电信运营商封杀宽带1拖N引发用户抗议

几台电脑合用一条线上网会带来网络速度不稳定、容易掉线等问题，同时给服务器带来了更重的负担。

最近，一些地方出现了电信运营商封杀宽带用户多台电脑共享一条ADSL线路上网的事件，在社会上引发了热烈的讨论。那么，运营商到底应不应该封杀ADSL“1拖N”用户呢？对于宽带上网“1拖N”问题应该如何看待和处理呢？

电信公司的网络负责人透露，电信和用户在签署宽带服务协议时已经明确告知，未经电信公司书面同意，用户不得将电信提供的宽带接入服务提供给第三方使用。通过分析检查同一IP地址的数据包是否有多个MAC地址，就可以判定用户是不是共享上网，这是可监控的。监控的目的是防止黑网吧和一些出租屋业主非法串机、多家合用。几台电脑合用一条线上网会带来网络速度不稳定、容易掉线等问题，同时给服务器带来了更重的负担。

用户方则认为，上网费用太贵，才会出此下策，多接几台电脑也没多占流量。而从法律的角度来说，就合同本身而言，用户超出了“一拖二”范围，确实违反了消费合同，电信封杀亦是有所依据的。但一些法律人士同时认为，合同本身制订得却未必合理。家庭用户从没有电脑到一台电脑到多台电脑，是社会发展的必然趋势，电信应该随时调整服务范围，根据用户增长的需求提供更好的服务，而不是去抑制用户的需求。电信应该充分考虑家庭用户的消费承受能力。

笔者认为，电信运营商应该正确地看待并处理好宽带上网共享问题，否则会造成宽带用户的大量流失。宽带上网共享从一个侧面反映了我国宽带上网的需求大量增加，这对运营商来说是好的方面。截至今年7月，我国网民总人数已达1.62亿，仅次于美国2.11亿的网民规模，位居世界第二。我国网民规模正跨入新一轮快速增长阶段。与2006年年末相比，半年新增网民2500万。相当于半年内，每1分钟就新增接近100个网民。1.62亿网民中，宽带网民(含专线)已经达到1.22亿，半年增加了1800万人。宽带上网需求的激增给电信企业带来了更宽广的业务发展空间。

而从资费角度考虑，我国的互联网上网费用确实偏高，这应该是“1拖N”现象产生的一个重要原因。世界银行今年5月发布报告显示，尽管中国拥有世界第二大互联网和宽带市场，但目前中国互联网使用价格占收入水平的比重仍然偏高。我国网民平均每月实际花费的上网费用为83.5元，发达国家互联网使用价格不到其收入水平的1%，而中国的比例超过10%，是发达国家的10倍，也高于东亚及太平洋地区约8%的平均水平。如果按绝对的货币价格计算，美国人只要以中国人1/12.88的价格就能买回相同的信息量。

但就目前而言，我国固网运营商收入增长乏力，主要靠宽带的发展带动营收上升，大幅降低上网费用不合时宜。电信企业可以通过大力发展宽带应用，增加网络带给用户的价值，使用户对付出的钞票觉得有所值；电信公司可在节假日进行多样化的营销，在不断扩大宽带用户规模的基础上，逐渐降低上网费，如此才能驱动用户主动装宽带。另外，电信企业也可大力发展宽带新业务，比如“我的e家”，让用户家里的两台或三台电脑共享一条ADSL线路，并添加一些增值服务，引导用户进入新业务的消费中来。对于恶意进行“1拖N”上网，不断发展下家组成小网吧牟利的商户，应该坚决打击，促进我国宽带产业健康发展。(

相对论

Principle of relativity
相对论是关于时空和引力的基本理论，主要由爱因斯坦(Albert Einstein)创立，分为狭义相对论(特殊相对论)和广义相对论(一般相对论)。相对论的基本假设是光速不变原理，相对性原理和等效原理。相对论和量子力学是现代物理学的两大基本支柱。奠定了经典物理学基础的经典力学，不适用于高速运动的物体和微观条件下的物体。相对论解决了高速运动问题；量子力学解决了微观亚原子条件下的问题。相对论极大的改变了人类对宇宙和自然的“常识性”观念，提出了“同时的相对性”，“四维时空”“弯曲空间”等全新的概念。

【相对论的提出过程】

除了量子理论以外，1905年刚刚得到博士学位的爱因斯坦发表的一篇题为《论动体的电动力学》的文章引发了二十世纪物理学的另一场革命。文章研究的是物体的运动对光学现象的影响，这是当时经典物理学面对的另一个难题。

十九世纪中叶，麦克斯韦建立了电磁场理论，并预言了以光速C传播的电磁波的存在。到十九世纪末，实验完全证实了麦克斯韦理论。电磁波是什么？它的传播速度C是对谁而言的呢？当时流行的看法是整个宇宙空间充满一种特殊物质叫做“以太”，电磁波是以太振动的传播。但人们发现，这是一个充满矛盾的理论。如果认为地球是在一个静止的以太中运动，那么根据速度迭加原理，在地球上沿不同方向传播的光的速度必定不一样，但是实验否定了这个结论。如果认为以太被地球带着走，又明显与天文学上的一些观测结果不符。

1887年迈克尔逊和莫雷利用光的干涉现象进行了非常精确的测量，仍没有发现地球有相对于以太的任何运动。对此，洛仑兹(H．A．Lorentz)提出了一个假设，认为一切在以太中运动的物体都要沿运动方向收缩。由此他证明了，即使地球相对以太有运动，迈克尔逊也不可能发现它。爱因斯坦从完全不同的思路研究了这一问题。他指出，只要摒弃牛顿所确立的绝对空间和绝对时间的概念，一切困难都可以解决，根本不需要什么以太。

爱因斯坦提出了两条基本原理作为讨论运动物体光学现象的基础。第一个叫做相对性原理。它是说：如果坐标系K'相对于坐标系K作匀速运动而没有转动，则相对于这两个坐标系所做的任何物理实验，都不可能区分哪个是坐标系K，哪个是坐标系K′。第二个原理叫光速不变原理，它是说光（在真空中）的速度c是恒定的，它不依赖于发光物体的运动速度。

从表面上看，光速不变似乎与相对性原理冲突。因为按照经典力学速度的合成法则，对于K′和K这两个做相对匀速运动的坐标系，光速应该不一样。爱因斯坦认为，要承认这两个原理没有抵触，就必须重新分析时间与空间的物理概念。

经典力学中的速度合成法则实际依赖于如下两个假设：

1．两个事件发生的时间间隔与测量时间所用的钟的运动状态没有关系；

2．两点的空间距离与测量距离所用的尺的运动状态无关。

爱因斯坦发现，如果承认光速不变原理与相对性原理是相容的，那么这两条假设都必须摒弃。这时，对一个钟是同时发生的事件，对另一个钟不一定是同时的，同时性有了相对性。在两个有相对运动的坐标系中，测量两个特定点之间的距离得到的数值不再相等。距离也有了相对性。

如果设K坐标系中一个事件可以用三个空间坐标x、y、z和一个时间坐标t来确定，而K′坐标系中同一个事件由x′、y′、z′和t′来确定，则爱因斯坦发现，x′、y′、z′和t′可以通过一组方程由x、y、z和t求出来。两个坐标系的相对运动速度和光速c是方程的唯一参数。这个方程最早是由洛仑兹得到的，所以称为洛仑兹变换。

利用洛仑兹变换很容易证明，钟会因为运动而变慢，尺在运动时要比静止时短，速度的相加满足一个新的法则。相对性原理也被表达为一个明确的数学条件，即在洛仑兹变换下，带撇的空时变量x'、y'、z'、t'将代替空时变量x、y、z、t，而任何自然定律的表达式仍取与原来完全相同的形式。人们称之为普遍的自然定律对于洛仑兹变换是协变的。这一点在我们探索普遍的自然定律方面具有非常重要的作用。

此外，在经典物理学中，时间是绝对的。它一直充当着不同于三个空间坐标的独立角色。爱因斯坦的相对论把时间与空间联系起来了。认为物理的现实世界是各个事件组成的，每个事件由四个数来描述。这四个数就是它的时空坐标t和x、y、z，它们构成一个四维的连续空间，通常称为闵可夫斯基四维空间。在相对论中，用四维方式来考察物理的现实世界是很自然的。狭义相对论导致的另一个重要的结果是关于质量和能量的关系。在爱因斯坦以前，物理学家一直认为质量和能量是截然不同的，它们是分别守恒的量。爱因斯坦发现，在相对论中质量与能量密不可分，两个守恒定律结合为一个定律。他给出了一个著名的质量-能量公式：E＝mc^2，其中c为光速。于是质量可以看作是它的能量的量度。计算表明，微小的质量蕴涵着巨大的能量。这个奇妙的公式为人类获取巨大的能量，制造原子弹和氢弹以及利用原子能发电等奠定了理论基础。

