Optical Clocks and Relativity

Optical Clocks and Relativity

According to Einstein's theory of relativity, space and time are not fixed concepts, but instead are relative to an observer and their frame of reference. In the so-called twin paradox, a twin sibling who travels on a fast-moving rocket ship returns home younger than the other twin, and this "time dilation" can be quantified by comparing the tick rates of identical clocks that accompany the traveler and the stationary observer. Another consequence of Einstein's theory is that clocks run more slowly near massive objects like Earth owing to their gravitational fields. For example, if two identical clocks are separated vertically by 1 km near the surface of Earth, the higher clock emits about three more second-ticks than the lower one in a million years. In the 24 Sep 2010 Science, Chou et al. demonstrated the effects of relativity at distances and timeframes more familiar to our daily lives using super-accurate optical atomic clocks, which exploit the fact that the electrons in an atom occupy "states" with distinct energies and can hop between two states by emitting or absorbing electromagnetic waves of a set frequency (see the Science NOW story by A. Cho). By comparing two such clocks connected by a 75-meter length of optical fiber, the team was able to detect relativistic time dilation due to velocities of several meters per second and, separately, due to a change in height of just 33 centimeters meters (listen to the related podcast interview with lead author Chin-wen Chou). The technique might be useful in geodesy (measuring the size and shape of the Earth), hydrology, and space-based tests of fundamental physics.

The Relativity of Wrong

1 Isaac Asimov I s a a c A s i m o v The Relativity of Wrong received a letter the other day. It was handwrit-ten in crabbed penmanship so that it was very diffi-cult to read. Nevertheless, I tried to make it out just in case it might prove to be important. In the first sentence, the writer told me he was majoring in En g lish literature, but felt he needed to teach me science. (I sighed a bit, for I knew very few En g lish Lit majors who are equipped to teach me science, but I am very aware of the vast state of my ignorance and I am prepared to learn as much as I can from anyone, so I read on.)It seemed that in one of my innumerable essays, I had expressed a certain gladness at living in a century in which we finally got the basis of the universe straight.I didn’t go into detail in the matter, but what I meant was that we now know the basic rules governing the universe, together with the gravitational inter-relationships of its gross components, as shown in the theory of relativity worked out between 1905 and 1916. We also know the basic rules governing the subatomic particles and their interrelationships, since these are very neatly described by the quantum theory worked out between 1900 and 1930. What’s more, we have found that the galaxies and clusters of galaxies are the basic units of the physical universe, as discovered between 1920 and 1930.1These are all twentieth- c entury discoveries, you see.The young specialist in En g lish Lit, having quoted me, went on to lecture me severely on the fact that in every century people have thought they under-stood the universe at last, and in every century they w ere proved to be wrong. It follows that the one thing we can say about our modern “knowledge” is that it is wrong. The young man then quoted with approval what Socrates had said on learning that the Delphic oracle had proclaimed him the wisest man in Greece.2 “If I am the wisest man,” said Socrates, “it is because I alone know that I know nothing.” The implication was that I was very foolish because I was under the impression I knew a great deal. My answer to him was, “John, when people thought the earth was flat, they w ere wrong. When people thought the earth was spherical, they w ere wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.”1. A lbert Einstein (1879–1955) announced the special theory of relativity in 1905 and developed the general theory of relativity over the next de c ade; physicist Maxwell Planck (1858–1947) and others developed quantum theory; astronomer Edwin Hubble (1889–1953) demonstrated the existence of external galaxies in 1924. 2. S ocrates (c. 470–399 b.c.e.), ancient Greek phi l os o p her; Delphic oracle or Pythia, priestess of the Temple of Apollo on Mount Parnassus.I Published in the Skeptical Inquirer (1989), the journal of the Committee for Scientific Investigation of Claims of the Paranormal (CSICOP), now the Committee for Skeptical Inquiry. 5

