute for Advanced Study in Princeton, N.J., suggest that entanglement between a black hole and the radiation it has emitted creates a wormhole—a back-door entrance into the hole. That may help preserve information and ensure that black hole physics is reversible.

Whereas these string theory ideas work only for specific geometries and reconstruct only a single dimension of space, some researchers have sought to explain how all of space can emerge from scratch. For instance, ChunJun Cao, Spyridon Michalakis and Sean M. Carroll, all at the California Institute of Technology, begin with a minimalist quantum description of a system, formulated with no direct reference to spacetime or even to matter. If it has the right pattern of correlations, the system can be cleaved into component parts that can be identified as different regions of spacetime. In this model, the degree of entanglement defines a notion of spatial distance.

In physics and, more generally, in the natural sciences, space and time are the foundation of all theories. Yet we never see spacetime directly. Rather we infer its existence from our everyday experience. We assume that the most economical account of the phenomena we see is some mechanism that operates within spacetime. But the bottom-line lesson of quantum gravity is that not all phenomena neatly fit within spacetime. Physicists will need to find some new foundational structure, and when they do, they will have completed the revolution that began just more than a century ago with Einstein.

Nature 557, S3-S6 (2018)

doi: 10.1038/d41586-018-05095-z

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# 量子力学无神秘，大神们请走开！—— 唯物主义世界观是中华民族的立国之本，不容颠覆

## 量子力学无神秘，大神们请走开！—— 唯物主义世界观是中华民族的立国之本，不容颠覆 ——

2018-04-22    梅晓春    梅晓春原创物理

2017年11月26日上午，在《2017金华发展大会发展论坛》上，潘建伟做了发言，说量子力学证明，可以把一个人瞬间从金华送回北京。此前潘建伟多次说，杯子可以隐形态瞬间传输。但这次他说的是人，人也可以被隐形态瞬间传输。比如他本人可以瞬间从金华消失，然后在北京瞬间被重新构造出来，之间隔离千山万水。

“我们原来认为世界是物质的，没有神，没有特异功能，意识是和物质相对立的另一种存在。

# Quantum Frontiers

## A blog by the Institute for Quantum Information and Matter @ Caltech

Quantum computing is advancing very fast, having many breakthroughs. One leading institute is at Caltech, Institute for Quantum Information and Matter, a National Science Foundation Physics Frontiers Center (just received 65 million dollars new funding for this new research, see http://iqim.caltech.edu/ ).

# The math of multiboundary wormholes

Xi Dong, Alex Maloney, Henry Maxfield and I recently posted a paper to the arXiv with the title: Phase Transitions in 3D Gravity and Fractal Dimension. In other words, we’ll get about ten readers per year for the next few decades. Despite the heady title, there’s deep geometrical beauty underlying this work. In this post I want to outline the origin story and motivation behind this paper.

There are two different branches to the origin story. The first was my personal motivation and the second is related to how I came into contact with my collaborators (who began working on the same project but with different motivation, namely to explain a phase transition described in this paper by Belin, Keller and Zadeh.)

During the first year of my PhD at Caltech I was working in the mathematics department and I had a few brief but highly influential interactions with Nikolai Makarov while I was trying to find a PhD advisor. His previous student, Stanislav Smirnov, had recently won a Fields Medal for his work studying Schramm-Loewner evolution (SLE) and I was captivated by the beauty of these objects.

SLE example from Scott Sheffield’s webpage. SLEs are the fractal curves that form at the interface of many models undergoing phase transitions in 2D, such as the boundary between up and down spins in a 2D magnet (Ising model.)

One afternoon, I went to Professor Makarov’s office for a meeting and while he took a brief phone call I noticed a book on his shelf called Indra’s Pearls, which had a mesmerizing image on its cover. I asked Professor Makarov about it and he spent 30 minutes explaining some of the key results (which I didn’t understand at the time.) When we finished that part of our conversation Professor Makarov described this area of math as “math for the future, ahead of the tools we have right now” and he offered for me to borrow his copy. With a description like that I was hooked. I spent the next six months devouring this book which provided a small toehold as I tried to grok the relevant mathematics literature. This year or so of being obsessed with Kleinian groups (the underlying objects in Indra’s Pearls) comes back into the story soon. I also want to mention that during that meeting with Professor Makarov I was exposed to two other ideas that have driven my research as I moved from mathematics to physics: quasiconformal mappings and the simultaneous uniformization theorem, both of which will play heavy roles in the next paper I release.  In other words, it was a pretty important 90 minutes of my life.