对爱因斯坦引入的这些全新的概念，大部分物理学家，其中包括相对论变换关系的奠基人洛仑兹，都觉得难以接受。旧的思想方法的障碍，使这一新的物理理论直到一代人之后才为广大物理学家所熟悉，就连瑞典皇家科学院，1922年把诺贝尔奖金授予爱因斯坦时，也只是说“由于他对理论物理学的贡献，更由于他发现了光电效应的定律。”对于相对论只字未提。

爱因斯坦于1915年进一步建立起了广义相对论。狭义相对性原理还仅限于两个相对做匀速运动的坐标系，而在广义相对论性原理中匀速运动这个限制被取消了。他引入了一个等效原理，认为我们不可能区分引力效应和非匀速运动，即非匀速运动和引力是等效的。他进而分析了光线在靠近一个行量附近穿过时会受到引力而弯折的现象，认为引力的概念本身完全不必要。可以认为行星的质量使它附近的空间变成弯曲，光线走的是最短程线。基于这些讨论，爱因斯坦导出了一组方程，它们可以确定由物质的存在而产生的弯曲空间几何。利用这个方程，爱因斯坦计算了水星近日点的位移量，与实验观测值完全一致，解决了一个长期解释不了的困难问题，这使爱因斯坦激动不已。他在写给埃伦菲斯特的信中这样写道：“……方程给出了近日点的正确数值，你可以想象我有多高兴！有好几天，我高兴得不知怎样才好。”

1915年11月25日，爱因斯坦把题为“万有引力方程”的论文提交给了柏林的普鲁士科学院，完整地论述了广义相对论。在这篇文章中他不仅解释了天文观测中发现的水星轨道近日点移动之谜，而且还预言：星光经过太阳会发生偏折，偏折角度相当于牛顿理论所预言的数值的两倍。第一次世界大战延误了对这个数值的测定。1919年5月25日的日全食给人们提供了大战后的第一次观测机会。英国人爱丁顿奔赴非洲西海岸的普林西比岛，进行了这一观测。11月6日，汤姆逊在英国皇家学会和皇家天文学会联席会议上郑重宣布：得到证实的是爱因斯坦而不是牛顿所预言的结果。他称赞道“这是人类思想史上最伟大的成就之一。爱因斯坦发现的不是一个小岛，而是整整一个科学思想的新大陆。”泰晤士报以“科学上的革命”为题对这一重大新闻做了报道。消息传遍全世界，爱因斯坦成了举世瞩目的名人。广义相对论也被提高到神话般受人敬仰的宝座。

从那时以来，人们对广义相对论的实验检验表现出越来越浓厚的兴趣。但由于太阳系内部引力场非常弱，引力效应本身就非常小，广义相对论的理论结果与牛顿引力理论的偏离很小，观测非常困难。七十年代以来，由于射电天文学的进展，观测的距离远远突破了太阳系，观测的精度随之大大提高。特别是1974年9月由麻省理工学院的泰勒和他的学生惠斯勒，用305米口径的大型射电望远镜进行观测时，发现了脉冲双星，它是一个中子星和它的伴星在引力作用下相互绕行，周期只有0.323天，它的表面的引力比太阳表面强十万倍，是地球上甚至太阳系内不可能获得的检验引力理论的实验室。经过长达十余年的观测，他们得到了与广义相对论的预言符合得非常好的结果。由于这一重大贡献，泰勒和惠斯勒获得了1993年诺贝尔物理奖。


【狭义相对论】

马赫和休谟的哲学对爱因斯坦影响很大。马赫认为时间和空间的量度与物质运动有关。时空的观念是通过经验形成的。绝对时空无论依据什么经验也不能把握。休谟更具体的说：空间和广延不是别的，而是按一定次序分布的可见的对象充满空间。而时间总是又能够变化的对象的可觉察的变化而发现的。1905年爱因斯坦指出，迈克尔逊和莫雷实验实际上说明关于“以太”的整个概念是多余的，光速是不变的。而牛顿的绝对时空观念是错误的。不存在绝对静止的参照物，时间测量也是随参照系不同而不同的。他用光速不变和相对性原理提出了洛仑兹变换。创立了狭义相对论。

狭义相对论是建立在四维时空观上的一个理论，因此要弄清相对论的内容，要先对相对论的时空观有个大体了解。在数学上有各种多维空间，但目前为止，我们认识的物理世界只是四维，即三维空间加一维时间。现代微观物理学提到的高维空间是另一层意思，只有数学意义，在此不做讨论。

四维时空是构成真实世界的最低维度，我们的世界恰好是四维，至于高维真实空间，至少现在我们还无法感知。我在一个帖子上说过一个例子，一把尺子在三维空间里（不含时间）转动，其长度不变，但旋转它时，它的各坐标值均发生了变化，且坐标之间是有联系的。四维时空的意义就是时间是第四维坐标，它与空间坐标是有联系的，也就是说时空是统一的，不可分割的整体，它们是一种“此消彼长”的关系。

四维时空不仅限于此，由质能关系知，质量和能量实际是一回事，质量（或能量）并不是独立的，而是与运动状态相关的，比如速度越大，质量越大。在四维时空里，质量（或能量）实际是四维动量的第四维分量，动量是描述物质运动的量，因此质量与运动状态有关就是理所当然的了。在四维时空里，动量和能量实现了统一，称为能量动量四矢。另外在四维时空里还定义了四维速度，四维加速度，四维力，电磁场方程组的四维形式等。值得一提的是，电磁场方程组的四维形式更加完美，完全统一了电和磁，电场和磁场用一个统一的电磁场张量来描述。四维时空的物理定律比三维定律要完美的多，这说明我们的世界的确是四维的。可以说至少它比牛顿力学要完美的多。至少由它的完美性，我们不能对它妄加怀疑。

相对论中，时间与空间构成了一个不可分割的整体——四维时空，能量与动量也构成了一个不可分割的整体——四维动量。这说明自然界一些看似毫不相干的量之间可能存在深刻的联系。在今后论及广义相对论时我们还会看到，时空与能量动量四矢之间也存在着深刻的联系。

狭义相对论基本原理

物质在相互作用中作永恒的运动，没有不运动的物质，也没有无物质的运动，由于物质是在相互联系，相互作用中运动的，因此，必须在物质的相互关系中描述运动，而不可能孤立的描述运动。也就是说，运动必须有一个参考物，这个参考物就是参考系。

伽利略曾经指出，运动的船与静止的船上的运动不可区分，也就是说，当你在封闭的船舱里，与外界完全隔绝，那么即使你拥有最发达的头脑，最先进的仪器，也无从感知你的船是匀速运动，还是静止。更无从感知速度的大小，因为没有参考。比如，我们不知道我们整个宇宙的整体运动状态，因为宇宙是封闭的。爱因斯坦将其引用，作为狭义相对论的第一个基本原理：狭义相对性原理。其内容是：惯性系之间完全等价，不可区分。

著名的麦克尔逊·莫雷实验彻底否定了光的以太学说，得出了光与参考系无关的结论。也就是说，无论你站在地上，还是站在飞奔的火车上，测得的光速都是一样的。这就是狭义相对论的第二个基本原理，光速不变原理。

由这两条基本原理可以直接推导出相对论的坐标变换式，速度变换式等所有的狭义相对论内容。比如速度变幻，与传统的法则相矛盾，但实践证明是正确的，比如一辆火车速度是10m/s，一个人在车上相对车的速度也是10m/s，地面上的人看到车上的人的速度不是20m/s，而是(20-10^(-15))m/s左右。在通常情况下，这种相对论效应完全可以忽略，但在接近光速时，这种效应明显增大，比如，火车速度是0.99倍光速，人的速度也是0.99倍光速，那么地面观测者的结论不是1.98倍光速，而是0.999949倍光速。车上的人看到后面的射来的光也没有变慢，对他来说也是光速。因此，从这个意义上说，光速是不可超越的，因为无论在那个参考系，光速都是不变的。速度变换已经被粒子物理学的无数实验证明，是无可挑剔的。正因为光的这一独特性质，因此被选为四维时空的唯一标尺。