Introduction to General Relativity

Introduction to General Relativity – Handout Lin “Jimmie” Haipeng, Wang “Richie” Yunchong 2013.11.13 What is General Relativity? …the geometric theory of gravitation published by Albert Einstein in 1916 and the current description of gravitation in modern physics. Geometric means that the presence of mass “curves” spacetime like a trampoline and results in gravity. Why do we need it? War of Theories: 1905: Albert Einstein published his theory of special relativity reconciling Newton's laws of motion with electrodynamics. Special relativity changed physics’ basic frameworks like “Space” and “Time”. Quick Review of Special Relativity -Speed of Light does not change, anywhere, any way. o Time and Space are not absolute. -There is no absolute “fast” or “slow” or “at the same time”. o All rules of physics are the same in any inertial reference frame. o All inertial reference frames are equal. (You can’t distinguish between any one) Problems: VS Classical Physics - Time and Space are no longer absolute ^^ This resulted in a new framework for Physics. Existing theories like Newton’s Gravity Theory no longer worked. (Since mass changes, time and space are no longer absolute, etc.) Several physicists, including Einstein, searched for a theory that would reconcile Newton's law of gravity and special relativity. Newton’s Gravitational Model is failing ?Time and space are no longer absolute, mass isn’t either ?Half of what Newton’s Gravitational Model is using is failing ?Astrophysics says it doesn’t work out ?Light is deflecting? Time is passing differently due to Gravity? ?Newton isn’t saying it all With that, let’s follow the steps of Einstein for a basic understanding of GR 1 Equivalence Principle Special Relativity: You can’t distinguish between inertial reference frames General Relativity: You can't distinguish between ANY reference frames. “Roughly speaking, the principle states that a person in a free-falling elevator cannot tell that they are in free fall. Every experiment in such a free-falling environment has the same results as it would for an observer at rest or moving uniformly in deep space, far from all sources of gravity.” 2 Accelerating Reference Frames You experi ence acceleration (“Gravity”) in accelerating reference frames Such an additional force due to non-uniform relative motion of two reference frames is called a pseudo-force. 3 Gravity “acceleration” also causes time to go slower. Imagine a disk spinning. On the outer part, v is larger (v=wR) so time is slower there. Acceleration is larger, and according to equivalence principles – its gravity, so gravity causes slower time too. Imagine rays of light.

欧洲文化入门--10年真题

2010年10月高等教育自学考试北京市命题考试 欧洲文化入门试卷 第一部分选择题 (共40分2 points each) 1(The Romans conquered Greece in ( A(146 B(C( B(500 B(C( C(700 B(C( D(1200 B(C( 2(The playwright who contributed greatly to Greek tragic art was A(Sophocles B(Aristophanes C(Herodotus D(Homer 3(The greatest of Latin poets was A(Horace B(Virgil C(Homer D(Cicero 4(Daniel was taken prisoner to after the fall of Jerusalem. A(Egypt B(Persia C(Babylon D(Assyria 5(David was ( A(a Hebrew king B(the boy who killed Goliath C(the man who made Jerusalem the capital D(all of the above 6(In the formative period of feudalism, the bishops were themselves A(scholars B(hermits C(feudal lords D(knights 7(As a result of the Crusades，luxuries of the East poured into the West(They were spices( perfume(hand(woven carpets and ( A(tea B(Chinaware C(silk D(silverware 8(Martin Luther held that was the supreme authority( A(the Church B(the Bible C(the Pope D(Jesus 9(Ophelia is a character in Shakespeare’s ( A(Hamlet B(Othello C(Macbeth D(Merchant of Venice 10(The Reformation shattered Medieval Church’s stifling control over man(thus paving the