Google image search for “Indra’s Pearls”. The math underlying Indra’s Pearls sits at the intersection of hyperbolic geometry, complex analysis and dynamical systems. Mathematicians oftentimes call this field the study of “Kleinian groups”. Most of these figures were obtained by starting with a small number of Mobius transformations (usually two or three) and then finding the fixed points for all possible combinations of the initial transformations and their inverses. Indra’s Pearls was written by David Mumford, Caroline Series and David Wright. I couldn’t recommend it more highly.

My life path then hit a discontinuity when I was recruited to work on a DARPA project, which led to taking an 18 month leave of absence from Caltech. It’s an understatement to say that being deployed in Afghanistan led to extreme introspection. While “down range” I had moments of clarity where I knew life was too short to work on anything other than ones’ deepest passions. Before math, the thing that got me into science was a childhood obsession with space and black holes. I knew that when I returned to Caltech I wanted to work on quantum gravity with John Preskill. I sent him an e-mail from Afghanistan and luckily he was willing to take me on as a student. But as a student in the mathematics department, I knew it would be tricky to find a project that involved all of: black holes (my interest), quantum information (John’s primary interest at the time) and mathematics (so I could get the degree.)

I returned to Caltech in May of 2012 which was only two months before the Firewall Paradox was introduced by Almheiri, Marolf, Polchinski and Sully. It was obvious that this was where most of the action would be for the next few years so I spent a great deal of time (years) trying to get sharp enough in the underlying concepts to be able to make comments of my own on the matter. Black holes are probably the closest things we have in Nature to the proverbial bottomless pit, which is an apt metaphor for thinking about the Firewall Paradox. After two years I was stuck. I still wasn’t close to confident enough with AdS/CFT to understand a majority of the promising developments. And then at exactly the right moment, in the summer of 2014, Preskill tipped my hat to a paper titled Multiboundary Wormholes and Holographic Entanglement by Balasubramanian, Hayden, Maloney, Marolf and Ross. It was immediately obvious to me that the tools of Indra’s Pearls (Kleinian groups) provided exactly the right language to study these “multiboundary wormholes.” But despite knowing a bridge could be built between these fields, I still didn’t have the requisite physics mastery (AdS/CFT) to build it confidently.

Before mentioning how I met my collaborators and describing the work we did together, let me first describe the worlds that we bridged together.

3D Gravity and Universality

As the media has sensationalized to death, one of the most outstanding questions in modern physics is to discover and then understand a theory of quantum gravity.  As a quick aside, Quantum gravity is just a placeholder name for such a theory. I used italics because physicists have already discovered candidate theories, such as string theory and loop quantum gravity (I’m not trying to get into politics, just trying to demonstrate that there are multiple candidate theories). But understanding these theories — carrying out all of the relevant computations to confirm that they are consistent with Nature and then doing experiments to verify their novel predictions — is still beyond our ability. Surprisingly, without knowing the specific theory of quantum gravity that guides Nature’s hand, we’re still able to say a number of universal things that must be true for any theory of quantum gravity. The most prominent example being the holographic principle which comes from the entropy of black holes being proportional to the surface area encapsulated by the black hole’s horizon (a naive guess says the entropy should be proportional to the volume of the black hole; such as the entropy of a glass of water.) Universal statements such as this serve as guideposts and consistency checks as we try to understand quantum gravity.

It’s exceedingly rare to find universal statements that are true in physically realistic models of quantum gravity. The holographic principle is one such example but it pretty much stands alone in its power and applicability. By physically realistic I mean: 3+1-dimensional and with the curvature of the universe being either flat or very mildly positively curved.  However, we can make additional simplifying assumptions where it’s easier to find universal properties. For example, we can reduce the number of spatial dimensions so that we’re considering 2+1-dimensional quantum gravity (3D gravity). Or we can investigate spacetimes that are negatively curved (anti-de Sitter space) as in the AdS/CFT correspondence. Or we can do BOTH! As in the paper that we just posted. The hope is that what’s learned in these limited situations will back-propagate insights towards reality.