狭义相对论效应

根据狭义相对性原理，惯性系是完全等价的，因此，在同一个惯性系中，存在统一的时间，称为同时性，而相对论证明，在不同的惯性系中，却没有统一的同时性，也就是两个事件(时空点)在一个关性系内同时，在另一个惯性系内就可能不同时，这就是同时的相对性，在惯性系中，同一物理过程的时间进程是完全相同的，如果用同一物理过程来度量时间，就可在整个惯性系中得到统一的时间。在今后的广义相对论中可以知道，非惯性系中，时空是不均匀的，也就是说，在同一非惯性系中，没有统一的时间，因此不能建立统一的同时性。

相对论导出了不同惯性系之间时间进度的关系，发现运动的惯性系时间进度慢，这就是所谓的钟慢效应。可以通俗的理解为，运动的钟比静止的钟走得慢，而且，运动速度越快，钟走的越慢，接近光速时，钟就几乎停止了。

尺子的长度就是在一惯性系中"同时"得到的两个端点的坐标值的差。由于"同时"的相对性，不同惯性系中测量的长度也不同。相对论证明，在尺子长度方向上运动的尺子比静止的尺子短，这就是所谓的尺缩效应，当速度接近光速时，尺子缩成一个点。

由以上陈述可知，钟慢和尺缩的原理就是时间进度有相对性。也就是说，时间进度与参考系有关。这就从根本上否定了牛顿的绝对时空观，相对论认为，绝对时间是不存在的，然而时间仍是个客观量。比如在下期将讨论的双生子理想实验中，哥哥乘飞船回来后是15岁，弟弟可能已经是45岁了，说明时间是相对的，但哥哥的确是活了15年，弟弟也的确认为自己活了45年，这是与参考系无关的，时间又是"绝对的"。这说明，不论物体运动状态如何，它本身所经历的时间是一个客观量，是绝对的，这称为固有时。也就是说，无论你以什么形式运动，你都认为你喝咖啡的速度很正常，你的生活规律都没有被打乱，但别人可能看到你喝咖啡用了100年，而从放下杯子到寿终正寝只用了一秒钟。

时钟佯谬或双生子佯谬

相对论诞生后，曾经有一个令人极感兴趣的疑难问题---双生子佯谬。一对双生子A和B，A在地球上，B乘火箭去做星际旅行，经过漫长岁月返回地球。爱因斯坦由相对论断言，二人经历的时间不同，重逢时B将比A年轻。许多人有疑问，认为A看B在运动，B看A也在运动，为什么不能是A比B年轻呢?由于地球可近似为惯性系，B要经历加速与减速过程，是变加速运动参考系，真正讨论起来非常复杂，因此这个爱因斯坦早已讨论清楚的问题被许多人误认为相对论是自相矛盾的理论。如果用时空图和世界线的概念讨论此问题就简便多了，只是要用到许多数学知识和公式。在此只是用语言来描述一种最简单的情形。不过只用语言无法更详细说明细节，有兴趣的请参考一些相对论书籍。我们的结论是，无论在那个参考系中，B都比A年轻。

为使问题简化，只讨论这种情形，火箭经过极短时间加速到亚光速，飞行一段时间后，用极短时间掉头，又飞行一段时间，用极短时间减速与地球相遇。这样处理的目的是略去加速和减速造成的影响。在地球参考系中很好讨论，火箭始终是动钟，重逢时B比A年轻。在火箭参考系内，地球在匀速过程中是动钟，时间进程比火箭内慢，但最关键的地方是火箭掉头的过程。在掉头过程中，地球由火箭后方很远的地方经过极短的时间划过半个圆周，到达火箭的前方很远的地方。这是一个"超光速"过程。只是这种超光速与相对论并不矛盾，这种"超光速"并不能传递任何信息，不是真正意义上的超光速。如果没有这个掉头过程，火箭与地球就不能相遇，由于不同的参考系没有统一的时间，因此无法比较他们的年龄，只有在他们相遇时才可以比较。火箭掉头后，B不能直接接受A的信息，因为信息传递需要时间。B看到的实际过程是在掉头过程中，地球的时间进度猛地加快了。在B看来，A现实比B年轻，接着在掉头时迅速衰老，返航时，A又比自己衰老的慢了。重逢时，自己仍比A年轻。也就是说，相对论不存在逻辑上的矛盾。

狭义相对论小结

相对论要求物理定律要在坐标变换(洛伦兹变化)下保持不变。经典电磁理论可以不加修改而纳入相对论框架，而牛顿力学只在伽利略变换中形势不变，在洛伦兹变换下原本简洁的形式变得极为复杂。因此经典力学与要进行修改，修改后的力学体系在洛伦兹变换下形势不变，称为相对论力学。

狭义相对论建立以后，对物理学起到了巨大的推动作用。并且深入到量子力学的范围，成为研究高速粒子不可缺少的理论，而且取得了丰硕的成果。然而在成功的背后，却有两个遗留下的原则性问题没有解决。第一个是惯性系所引起的困难。抛弃了绝对时空后，惯性系成了无法定义的概念。我们可以说惯性系是惯性定律在其中成立的参考系。惯性定律实质一个不受外力的物体保持静止或匀速直线运动的状态。然而"不受外力"是什么意思?只能说，不受外力是指一个物体能在惯性系中静止或匀速直线运动。这样，惯性系的定义就陷入了逻辑循环，这样的定义是无用的。我们总能找到非常近似的惯性系，但宇宙中却不存在真正的惯性系，整个理论如同建筑在沙滩上一般。第二个是万有引力引起的困难。万有引力定律与绝对时空紧密相连，必须修正，但将其修改为洛伦兹变换下形势不变的任何企图都失败了，万有引力无法纳入狭义相对论的框架。当时物理界只发现了万有引力和电磁力两种力，其中一种就冒出来捣乱，情况当然不会令人满意。

爱因斯坦只用了几个星期就建立起了狭义相对论，然而为解决这两个困难，建立起广义相对论却用了整整十年时间。为解决第一个问题，爱因斯坦干脆取消了惯性系在理论中的特殊地位，把相对性原理推广到非惯性系。因此第一个问题转化为非惯性系的时空结构问题。在非惯性系中遇到的第一只拦路虎就是惯性力。在深入研究了惯性力后，提出了著名的等性原理，发现参考系问题有可能和引力问题一并解决。几经曲折，爱因斯坦终于建立了完整的广义相对论。广义相对论让所有物理学家大吃一惊，引力远比想象中的复杂的多。至今为止爱因斯坦的场方程也只得到了为数不多的几个确定解。它那优美的数学形式至今令物理学家们叹为观止。就在广义相对论取得巨大成就的同时，由哥本哈根学派创立并发展的量子力学也取得了重大突破。然而物理学家们很快发现，两大理论并不相容，至少有一个需要修改。于是引发了那场著名的论战：爱因斯坦VS哥本哈根学派。直到现在争论还没有停止，只是越来越多的物理学家更倾向量子理论。爱因斯坦为解决这一问题耗费了后半生三十年光阴却一无所获。不过他的工作为物理学家们指明了方向：建立包含四种作用力的超统一理论。目前学术界公认的最有希望的候选者是超弦理论与超膜理论。

【广义相对论】

相对论问世，人们看到的结论就是：四维弯曲时空，有限无边宇宙，引力波，引力透镜，大爆炸宇宙学说，以及二十一世纪的主旋律--黑洞等等。这一切来的都太突然，让人们觉得相对论神秘莫测，因此在相对论问世头几年，一些人扬言"全世界只有十二个人懂相对论"。甚至有人说"全世界只有两个半人懂相对论"。更有甚者将相对论与"通灵术"，"招魂术"之类相提并论。其实相对论并不神秘，它是最脚踏实地的理论，是经历了千百次实践检验的真理，更不是高不可攀的。

相对论应用的几何学并不是普通的欧几里得几何，而是黎曼几何。相信很多人都知道非欧几何，它分为罗氏几何与黎氏几何两种。黎曼从更高的角度统一了三种几何，称为黎曼几何。在非欧几何里，有很多奇怪的结论。三角形内角和不是180度，圆周率也不是3.14等等。因此在刚出台时，倍受嘲讽，被认为是最无用的理论。直到在球面几何中发现了它的应用才受到重视。

空间如果不存在物质，时空是平直的，用欧氏几何就足够了。比如在狭义相对论中应用的，就是四维伪欧几里得空间。加一个伪字是因为时间坐标前面还有个虚数单位i。当空间存在物质时，物质与时空相互作用，使时空发生了弯曲，这是就要用非欧几何。