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比较PageRank算法和HITS算法的优缺点

题目：请比较PageRank算法和HITS算法的优缺点，除此之外，请再介绍2种用于搜索引擎检索结果的排序算法，并举例说明。 答： 1998年，Sergey Brin和Lawrence Page[1]提出了PageRank算法。该算法基于“从许多优质的网页链接过来的网页，必定还是优质网页”的回归关系，来判定网页的重要性。该算法认为从网页A导向网页B的链接可以看作是页面A对页面B的支持投票，根据这个投票数来判断页面的重要性。当然，不仅仅只看投票数，还要对投票的页面进行重要性分析，越是重要的页面所投票的评价也就越高。根据这样的分析，得到了高评价的重要页面会被给予较高的PageRank值，在检索结果内的名次也会提高。PageRank是基于对“使用复杂的算法而得到的链接构造”的分析，从而得出的各网页本身的特性。 HITS 算法是由康奈尔大学( Cornell University ) 的JonKleinberg 博士于1998 年首先提出。Kleinberg认为既然搜索是开始于用户的检索提问，那么每个页面的重要性也就依赖于用户的检索提问。他将用户检索提问分为如下三种：特指主题检索提问（specific queries，也称窄主题检索提问）、泛指主题检索提问（Broad-topic queries，也称宽主题检索提问）和相似网页检索提问（Similar-page queries）。HITS 算法专注于改善泛指主题检索的结果。 Kleinberg将网页（或网站）分为两类，即hubs和authorities，而且每个页面也有两个级别，即hubs（中心级别）和authorities（权威级别）。Authorities 是具有较高价值的网页，依赖于指向它的页面；hubs为指向较多authorities的网页，依赖于它指向的页面。HITS算法的目标就是通过迭代计算得到针对某个检索提问的排名最高的authority的网页。 通常HITS算法是作用在一定范围的，例如一个以程序开发为主题的网页，指向另一个以程序开发为主题的网页，则另一个网页的重要性就可能比较高，但是指向另一个购物类的网页则不一定。在限定范围之后根据网页的出度和入度建立一个矩阵，通过矩阵的迭代运算和定义收敛的阈值不断对两个向量authority 和hub值进行更新直至收敛。 从上面的分析可见，PageRank算法和HITS算法都是基于链接分析的搜索引擎排序算法，并且在算法中两者都利用了特征向量作为理论基础和收敛性依据。

A Note on Aryabhata’s Principle of Relativity

A Note on Aryabhata’s Principle of Relativity Abhishek Parakh Abstract: This paper presents the principle of relativity of motion as described in Aryabhata’s text Aryabhatiya. This principle is likely to have been instrumental in the framing of Aryabhata’s theory that the earth rotated on its axis and, therefore, it has played a very important role in the history of astronomy. 1Introduction It is not generally known that the first clear description of relativity was provided by Aryabhata [1], the great Indian astronomer, who was born in 476 CE. In this note, we present the relevant section from Gola-pada (Astronomical Section) in his book Aryabhatiya, which proves that Aryabhata was fully aware of the relativity of motion. Aryabhata, occupies an important place in the history of mathematics and astronomy. He took the earth to rotate on its axis and he gave planet periods with respect to the sun. For some recent papers on Aryabhata’s work, see [2-7], and for books, see [8-10]. In [3], Aryabhata’s ideas related to the size of the planetary system are discussed, and in [4], the origin of his planetary parameters is discussed. Thurston, in his essay [9], summarizes: “Not only did Aryabhata believe that the earth rotates, but there are glimmerings in his system (and other similar Indian systems) of a possible underlying theory in which the earth (and the planets) orbits the sun, rather than the sun orbiting the earth.” In Gola-pada, Aryabhata presents 50 shlokas (stanzas) that deal with the motion of the sun, moon and the planets. His text also describes the motion of the celestial sphere as seen by those on the equator and by those on the north and south poles; and gives rules relating to the various problems of spherical astronomy. It also deals with the calculation and graphical representation of the eclipses and the visibility of the planets. This article discusses his principle of relativity, and we argue that it must have helped him to reach the conclusion that the earth rotated on its axis. 2Relativity in Aryabhatiya The following shloka 9(stanza 9), from Gola-pada (Astronomical Section) of Aryabhatiya, presents his principle of relativity in a cryptic form: ?????????? ???: ?????????????????? ?? ? ?????? ???? ? ?????????????? ???????? ?? ? ??

The cultural relativity of organizational practices and theories

The Cultural Relativity of Organizational Practices and Theories Author(s): Geert Hofstede Source: Journal of International Business Studies, Vol. 14, No. 2, Special Issue on Cross-Cultural Management (Autumn, 1983), pp. 75-89 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . https://www.wendangku.net/doc/4c7543963.html,/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@https://www.wendangku.net/doc/4c7543963.html,. Palgrave Macmillan Journals is collaborating with JSTOR to digitize, preserve and extend access to Journal of International Business Studies. https://www.wendangku.net/doc/4c7543963.html,