The motivation for going to 2+1-dimensions is that gravity (general relativity) is much simpler here. This is explained eloquently in section II of Steve Carlip’s notes here. In 2+1-dimensions, there are no “local”/”gauge” degrees of freedom. This makes thinking about quantum aspects of these spacetimes much simpler.

The standard motivation for considering negatively curved spacetimes is that it puts us in the domain of AdS/CFT, which is the best understood model of quantum gravity. However, it’s worth pointing out that our results don’t rely on AdS/CFT. We consider negatively curved spacetimes (negatively curved Lorentzian manifolds) because they’re related to what mathematicians call hyperbolic manifolds (negatively curved Euclidean manifolds), and mathematicians know a great deal about these objects. It’s just a helpful coincidence that because we’re working with negatively curved manifolds we then get to unpack our statements in AdS/CFT.

Multiboundary wormholes

Finding solutions to Einstein’s equations of general relativity is a notoriously hard problem. Some of the more famous examples include: Minkowski space, de-Sitter space, anti-de Sitter space and Schwarzschild’s solution (which describes perfectly symmetrical and static black holes.) However, there’s a trick! Einstein’s equations only depend on the local curvature of spacetime while being insensitive to global topology (the number of boundaries and holes and such.) If M is a solution of Einstein’s equations and $\Gamma$ is a discrete subgroup of the isometry group of $M$, then the quotient space $M/\Gamma$ will also be a spacetime that solves Einstein’s equations! Here’s an example for intuition. Start with 2+1-dimensional Minkowski space, which is just a stack of flat planes indexed by time. One example of a “discrete subgroup of the isometry group” is the cyclic group generated by a single translation, say the translation along the x-axis by ten meters. Minkowski space quotiented by this group will also be a solution of Einstein’s equations, given as a stack of 10m diameter cylinders indexed by time.

Start with 2+1-dimensional Minkowski space which is just a stack of flat planes index by time. Think of the planes on the left hand side as being infinite. To “quotient” by a translation means to glue the green lines together which leaves a cylinder for every time slice. The figure on the right shows this cylinder universe which is also a solution to Einstein’s equations.

D+1-dimensional Anti-de Sitter space ($AdS_{d+1}$) is the maximally symmetric d+1-dimensional Lorentzian manifold with negative curvature. Our paper is about 3D gravity in negatively curved spacetimes so our starting point is $AdS_3$ which can be thought of as a stack of Poincare disks (or hyperbolic sheets) with the time dimension telling you which disk (sheet) you’re on. The isometry group of $AdS_3$ is a group called $SO(2,2)$ which in turn is isomorphic to the group $SL(2, R) \times SL(2, R)$. The group $SL(2,R) \times SL(2,R)$ isn’t a very common group but a single copy of $SL(2,R)$ is a very well-studied group. Discrete subgroups of it are called Fuchsian groups. Every element in the group should be thought of as a 2×2 matrix which corresponds to a Mobius transformation of the complex plane. The quotients that we obtain from these Fuchsian groups, or the larger isometry group yield a rich infinite family of new spacetimes, which are called multiboundary wormholes. Multiboundary wormholes have risen in importance over the last few years as powerful toy models when trying to understand how entanglement is dispersed near black holes (Ryu-Takayanagi conjecture) and for how the holographic dictionary works in terms of mapping operators in the boundary CFT to fields in the bulk (entanglement wedge reconstruction.)

Three dimensional AdS can be thought of as a stack of hyperboloids indexed by time. It’s convenient to use the Poincare disk model for the hyperboloids so that the entire spacetime can be pictured in a compact way. Despite how things appear, all of the triangles have the same “area”.

I now want to work through a few examples.