相对论预言了引力波的存在，发现了引力场与引力波都是以光速传播的，否定了万有引力定律的超距作用。当光线由恒星发出，遇到大质量天体，光线会重新汇聚，也就是说，我们可以观测到被天体挡住的恒星。一般情况下，看到的是个环，被称为爱因斯坦环。爱因斯坦将场方程应用到宇宙时，发现宇宙不是稳定的，它要么膨胀要么收缩。当时宇宙学认为，宇宙是无限的，静止的，恒星也是无限的。于是他不惜修改场方程，加入了一个宇宙项，得到一个稳定解，提出有限无边宇宙模型。不久哈勃发现著名的哈勃定律，提出了宇宙膨胀学说。爱因斯坦为此后悔不已，放弃了宇宙项，称这是他一生最大的错误。在以后的研究中，物理学家们惊奇的发现，宇宙何止是在膨胀，简直是在爆炸。极早期的宇宙分布在极小的尺度内，宇宙学家们需要研究粒子物理的内容来提出更全面的宇宙演化模型，而粒子物理学家需要宇宙学家们的观测结果和理论来丰富和发展粒子物理。这样，物理学中研究最大和最小的两个目前最活跃的分支：粒子物理学和宇宙学竟这样相互结合起来。就像高中物理序言中说的那样，如同一头怪蟒咬住了自己的尾巴。值得一提的是，虽然爱因斯坦的静态宇宙被抛弃了，但它的有限无边宇宙模型却是宇宙未来三种可能的命运之一，而且是最有希望的。近年来宇宙项又被重新重视起来了。黑洞问题将在今后的文章中讨论。黑洞与大爆炸虽然是相对论的预言，它们的内容却已经超出了相对论的限制，与量子力学，热力学结合的相当紧密。今后的理论有希望在这里找到突破口。

广义相对论基本原理

由于惯性系无法定义，爱因斯坦将相对性原理推广到非惯性系，提出了广义相对论的第一个原理：广义相对性原理。其内容是，所有参考系在描述自然定律时都是等效的。这与狭义相对性原理有很大区别。在不同参考系中，一切物理定律完全等价，没有任何描述上的区别。但在一切参考系中，这是不可能的，只能说不同参考系可以同样有效的描述自然律。这就需要我们寻找一种更好的描述方法来适应这种要求。通过狭义相对论，很容易证明旋转圆盘的圆周率大于3.14。因此，普通参考系应该用黎曼几何来描述。第二个原理是光速不变原理：光速在任意参考系内都是不变的。它等效于在四维时空中光的时空点是不动的。当时空是平直的，在三维空间中光以光速直线运动，当时空弯曲时，在三维空间中光沿着弯曲的空间运动。可以说引力可使光线偏折，但不可加速光子。第三个原理是最著名的等效原理。质量有两种，惯性质量是用来度量物体惯性大小的，起初由牛顿第二定律定义。引力质量度量物体引力荷的大小，起初由牛顿的万有引力定律定义。它们是互不相干的两个定律。惯性质量不等于电荷，甚至目前为止没有任何关系。那么惯性质量与引力质量(引力荷)在牛顿力学中不应该有任何关系。然而通过当代最精密的试验也无法发现它们之间的区别，惯性质量与引力质量严格成比例(选择适当系数可使它们严格相等)。广义相对论将惯性质量与引力质量完全相等作为等效原理的内容。惯性质量联系着惯性力，引力质量与引力相联系。这样，非惯性系与引力之间也建立了联系。那么在引力场中的任意一点都可以引入一个很小的自由降落参考系。由于惯性质量与引力质量相等，在此参考系内既不受惯性力也不受引力，可以使用狭义相对论的一切理论。初始条件相同时，等质量不等电荷的质点在同一电场中有不同的轨道，但是所有质点在同一引力场中只有唯一的轨道。等效原理使爱因斯坦认识到，引力场很可能不是时空中的外来场，而是一种几何场，是时空本身的一种性质。由于物质的存在，原本平直的时空变成了弯曲的黎曼时空。在广义相对论建立之初，曾有第四条原理，惯性定律：不受力(除去引力，因为引力不是真正的力)的物体做惯性运动。在黎曼时空中，就是沿着测地线运动。测地线是直线的推广，是两点间最短(或最长)的线，是唯一的。比如，球面的测地线是过球心的平面与球面截得的大圆的弧。但广义相对论的场方程建立后，这一定律可由场方程导出，于是惯性定律变成了惯性定理。值得一提的是，伽利略曾认为匀速圆周运动才是惯性运动，匀速直线运动总会闭合为一个圆。这样提出是为了解释行星运动。他自然被牛顿力学批的体无完肤，然而相对论又将它复活了，行星做的的确是惯性运动，只是不是标准的匀速圆周而已。

蚂蚁与蜜蜂的几何学

设想有一种生活在二维面上的扁平蚂蚁，因为是二维生物，所以没有第三维感觉。如果蚂蚁生活在大平面上，就从实践中创立欧氏几何。如果它生活在一个球面上，就会创立一种三角和大于180度，圆周率小于3.14的球面几何学。但是，如果蚂蚁生活在一个很大的球面上，当它的"科学"还不够发达，活动范围还不够大，它不足以发现球面的弯曲，它生活的小块球面近似于平面，因此它将先创立欧氏几何学。当它的"科学技术"发展起来时，它会发现三角和大于180度，圆周率小于3.14等"实验事实"。如果蚂蚁够聪明，它会得到结论，它们的宇宙是一个弯曲的二维空间，当它把自己的"宇宙"测量遍了时，会得出结论，它们的宇宙是封闭的(绕一圈还会回到原地)，有限的，而且由于"空间"(曲面)的弯曲程度(曲率)处处相同，它们会将宇宙与自己的宇宙中的圆类比起来，认为宇宙是"圆形的"。由于没有第三维感觉，所以它无法想象，它们的宇宙是怎样弯曲成一个球的，更无法想象它们这个"无边无际"的宇宙是存在于一个三维平直空间中的有限面积的球面。它们很难回答"宇宙外面是什么"这类问题。因为，它们的宇宙是有限无边的封闭的二维空间，很难形成"外面"这一概念。

对于蚂蚁必须借助"发达的科技"才能发现的抽象的事实，一只蜜蜂却可以很容易凭直观形象的描述出来。因为蜜蜂是三维空间的生物，对于嵌在三维空间的二维曲面是"一目了然"的，也很容易形成球面的概念。蚂蚁凭借自己的"科学技术"得到了同样的结论，却很不形象，是严格数学化的。

由此可见，并不是只有高维空间的生物才能发现低维空间的情况，聪明的蚂蚁一样可以发现球面的弯曲，并最终建立起完善的球面几何学，其认识深度并不比蜜蜂差多少。

黎曼几何是一个庞大的几何公理体系，专门用于研究弯曲空间的各种性质。球面几何只是它极小的一个分支。它不仅可用于研究球面，椭圆面，双曲面等二维曲面，还可用于高维弯曲空间的研究。它是广义相对论最重要的数学工具。黎曼在建立黎曼几何时曾预言，真实的宇宙可能是弯曲的，物质的存在就是空间弯曲的原因。这实际上就是广义相对论的核心内容。只是当时黎曼没有像爱因斯坦那样丰富的物理学知识，因此无法建立广义相对论。

广义相对论的实验验证

爱因斯坦在建立广义相对论时，就提出了三个实验，并很快就得到了验证：(1)引力红移(2)光线偏折(3)水星近日点进动。直到最近才增加了第四个验证：(4)雷达回波的时间延迟。

(1)引力红移：广义相对论证明，引力势低的地方固有时间的流逝速度慢。也就是说离天体越近，时间越慢。这样，天体表面原子发出的光周期变长，由于光速不变，相应的频率变小，在光谱中向红光方向移动，称为引力红移。宇宙中有很多致密的天体，可以测量它们发出的光的频率，并与地球的相应原子发出的光作比较，发现红移量与相对论语言一致。60年代初，人们在地球引力场中利用伽玛射线的无反冲共振吸收效应(穆斯堡尔效应)测量了光垂直传播22。5M产生的红移，结果与相对论预言一致。

(2)光线偏折：如果按光的波动说，光在引力场中不应该有任何偏折，按半经典式的"量子论加牛顿引力论"的混合产物，用普朗克公式E=hr和质能公式E=MC^2求出光子的质量，再用牛顿万有引力定律得到的太阳附近的光的偏折角是0.87秒，按广义相对论计算的偏折角是1.75秒，为上述角度的两倍。1919年，一战刚结束，英国科学家爱丁顿派出两支考察队，利用日食的机会观测，观测的结果约为1.7秒，刚好在相对论实验误差范围之内。引起误差的主要原因是太阳大气对光线的偏折。最近依靠射电望远镜可以观测类星体的电波在太阳引力场中的偏折，不必等待日食这种稀有机会。精密测量进一步证实了相对论的结论。