general theory of relativity

XVIII. Special and General Principle of Relativity 1 THE BASAL principle, which was the pivot of all our previous considerations, was the special principle of relativity, i.e. the principle of the physical relativity of all uniform motion. Let us once more analyse its meaning carefully. It was at all times clear that, from the point of view of the idea it 2 conveys to us, every motion must only be considered as a relative motion. Returning to the illustration we have frequently used of the embankment and the railway carriage, we can express the fact of the motion here taking place in the following two forms, both of which are equally justifiable: a.The carriage is in motion relative to the embankment. b.The embankment is in motion relative to the carriage. 3 In (a) the embankment, in (b) the carriage, serves as the body of reference in our statement of the motion taking place. If it is simply a question of detecting or of describing the motion involved, it is in principle immaterial to what reference-body we refer the motion. As already mentioned, this is self-evident, but it must not be confused with the much more comprehensive statement called “the principle

萨丕尔-沃尔夫假说

萨丕尔－沃尔夫假设 主要内容 美国人萨丕尔及其弟子沃尔夫提出的有关语言与思维关系的假设是这个领域里至今为止最具争议的理论。 沃尔夫首先提出，所有高层次的思维都倚赖于语言。说得更明白一些，就是语言决定思维，这就是语言决定论这一强假设。由于语言在很多方面都有不同，沃尔夫还认为，使用不同语言的人对世界的感受和体验也不同，也就是说与他们的语言背景有关，这就是语言相对论。 Linguistic relativity stems from a question about the relationship between language and thought, about whether one's language determines the way one thinks. This question has given birth to a wide array of research within a variety of different disciplines, especially anthropology, cognitive science, linguistics, and philosophy. Among the most popular and controversial theories in this area of scholarly work is the theory of linguistic relativity (also known as the Sapir–Whorf hypothesis). An often cited "strong version" of the claim, first given by Lenneberg in 1953 proposes that the structure of our language in some way determines the way we perceive the world. A weaker version of this claim posits that language structure influences the world view adopted by the speakers of a given language, but does not determine it.[1] 由萨丕尔－沃尔夫假设的这种强假设可以得出这样的结论：根本没有真正的翻译，学习者也不可能学会另一种文化区的语言，除非他抛弃了他自己的思维模式，并习得说目的语的本族语者的思维模式。 词和意义 人们普遍接受了这一点：语言中的词汇只是一些无意义的标签，语言使用者用它们来引起情绪上的或行为上的反应，传递信息或引导听者的注意力。词和短语的意义在很

pagerank算法实验报告

PageRank算法实验报告 一、算法介绍 PageRank是Google专有的算法，用于衡量特定网页相对于搜索引擎索引中的其他网页而言的重要程度。它由Larry Page 和Sergey Brin在20世纪90年代后期发明。PageRank实现了将链接价值概念作为排名因素。 PageRank的核心思想有2点： 1.如果一个网页被很多其他网页链接到的话说明这个网页比较重要，也就是pagerank值会相对较高； 2.如果一个pagerank值很高的网页链接到一个其他的网页，那么被链接到的网页的pagerank值会相应地因此而提高。 若页面表示有向图的顶点，有向边表示链接，w(i,j)=1表示页面i存在指向页面j的超链接，否则w(i,j)=0。如果页面A存在指向其他页面的超链接，就将A 的PageRank的份额平均地分给其所指向的所有页面，一次类推。虽然PageRank 会一直传递，但总的来说PageRank的计算是收敛的。 实际应用中可以采用幂法来计算PageRank，假如总共有m个页面，计算如公式所示： r=A*x 其中A=d*P+（1-d)*(e*e'/m) r表示当前迭代后的PageRank，它是一个m行的列向量,x是所有页面的PageRank初始值。 P由有向图的邻接矩阵变化而来，P'为邻接矩阵的每个元素除以每行元素之和得到。 e是m行的元素都为1的列向量。 二、算法代码实现

三、心得体会 在完成算法的过程中，我有以下几点体会： 1、在动手实现的过程中，先将算法的思想和思路理解清楚，对于后续动手实现 有很大帮助。 2、在实现之前，对于每步要做什么要有概念，然后对于不会实现的部分代码先 查找相应的用法，在进行整体编写。 3、在实现算法后，在寻找数据验证算法的过程中比较困难。作为初学者，对于 数据量大的数据的处理存在难度，但数据量的数据很难寻找，所以难以进行实例分析。

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