BTZ black hole: this is the simplest possible example. It’s obtained by quotienting $AdS_3$ by a cyclic group $\langle A \rangle$, generated by a single matrix $A \in SL(2,R)$ which for example could take the form $A = \begin{pmatrix} e^{\lambda} & 0 \\ 0 & e^{-\lambda} \end{pmatrix}$. The matrix A acts by fractional linear transformation on the complex plane, so in this case the point $z \in \mathbb{C}$ gets mapped to $z\mapsto (e^{\lambda}z + 0)/(0z + e^{-\lambda}) = e^{2\lambda} z$. In this case

Start with$AdS_3$as a stack of hyperbolic half planes indexed by time. A quotient by A means that each hyperbolic half plane gets quotiented. Quotienting a constant time slice by the map$z \mapsto e^{2\lambda}z$gives a surface that’s topologically a cylinder. Using the picture above this means you glue together the solid black curves. The green and red segments become two boundary regions. We call it the BTZ black hole because when you add “time” it becomes impossible to send a signal from the green boundary to the red boundary, or vica versa. The dotted line acts as an event horizon.

Three boundary wormhole:

There are many parameterizations that we can choose to obtain the three boundary wormhole. I’ll only show schematically how the gluings go. A nice reference with the details is this paper by Henry Maxfield.

This is a picture of a constant time slice of$AdS_3$quotiented by the A and B above. Each time slice is given as a copy of the hyperbolic half plane with the black arcs and green arcs glued together (by the maps A and B). These gluings yield a pair of pants surface. Each of the boundary regions are causally disconnected from the others. The dotted lines are black hole horizons that illustrate where the causal disconnection happens.

Torus wormhole:

It’s simpler to write down generators for the torus wormhole; but following along with the gluings is more complicated. To obtain the three boundary wormhole we quotient $AdS_3$ by the free group $\langle A, B \rangle$ where $A = \begin{pmatrix} e^{\lambda} & 0 \\ 0 & e^{-\lambda} \end{pmatrix}$ and $B = \begin{pmatrix} \cosh \lambda & \sinh \lambda \\ \sinh \lambda & \cosh \lambda \end{pmatrix}$. (Note that this is only one choice of generators, and a highly symmetrical one at that.)

This is a picture of a constant time slice of$AdS_3$quotiented by the A and B above. Each time slice is given as a copy of the hyperbolic half plane with the black arcs and green arcs glued together (by the maps A and B). These gluings yield what’s called the “torus wormhole”. Topologically it’s just a donut with a hole cut out. However, there’s a causal structure when you add time to the mix where the dotted lines act as a black hole horizon, so that a message sent from behind the horizon will never reach the boundary.

Lorentzian to Euclidean spacetimes

So far we have been talking about negatively curved Lorentzian manifolds. These are manifolds that have a notion of both “time” and “space.” The technical definition involves differential geometry and it is related to the signature of the metric. On the other hand, mathematicians know a great deal about negatively curved Euclidean manifolds. Euclidean manifolds only have a notion of “space” (so no time-like directions.) Given a multiboundary wormhole, which by definition, is a quotient of $AdS_3/\Gamma$ where $\Gamma$ is a discrete subgroup of Isom($AdS_3$), there’s a procedure to analytically continue this to a Euclidean hyperbolic manifold of the form $H^3/ \Gamma_E$ where $H^3$ is three dimensional hyperbolic space and $\Gamma_E$ is a discrete subgroup of the isometry group of $H^3$, which is $PSL(2, \mathbb{C})$. This analytic continuation procedure is well understood for time-symmetric spacetimes but it’s subtle for spacetimes that don’t have time-reversal symmetry. A discussion of this subtlety will be the topic of my next paper. To keep this blog post at a reasonable level of technical detail I’m going to need you to take it on a leap of faith that to every Lorentzian 3-manifold multiboundary wormhole there’s an associated Euclidean hyperbolic 3-manifold. Basically you need to believe that given a discrete subgroup $\Gamma$ of $SL(2, R) \times SL(2, R)$ there’s a procedure to obtain a discrete subgroup $\Gamma_E$ of $PSL(2, \mathbb{C})$. Discrete subgroups of $PSL(2, \mathbb{C})$ are called Kleinian groups and quotients of $H^3$ by groups of this form yield hyperbolic 3-manifolds. These Euclidean manifolds obtained by analytic continuation arise when studying the thermodynamics of these spacetimes or also when studying correlation functions; there’s a sense in which they’re physical.