(3)水星近日点的进动：天文观测记录了水星近日点每百年移动5600秒，人们考虑了各种因素，根据牛顿理论只能解释其中的5557秒，只剩43秒无法解释。广义相对论的计算结果与万有引力定律(平方反比定律)有所偏差，这一偏差刚好使水星的近日点每百年移动43秒。

(4)雷达回波实验：从地球向行星发射雷达信号，接收行星反射的信号，测量信号往返的时间，来检验空间是否弯曲(检验三角形内角和)60年代，美国物理学家克服重重困难做成了此实验，结果与相对论预言相符。

仅仅依靠这些实验不足以说明相对论的正确性，只能说明它是比牛顿引力理论更精确的理论，因为它既包含牛顿引力论，又可以解释牛顿理论无法解释的现象。但不能保证这就是最好的理论，也不能保证相对论在时空极度弯曲的区域(比如黑洞)是否成立。因此，广义相对论仍面临考验。

Relativistic

Principle of relativity theory of relativity is on time and gravity of the basic theory, by Einstein (Albert Einstein) created is the special theory of relativity (special theory of relativity) and General Relativity (General Relativity). The basic assumption of relativity is the velocity of light invariance principle, the principle of relativity and the equivalence principle. The theory of relativity and quantum mechanics in modern physics the two basic pillars. Lay the foundation of classical physics of classical mechanics, not to the high-speed movement of objects and microeconomic conditions objects. Relativistic solve the problem of high-speed movement; Quantum mechanics to atomic micro-conditions problem. Relativistic greatly changed the nature of the universe and the "common-sense" concept, "while the relative" "Four-Dimensional Space-Time," "bending space," such as a brand new concept. [Relativistic the proposed process -- in addition to the quantum theory, 1905 has just received a doctorate Einstein published an article entitled "On the move -- the body dynamics," the article triggered in the 20th century physics another revolution. The article is a study of the movement of objects optical phenomena, which was then the classical physics are facing another problem. In mid-19th century, established Maxwell electromagnetic theory, and predicted that the velocity of light C to spread the existence of electromagnetic waves. End of the 19th century, experiments have confirmed the Maxwell theory. What is the electromagnetic wave? Its transmission speed in terms of who? C It was fashionable to view the entire universe is filled with a special material called "Ethernet" is the Ethernet electromagnetic vibration transmission. But people have found that this is a contradictory theory. If the earth is in a static Ethernet Motion, then according to the speed principle of superposition, Earth along different directions transmitted at the speed of light, it is not the same, but the experiment negate this conclusion. If Ethernet is the Earth with him, and obviously some of the astronomical observations are inconsistent. 1887 Michelson Morelli exhausted and the interference phenomena of the very precise measurement, still have not found the Earth Ethernet relative to any campaign. In this regard, Lorentz (H.A.Lorentz) proposed a hypothesis, that all the Ethernet objects moving along the direction of movement must contraction. He proved this, even if the Earth is relatively Ethernet campaign Michelson also found it impossible. Einstein completely different from the idea of the problem. He pointed out that as long as the abandoned Newton established the absolute space and absolute time the concept of all difficulties can be resolved. What do not need Ethernet. Einstein proposed two discussion of the basic tenets of moving objects based on the optical phenomenon. The first is called the principle of relativity. It is said : If the coordinates K 'in relation to coordinate K for the uniform movement without rotation, This will be equivalent to two coordinates done any physics experiment, it is impossible to distinguish between what is Coordinates K, Which is Coordinates K '. The second principle called Light the same principle, it is light (in a vacuum) the speed is constant, c It is not dependent on the luminous objects velocity. On the surface, the speed of light seems to be the same with the principle of relativity conflict. According to classical mechanics speed synthesis method for K 'and K so that two relatively uniform motion of the coordinate system, Light should not the same. Einstein that the two have to admit this does not contravene the principles, we must re-analysis of time and space physics concepts. Classical Mechanics speed synthesis dependent on the actual rules of the following two assumptions : 1. 2 incident and the time interval measurement of the time the 10-minute movement not; 2. 2:00 spatial distance and distance measurement used for the calculation of the non-state campaign. Einstein discovered that if the same principle of recognition speed of light and the principle of relativity is compatible, then these two assumptions have been made to get rid of. Then, the bell is a simultaneous outbreak of another bell is not necessarily the same time, simultaneously with relative. In two relative movement of a coordinate system, two specific measuring the distance between the points is not the numerical equivalent. Distance also made relative. If established K coordinate system can be an incident three space coordinates x, y, z coordinates and a time not to determine, K 'coordinate system with an incident from x', y ', z' and not 'to define, Einstein found that x', y ', z 'and not' can be adopted by a group equation x, y, z and t seek out. 2 coordinates the relative velocity and speed of light c is the only parameter equation. This is the first equation from the Lorentz, known as the Lorentz transformation. Using Lorentz transformation is easy to show that, because the bell will slow movement, the movement feet than static at short, add speed to meet a new law. Principle of Relativity has been a clear expression of the mathematical conditions in the Lorentz transformation, with the write-in space-time variables x ', y ', z', not 'will replace the space-time variables x, y, z, t, Any expression of the natural law still prefer the original exactly the same form. People generally call it the law of nature for the Lorentz transformation is the covariant. This is in our exploration of the universal law of nature has a very important role. Moreover, in the classical physics, time is absolute. It has acted as different from the three spatial coordinates of independent role. Einstein's theory of relativity time and space linked up. Physical reality that the world is composed of various events, each event from 4 to describe a few. This number is four times its coordinates t and x, y, z, which constitute a continuous four-dimensional space. commonly known as four-dimensional Minkowski space. In the theory of relativity, using four-dimensional approach to the physical inspection of the real world is very natural. Another special theory of relativity led to important findings on the quality and energy. Einstein in the past, physicists have always thought that mass and energy are totally different, they are conserved quantity respectively. Einstein found that the quality of the theory of relativity and energy are inseparable, two conservation law to a combination law. He is a well-known mass-energy equation : E=mc^2, c for the speed of light. So the quality can be seen as it is a measure of energy. Calculation shows that the quality of small contains enormous energy. The mysterious formula for human access to enormous energy, manufacture atomic and hydrogen bombs and the use of atomic energy generation such as laying a theoretical foundation. Einstein's introduction of these new concepts, most physicists. including relativistic transform the founder of Lorentz, find it difficult to accept. The old way of thinking of obstacles, so that the new physical theory until after generation for the majority of physicists are familiar with, Even the Royal Swedish Academy of Sciences, the 1922 Nobel Prize awards Einstein, just say "because he contribution to theoretical physics, Since he discovered the law of the photoelectric effect. "relativistic silent. Einstein in 1915 further establish general relativity. The principle of relativity is also limited to two relatively uniform motion so the coordinates, and the theory of general relativity in which the uniform movement restrictions were abolished. He introduced an equivalence principle, do not think we can distinguish between gravitational effects and non-uniform motion, that is non-uniform motion and gravity are equivalent. He further analysis of the light in the near vicinity of a volume will be through and curved gravitational phenomena, that the very concept of gravitational totally unnecessary. It that the quality of the planets make it into space near the bending of light is taking the most short lines. Based on these discussions, Einstein derived an equation group, They can be identified by the presence of substances resulting from the bending of space geometry. Use of this equation, Einstein calculated the transit point of the recent displacement, with the experimental observations exactly the same, a long-term solution can not explain the difficult issues, which makes Einstein excited about. Ailunfeishite he wrote in the letter reads : "... given the recent equations point to the correct value, You can imagine how happy I am! good days, I do not know how happy a better life. "November 25, 1915. Einstein entitled "gravity equation," the papers submitted to the Prussian Academy of Sciences in Berlin. complete exposition of general relativity. In this article he not only explained the astronomical observatory discovered in the recent transit point track mobile mystery, but also predicted : Star will happen after the sun deflection, deflection angle equivalent to Newton's theory predicted by the numerical twice. World War I delayed on the numerical results. May 25, 1919 Total Solar Eclipse to provide people with a war the first observation opportunities. British Eddington rushed to the African west coast of the island of Principe, this observation. November 6, Thomson in the British Royal Society and the Royal Astronomical Society joint meeting solemnly announced : confirmed the Einstein and Newton is not predicted by the results. He praised the Road "This is the history of human thought greatest achievements. Einstein found is not a small island, but a whole new world of scientific thinking. "The Times" scientific revolution "to the issue of a major news reported. Conveyed the news to the world, Einstein became world famous. General relativity has been increased to 1902 by people revere the throne. Since then, the people of the experimental tests of general relativity demonstrated increasingly strong interest. However, as the solar system within the gravitational field is very weak, gravitational effect itself is very small, general relativity theory with Newton's gravitational theory from the very small observation very difficult. Since the 1970s, as radio astronomy progress from the observation of the solar system far from a breakthrough. observation of a significant increase accuracy. In particular, in September 1974 from the Massachusetts Institute of Taylor and his students at Whistler, 305-meter with a large radio telescope observations, they found Pulse star. It is a neutron star and its companion star under the force of gravity mutual bypass, the cycle is only .323 days, Its surface gravity of the sun surface than 100,000 times stronger. Earth, even within the solar system can not be given the test gravitational theory laboratory. After more than 10 years of observation, they have with the predictions of general relativity with very good results. Because of this significant contribution, Taylor was whistle of the 1993 Nobel Prize for physics. [Special relativity -- Mach and Hume's philosophy of Einstein significant influence. Mach think that the time and space to measure and material movement. The concept of time and space is formed through experience. Absolute time and space no matter what experience can grasp. Hume more concretely : the extension of space and not anything else, but by order of a certain distribution of visible objects with space. And the time to change is always the target noticeable changes found. Einstein pointed out in 1905, Michelson and Morey experiment, in fact, demonstrated on the "Ethernet" the whole concept is redundant, the speed of light is constant. And Newton's absolute space-time is a wrong concept. There is no absolute static frame of reference, time is measured with reference to different different. He used the same speed of light and relativity principle of Lorentz transformation. Created the special theory of relativity. Special Relativity is built on the four-dimensional time and space of a theory, it should understand the theory of relativity, The first relativistic time and space to have a general understanding. In mathematics there are various three-dimensional space, but so far, we know of the physical world only recently, that is, three-dimensional space plus one time dimension. Modern physics micro-mentioned high-dimensional space is another layer of meaning, only mathematical, not in this discussion. Four-dimensional space-time is the real world constitute the minimum dimension, our world is just recently, true of high-dimensional space, at least now we can not perception. I said a message on an example of a ruler in 3D space (excluding time) rotation, the length unchanged. However, rotating it, the value of the coordinates of the changes, which coordinates between linked. Four-dimensional space-time means that time is the fourth dimension coordinates, and space coordinates are linked. That is time and space are unified and indivisible whole, which is a "shift" in relations. Four-dimensional space-time is not limited to this, by the mass-energy relation know, the actual quality and energy is one thing, mass (or energy) is not independent, but with the state of the campaign, such as greater speed, greater quality. In four-dimensional space-time, the mass (or energy) is a four-dimensional real momentum of the fourth dimension of weight and momentum is descriptive material amount, Therefore quality and the movement is a matter of course. In four-dimensional space-time, momentum and energy to achieve a unified, known as the four energy-momentum vector. Moreover, the four-dimensional space-time around the definition of the four-speed, four speed Vega, 4D, electromagnetic field equations of 4D format. What is worth mentioning is that the electromagnetic field equations of 4D form a more perfect, the complete reunification of electricity and magnetism, electric and magnetic fields using a uniform electromagnetic field tensor to describe. The four-dimensional space-time three-dimensional laws of physics than to perfect the law, which illustrates that our world is the four-dimensional. It can be said that at least than Newtonian mechanics to perfect the most. At least by its imperfections, we can not make improper doubt it. The theory of relativity, time and space constitute an indivisible whole -- four-dimensional space-time, Energy and momentum also constitute an indivisible whole -- 4D momentum. This explains the natural world seem to be irrelevant to the amount that may exist between profoundly linked. General relativity discussed in the future when we will see, time and energy-momentum four arrows also exist between the profound links. Special Relativity material in the basic tenets of interaction for the eternal movement, with no campaign material, Without the material is campaign material because of the interrelated and interaction of movement, therefore, The material must describe the relationship between movement, and not isolated describe movement. In other words, the movement must have a reference from the reference material is the reference system. Galileo has pointed out that the movement of ships and ship geostationary not distinguish between the movement, in other words, When you in a closed cabin, and completely isolated from the outside world, so even if you have the most-developed brain, the most advanced equipment, You have no perception of the ship was a uniform motion or stationary. Perceptual speed to any size, because there is no reference. For example, we do not know the entire universe of the overall movement, because the universe is closed. Einstein be invoked, the special theory of relativity as a fundamental principle : the principle of relativity. Its contents are : inertial system is entirely equivalent, could not be distinguished. Morey, the famous Michelson experiment complete denial of optical Ethernet doctrine, drawn-reference system has nothing to do with the conclusions. In other words, if you stand on the ground, or kept on the train, measured the speed of light is the same. This is the second special relativity principle, the same principle of the velocity of light. By the two basic tenets of this can be directly derived relativistic type of coordinate transformation, Transform-speed all the contents of the special theory of relativity. For example, speed changes, and the traditional rules of contradiction, but in practice prove to be correct. For example, a train speed is Surround Datahome, a person in the vehicle relative to the vehicle speed is Surround Datahome. on the ground to see the vehicle speed is not a feasible one. but (20-10^ (-15)) 1961. In ordinary circumstances, this relativistic effect can be completely ignored, but close to the velocity of light, the effect of such increases markedly, for example, Train speed is 0.99 times the speed of light, the rate is 0.99 times the speed of light. Then ground observation to the conclusion that the velocity of light instead of 1.98 times, but 0.999949 times the speed of light. Most people see behind the firing has not slowed light to him is the velocity of light. Therefore, in this sense, is not beyond the speed of light, because in that reference frame, the speed of light is constant. Transform speed particle physics have been numerous experiments show that is impeccable. Because of this unique optical properties, it was selected as the only four-dimensional space-time scale. According to the special theory of relativity effects of special relativity theory, inertial system is entirely equivalent, in an inertial system with, There reunification of the time, known as the same time, and the theory of relativity proved that the different inertial system, there is no uniform at the same time, is two events (space-time points) in a sexual relations within the same department, in another inertial system may not be within the same time, This is also the relative nature of the inertial reference frame, the same physical processes of the process is exactly the same time. If the same physical process to measure time, the entire inertial system can be unified time. In the future we can get the general relativity, non-inertial reference frame, time is uneven, that is to say, In the same non-inertial reference frame, no unity of time, it could not establish a unified simultaneously. Relativistic different inertial system is derived between the progress of time, the movement found time to slow progress inertial system, This is the so-called bell slow effect. Popular can understand that the clock movement than static bell slowly, but faster movement, the bell go more slowly. close to the speed of light, the bell is almost to a halt. The length of a ruler in an inertial reference frame "at the same time" the two ends of the coordinate value of the poor. Because "at the same time" the relative, different inertial measurement of the length varied. Relativity proved that the length of a ruler in the direction of the campaign ruler than static ruler short, this is the so-called ulnar reduction effect When close to the speed of light speed, the ruler folded and damaged a point. The above statement indicates that the slow bell foot and reduce the principle is the rate of progress is relative. In other words, the rate of progress with the reference system. This fundamentally negates Newton's absolute time and space, and the theory of relativity that absolute time did not exist, However, time is still an objective quantity. For example, the next issue to be discussed at the Twin ideal experiment, the brothers returned by the spacecraft is 15 years old, brother may have been 45 years old that time is relative, but my brother did live for 15 years. my brother did that to live 45 years, which is nothing to do with the reference system, the time is "absolute." This shows that regardless of how the object movement, which itself is going through a time of the objective, which is absolute. This is known as the inherent time. In other words, no matter what form your campaign, you would think you drink coffee normal speed, You patterns of life have not been disrupted, but other people might see you drink coffee with a hundred years, From the glass down to the death of only one second. Clock Paradox or TWIN PARADOX after the birth of the theory of relativity, had an extremely interesting and difficult problems -- TWIN PARADOX. One pair of twins A and B, A on Earth, B rocket done by the interplanetary travel, takes a long time to return to earth. Einstein's theory of relativity by the assertion that they experienced at different times, the reunion at B than A young. Many people doubt that the A look at the campaign B, B is A look at campaign Why is not more than B A young? As the Earth can be approximated as inertial system, B experienced deceleration and acceleration process. Variable speed up the movement of information, and truly it is very complicated discussion, Therefore, the Einstein has discussed the issues are clearly many people mistakenly believe that relativism is self-contradictory theories. If the world map and time line concept discussion of the issue on a more simple, but we had to use many formulas and mathematical knowledge. Here is the language used to describe a simple case. But language can not only provide more detail on the details, please refer to the interest in some relativistic books. Our conclusion is that in that reference frame, B than A young. To simplify the problem, only to discuss the situation, rocket after a very short period of time to accelerate the speed of light-flight after some time, U-turn with a very short time, flight time, a very short period of time with the Earth's encounters with the slowdown. This is the purpose of accelerating and decelerating omitted from the impact. In the earth reference system is very good discussion, and the rocket is always dynamic bell, again, when B than A young. When the rocket reference system, in uniform Earth is a dynamic process bell, the time within the process slower than the rocket, But the most crucial part of the rocket is turning process. U-turn in the course of the Earth by the rocket rear faraway places after a very short period of time for cross-half circle, Rocket reached the front faraway places. This is a "superluminal" process. The only Superluminal is not in contradiction with the theory of relativity, the "superluminal" does not convey any information, is not the real meaning of Superluminal. Without this U-turn course, rockets and the Earth will not be met, since different reference systems is no uniform time therefore can not be compared to their age, only when they encounter can be compared. U-turn after the rocket, not directly B A message for the transmission of information takes time. B see the actual process to make a U-turn in the course of the Earth's rate of progress suddenly accelerated. B seems, A. B. younger than reality, and then make a U-turn when the aging rapidly, back when A than their aging slow. Reunion, he has more than A young. In other words, the theory of relativity does not exist a logical contradiction. Summary of special relativity theory of relativity physics requirements in the law to coordinate transformation (Lorentz changes) remain unchanged. Classical electromagnetic theory can not change into the framework of the theory of relativity and Newton's mechanics only in the Galileo transform the situation unchanged, Lorentz transformation of the original concise format has become extremely complex. Classical mechanics and therefore to be amended, the revised mechanical system Lorentz transformation in the same situation, called relativistic mechanics. Since the establishment of special relativity, the physics has played a tremendous role in promoting. And in-depth account of quantum mechanics, to become a high-speed particles indispensable theory, and achieved fruitful results. But behind the success, there are two remaining issues of principle yet to be resolved. The first is caused by inertial system difficulties. Abandoned the absolute time and space, the inertial system has become impossible to define the concept. We can say yes inertial reference frame in which the law established reference system. Inertia without outside a real objects to remain static or uniform linear motion of the state. However, "without outside" What does it mean? Can say, is not subject to external objects in an inertial reference frame static or uniform linear motion. Thus, the definition of inertial system falls into a cycle of logic, such a definition is useless. We can always find the reference frame is very similar, but the universe does not exist real inertial system, Like all the theoretical construction on the beach in general. The second is the gravity of the difficulties. Law of Universal Gravitation and closely linked to absolute time and space, must be amended However, the revision of the Lorentz transformation of the same situation any attempt failed. gravity is not included in the framework of special relativity. At that time, the physical sector only discovered gravity and the electromagnetic force two, one on the surface disruption, and of course not satisfactory. Einstein used only a few weeks on the establishment of the special theory of relativity, but for solving these two problems, establishing general relativity is used for a whole decade. To address the first issue, Albert Einstein scrapped the inertial system in the theory of the special status put relativity principle that the promotion of non-inertial reference frame. So the first problem into a non-inertial reference frame the space-time structure. Non-inertial reference frame in the first encounter only stumbling block is inertia. In-depth study of inertial force, a well-known principle of reciprocity. found a reference to the problem of gravitational potential and solve problems together. After many twists and turns, Einstein finally established a complete and general relativity. General relativity all physicists were shocked, imagine the gravitational far more complex. So far Einstein's field equations are only a small number of identified solutions. It beautiful mathematical form has so physicists have marveled. In general relativity made tremendous achievements, created by the Copenhagen School and the development of quantum mechanics have made a major breakthrough. But physicists have quickly discovered, the two incompatible theories, at least one needs to be revised. So that triggered the famous polemic : Einstein VS Copenhagen school. Even today controversy has not stopped, but a growing number of physicists is more inclined to quantum theory. Einstein to solve this problem after half a lifetime spent time in 30 years but to no avail. But his work for physicists have pointed out the direction : the establishment of the force contains four super-unified theory. Currently academia recognized as the most promising candidate is the ultra-superstring theory and theory of film theory. [Advent of general relativity -- the theory of relativity, people see the conclusion was : four-dimensional curved space-time, limited the limitless universe, gravitational waves, LENSING, big bang theory, as well as the theme of the 21st century -- a black hole, and so on. All of this has come too suddenly, so that the people feel that the mystery of relativity, the theory of relativity developed in the first few years, Some people threatened that "only 12 individuals worldwide to understand the theory of relativity." Some even say that "the world only two and a half people to understand the theory of relativity." Even more to the theory of relativity and the "Dianetics", "Spiritualism," which is par. In fact, the theory of relativity is mysterious, it is the most down-to-earth