TLDR: you start with a 2+1-d Lorentzian 3-manifold obtained as a quotient $AdS_3/\Gamma$and analytic continuation gives a Euclidean 3-manifold obtained as a quotient $H^3/\Gamma_E$ where $H^3$ is 3-dimensional hyperbolic space and $\Gamma_E$ is a discrete subgroup of $PSL(2,\mathbb{C})$ (Kleinian group.)

Limit sets:

Every Kleinian group $\Gamma_E = \langle A_1, \dots, A_g \rangle \subset PSL(2, \mathbb{C})$ has a fractal that’s naturally associated with it. The fractal is obtained by finding the fixed points of every possible combination of generators and their inverses. Moreover, there’s a beautiful theorem of Patterson, Sullivan, Bishop and Jones that says the smallest eigenvalue $\lambda_0$ of the spectrum of the Laplacian on the quotient Euclidean spacetime $H^3 / \Gamma_E$ is related to the Hausdorff dimension of this fractal (call it $D$) by the formula $\lambda_0 = D(2-D)$. This smallest eigenvalue controls a number of the quantities of interest for this spacetime but calculating it directly is usually intractable. However, McMullen proposed an algorithm to calculate the Hausdorff dimension of the relevant fractals so we can get at the spectrum efficiently, albeit indirectly.

This is a screen grab of Figure 2 from our paper. These are two examples of fractals that emerge when studying these spacetimes. Both of these particular fractals have a 3-fold symmetry. They have this symmetry because these particular spacetimes came from looking at something called “n=3 Renyi entropies”. The number q indexes a one complex dimensional family of spacetimes that have this 3-fold symmetry. These Kleinian groups each have two generators that are described in section 2.3 of our paper.

What we did

Our primary result is a generalization of the Hawking-Page phase transition for multiboundary wormholes. To understand the thermodynamics (from a 3d quantum gravity perspective) one starts with a fixed boundary Riemann surface and then looks at the contributions to the partition function from each of the ways to fill in the boundary (each of which is a hyperbolic 3-manifold). We showed that the expected dominant contributions, which are given by handlebodies, are unstable when the kinetic operator $(\nabla^2 - m^2)$ is negative, which happens whenever the Hausdorff dimension of the limit set of $\Gamma_E$ is greater than the lightest scalar field living in the bulk. One has to go pretty far down the quantum gravity rabbit hole (black hole) to understand why this is an interesting research direction to pursue, but at least anyone can appreciate the pretty pictures!

This entry was posted in Uncategorized by shaunmaguire. Bookmark the permalink.

I have a complicated existence. I’m a partner at GV (formerly Google Ventures) but also finishing my PhD at Caltech. It’s astonishing that they gave the keys to this blog to hooligans like myself.

## 4 THOUGHTS ON “THE MATH OF MULTIBOUNDARY WORMHOLES”

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From personal bias, your multiboundary black holes resemble a bronchial tree fractal.

In that same picture where the event horizons are represented by dotted lines, curious what your math shows at the cosmological horizons, the other causally disconnected place in our universe, in the sense that beyond which, like from inside black holes, photons could never reach back to us?

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Sean, old pal…
“Before mentioning how I met my collaborators”: did I miss this part or did you leave it out? I’ve heard your Afghanistan story before… and I find you and your life more interesting than your work 😉

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Sorry, Shaun, I see I somehow typed the wrong spelling of your name. I encourage you to do the same to me as fitting retribution.

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great post, tempted to re-blog it.

• Schrödinger in Space: An artist’s impression of research presented in Batygin (2018), MNRAS 475, 4. Propagation of waves through an astrophysical disk can be understood using Schrödinger’s equation – a cornerstone of quantum mechanics.
Credit: James Tuttle Keane, California Institute of Technology
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03/05/2018

# Massive Astrophysical Objects Governed by Subatomic Equation

The Schrödinger Equation makes an unlikely appearance at the astronomical scale

Quantum mechanics is the branch of physics governing the sometimes-strange behavior of the tiny particles that make up our universe. Equations describing the quantum world are generally confined to the subatomic realm—the mathematics relevant at very small scales is not relevant at larger scales, and vice versa. However, a surprising new discovery from a Caltech researcher suggests that the Schrödinger Equation—the fundamental equation of quantum mechanics—is remarkably useful in describing the long-term evolution of certain astronomical structures.