theory, which is experiencing a never practice the truth, More than sky high. Application of the theory of relativity is not an ordinary geometry Euclid geometry, but Riemannian geometry. I believe many people are aware of Non-Euclidean Geometry, it is divided into Roche geometry and geometric Lei two. Riemann higher from the perspective of the reunification of the three geometry, as Riemannian geometry. In non-euclidean geometry, a lot of strange conclusions. Triangle interior angle of 180 degrees and is not, circle rate is not 3.14, and so on. So in just issued, greatly ridiculed, considered to be the most useless theories. In spherical geometry until found its application will be heard. If there is no space material, space-time is flat, with Euclidean geometry sufficient. For example, in the application of the special theory of relativity, is four-dimensional pseudo-Euclidean space. Canada is a pseudo-character coordinates of time before there is imaginary unit i. When the existence of material space, material and time interaction, so that a curved space-time, it is we must use non-euclidean geometry. Relativity predicted the existence of gravitational waves, he found the gravitational field and gravitational waves are transmitted to the speed of light. negation of the law of gravity away from the role of super. When light from the stars issued, and encountered quality objects and the light will be re-like, say, We can observe objects blocked by the star. Under normal circumstances, is to see the ring, known as the Einstein ring. Einstein's field equations will be applied to the universe and found that the universe was not stable, it either expanding or shrinking. At that time, cosmology that the universe is infinite, static, the stars is unlimited. So he does not hesitate to amend the equation, the inclusion of a universe term, a stable solution, a limited limitless universe model. Hubble discovered near the famous Hubble's law, the expansion of the universe theory. Einstein regret this very much and abandoned the universe projects, saying that this is his life's biggest mistake. In future research, physicists were surprised to discover that the universe is in addition to expansion, it is in the explosion. Very early universe distribution in a small scale, NASDA scientists need to study the contents of particle physics to a more comprehensive model of the evolution of the universe. Particle physicists and scientists need universe of observational results and theoretical to enrich and develop particle physics. This study physics largest and the smallest two of the most active branches : particle physics and cosmology has such mutual together. Like high school physics preamble said, as a Guaimang bite its own tail. It is worth mentioning that although Einstein's static universe was discarded, But its limited limitless universe model of the universe has three possible future fate, but also the most promising. In recent years the universe items will be re-emphasized the. Black hole problem will in future articles discussed. Black hole and the big bang is a relativistic predictions, but their content has exceeded the limits of the theory of relativity. and quantum mechanics, thermodynamics combination of very close. Future Theory hope to find a breakthrough here. The basic principles of general relativity can not be defined as inertial system, Einstein relativity principle will be extended to non-inertial reference frame. of the first general relativity theory : general relativity theory. Its content is, all reference system described in the natural law, they are equivalent. This is the principle of relativity a great difference. In different reference systems, all the laws of physics are equivalent, no description of the difference. But in all reference system, this is impossible, only that different reference systems can be equally effective, the description of natural law. This requires that we find a better way to meet the description of such a request. Through the special theory of relativity, it is easy to show that the rotating disc circumference is greater than 3.14. Therefore, the general frame of reference should be used to describe the Riemannian geometry. The second principle is the same principle at Light Speed : the speed of light with arbitrary reference system are the same. It equivalent to the four-dimensional space-time - the time which is not changed. At that time, the space is flattened, in three-dimensional space with the velocity of light-line movement, then bending space, in 3D space along the curved-space movement. Gravity can be light deflection, but not accelerate the photon. The third principle is the most famous equivalence principle. There are two quality, the quality of inertia is used to measure the size of objects inertia, the first by Newton's second law definition. Quality Metrics gravitational gravitational objects the size of the Security Council, initially by Newton's Law of Universal Gravitation definition. They are independent from the two laws. Inertial mass is not the same as the charge, or even the present, there is no relationship. Then inertial mass and gravitational mass (gravitational Netherlands) in Newtonian mechanics should not have any relations. But with the most sophisticated contemporary pilot also unable to detect the differences among them. inertial mass and gravitational mass strictly proportional to (choose appropriate coefficient would enable them to strictly equivalent). General relativity will inertial mass and gravitational mass as a fully equal to the equivalence principle. Inertial mass contact with the inertia force, gravitational mass and gravitational linked. Thus, non-inertial reference frame and gravity have also established ties. Then in the gravitational field of any point can introduce a small landing free reference system. As the inertial mass and gravitational mass equal to the reference system is not within the inertial forces are not subject to gravity and can use all the special theory of relativity theory. Initial conditions, and other charges ranging from the quality of the particle in the same field are different orbits, But all particles in the same gravitational field is only track. Einstein equivalence principle so that recognizes that the gravitational field is most likely not the time foreign market, but a geometric field, space-time itself is a character. Due to the existence of material originally straight time and space into a curved Riemann time. In general relativity was established, had a fourth principle, the law of inertia : not force (gravitational removed, because gravity is not the real power) of objects so habitual movement. Riemann in time and space, is along the geodesic campaign. Geodesic line is the spread between two points is the shortest (or longest), it is the only one. For example, the geodesic sphere is the Center off the plane and spherical interception of the great circle arc. However, the field equations of general relativity established, the law of the market equation can be derived, so inertia into inertia theorem. It is worth mentioning that Galileo had that uniform circular motion is the inertial motion, uniform linear motion Association for the closure of a circle. This was raised in order to explain planetary motion. Naturally he was awarded the Newtonian mechanics completely, but it will relativistic revival of the planet is so habitual movement, only instead of the standard uniform circular it. Ants and bees geometric vision of life in a two-dimensional flat surface ants because it is two-dimensional biological, there is no sense of the third dimension. If ants living in the big plane, from the practice created Euclidean geometry. If it lives in a spherical surface, it will create a triangle and the more than 180 degrees, Circle rate of less than 3.14 of spherical geometry. However, if the ants live in a big sphere, but when it is the "science" was not fully developed, the range of activities is still not big enough. It found insufficient spherical bending, a small sphere of life is similar plane, it would first create Euclidean geometry. When it is the "science and technology" developed, it will find Triangle and more than 180 degrees, Circle rate of less than 3.14, and so on "empirical facts." If ants smart enough, it will come to a conclusion that their universe is a winding two-dimensional space. When it put its own "universe" of the measurement times, come to the conclusion Their universe is closed (once around will return to the in situ), limited, and because "space" (surface) level of bending (curvature) the same everywhere, They will be their own universe and the universe round analogy, holding that the universe is "the circular." Since no third-dimensional feel, so it can not imagine that their universe is how to bend into a ball. They can not even imagine the "myriad" of the universe exist in a three-dimensional space in the flat area of limited sphere. They are very difficult to answer "what is outside the universe," such problems. Because their power is limited universe of closed two-dimensional space, it is difficult to form the "outside" of the concept. For ants must use "advanced technology" can be found in abstract facts, Bees can be a very easy visual image with the description out. Because bees is the three-dimensional space of biological, embedded in three-dimensional space of two-dimensional surface is "transparent", It will be very easy to form spherical concept. Ant on its own "science and technology" has had the same conclusions, but I do not image, is the strict mathematics. This shows that not only the high-dimensional space can be found biological low-dimensional space. smart like ants can be found spherical bending, and eventually establish a complete spherical geometry. its deep understanding not worse than the number of bees. Riemannian geometry is a huge geometric justice system, specifically for the study of space bending nature. Spherical geometry it is a small branch. It can be used not only spherical, oval face, such as the two-dimensional surface-surface, but also for high-dimensional curved space research. It is the most important general relativity mathematical tool. Riemann Riemannian geometry of the building had predicted that the reality of the universe may be curved, material existence is a bending of space reasons. This is, in fact, the core of general relativity. Riemann only that Einstein did not like the rich knowledge of physics, it is not possible to establish general relativity. Experimental verification of general relativity Einstein's general relativity in the establishment, on the three experiments, and will soon be tested : (1) gravitational redshift (2) The deflection of light (3) transit point into action recently. Until recently the addition of a fourth test : (4) radar echo time delay. (1) gravitational redshift : general relativity proved that the gravitational potential of low inherent time goes slow. That is to say the more objects from the past, the slower the time. This celestial body, the surface atoms the long-cycle changes, the same as the velocity of light, the corresponding frequency smaller, in the red spectrum to the direction of movement, known as the gravitational redshift. Universe there are many compact objects, which can measure the frequency of light, Earth and the corresponding atomic-issued for comparison and found that the volume shift language consistent with the theory of relativity. The early 1960s, People in the earth's gravity field using gamma rays without kick resonance absorption effect (Mossbauer effect) measurement of the optical vertical - Sowing the redshift 22.5M results consistent with the theory of relativity predicted. (2) The deflection of light : If the volatility of light, and in the gravitational field there should not be any deflection. by the semi-classical style of "quantum Newton's gravitational theory plus" hybrid product Planck formula used E=hr and quality can be obtained formula E=MC^2 photon quality, Newton's Law of Universal Gravitation reuse the sun near the light deflection angle of 0.87 seconds. Calculation of general relativity by the deflection angle of 1.75 seconds for the above point twice. 1919, a war has just ended, British scientists Eddington sent two inspection teams, the opportunity to use solar eclipse observation, Observing the results about 1.7 seconds, just in relativistic experimental error range. Error caused the solar atmosphere is mainly due to the deflection of light. Recently rely on the radio telescope observations of quasars can airwaves in the sun's gravitational field deflection. without waiting for the sun this rare opportunity. Precise measurement confirmed the conclusions of the theory of relativity. (3) the transit points into the recent actions : astronomical observatory has recently recorded the transit point for every 56 seconds Mobile century, People consider various factors, according to Newton's theory can only explain the 5557 seconds, 43 seconds left unexplained. General relativity with the results Law of Universal Gravitation (inverse square law) is misplaced, just so that the deviation of the recent transit point every 43 seconds Mobile centuries. (4) Radar Experiment : From the Earth to the planetary launch radar signal reception planet reflectance signal Measurement of the signal from time to test whether the bending of space (and the interior angle triangle test) 1960 American physicists have overcome numerous difficulties caused by this experiment results in line with the predictions of relativity. Rely solely on these experiments not enough to show the correctness of the theory of relativity. only that it is more than Newtonian gravitational theory more precise theory, because it includes Newton's gravitational theory can explain Newton's theory can not explain the phenomenon. But can not guarantee that this is the best theory there is no guarantee that the extreme relativistic bending time and space in the region (such as a black hole) is substantiated. Therefore, the test of general relativity is still facing.