The work, done by Konstantin Batygin (MS ’10, PhD ’12), a Caltech assistant professor of planetary science and Van Nuys Page Scholar, is described in a paper appearing in the March 5 issue of Monthly Notices of the Royal Astronomical Society.

Massive astronomical objects are frequently encircled by groups of smaller objects that revolve around them, like the planets around the sun. For example, supermassive black holes are orbited by swarms of stars, which are themselves orbited by enormous amounts of rock, ice, and other space debris. Due to gravitational forces, these huge volumes of material form into flat, round disks. These disks, made up of countless individual particles orbiting en masse, can range from the size of the solar system to many light-years across.

Astrophysical disks of material generally do not retain simple circular shapes throughout their lifetimes. Instead, over millions of years, these disks slowly evolve to exhibit large-scale distortions, bending and warping like ripples on a pond. Exactly how these warps emerge and propagate has long puzzled astronomers, and even computer simulations have not offered a definitive answer, as the process is both complex and prohibitively expensive to model directly.

While teaching a Caltech course on planetary physics, Batygin (the theorist behind the proposed existence of Planet Nine) turned to an approximation scheme called perturbation theory to formulate a simple mathematical representation of disk evolution. This approximation, often used by astronomers, is based upon equations developed by the 18th-century mathematicians Joseph-Louis Lagrange and Pierre-Simon Laplace. Within the framework of these equations, the individual particles and pebbles on each particular orbital trajectory are mathematically smeared together. In this way, a disk can be modeled as a series of concentric wires that slowly exchange orbital angular momentum among one another.

As an analogy, in our own solar system one can imagine breaking each planet into pieces and spreading those pieces around the orbit the planet takes around the sun, such that the sun is encircled by a collection of massive rings that interact gravitationally. The vibrations of these rings mirror the actual planetary orbital evolution that unfolds over millions of years, making the approximation quite accurate.

Using this approximation to model disk evolution, however, had unexpected results.

“When we do this with all the material in a disk, we can get more and more meticulous, representing the disk as an ever-larger number of ever-thinner wires,” Batygin says. “Eventually, you can approximate the number of wires in the disk to be infinite, which allows you to mathematically blur them together into a continuum. When I did this, astonishingly, the Schrödinger Equation emerged in my calculations.”

The Schrödinger Equation is the foundation of quantum mechanics: It describes the non-intuitive behavior of systems at atomic and subatomic scales. One of these non-intuitive behaviors is that subatomic particles actually behave more like waves than like discrete particles—a phenomenon called wave-particle duality. Batygin’s work suggests that large-scale warps in astrophysical disks behave similarly to particles, and the propagation of warps within the disk material can be described by the same mathematics used to describe the behavior of a single quantum particle if it were bouncing back and forth between the inner and outer edges of the disk.

The Schrödinger Equation is well studied, and finding that such a quintessential equation is able to describe the long-term evolution of astrophysical disks should be useful for scientists who model such large-scale phenomena. Additionally, adds Batygin, it is intriguing that two seemingly unrelated branches of physics—those that represent the largest and the smallest of scales in nature—can be governed by similar mathematics.

“This discovery is surprising because the Schrödinger Equation is an unlikely formula to arise when looking at distances on the order of light-years,” says Batygin. “The equations that are relevant to subatomic physics are generally not relevant to massive, astronomical phenomena. Thus, I was fascinated to find a situation in which an equation that is typically used only for very small systems also works in describing very large systems.”

“Fundamentally, the Schrödinger Equation governs the evolution of wave-like disturbances.” says Batygin. “In a sense, the waves that represent the warps and lopsidedness of astrophysical disks are not too different from the waves on a vibrating string, which are themselves not too different from the motion of a quantum particle in a box. In retrospect, it seems like an obvious connection, but it’s exciting to begin to uncover the mathematical backbone behind this reciprocity.”

The paper is titled “Schrödinger Evolution of Self-Gravitating Disks.” Funding was provided by the David and Lucile Packard Foundation.

Written by Lori Dajose