姚明后半程冲刺不如刘翔 扬言夏天找回速度

体力速度是关键

同为来自上海的国际巨星，姚明（编辑姚明资料）的后半程冲刺能力，显然要比刘翔差些。尽管季后赛七场大战下来，姚明的场均得分和常规赛并无二样，也有25.1分进账，但命中率却大大下降了。常规赛时，他的命中率为51.6％，到了季后赛则下降了7.6个百分点。除了季后赛更为残酷和对手对他更为严密的盯防外，姚明自身冲刺能力的不足，也因此而暴露出来。【陈敏盘点姚明赛季之一：姚明曾猜想挑选四强对手 受伤影响季后赛发挥】

对此，姚明坦言：“像第四场的第三节，爵士一下子加速，有一阵我实在跑不动了，就到场边跟教练说：‘让我歇会儿吧。’然后就在板凳上看着比分立刻被彻底拉开而特别后悔。我应该顶下来的，这不全是体能的原因，盐湖城是高原，我的体能在那里打了折扣，但我不想拿这当借口。比赛之中你到底有多少体能取决于你在比赛里积累的信心多少。”

除了信心之外，爆发力也显得极为关键。季后赛七场比赛下来，姚明总共得到176分，只比麦迪少了1分，但却和麦迪一样拿得如此悄无声息。因为其中有66分是来自于罚球线，而其他的得分中并没有让人看到太多大涨士气的有效强攻或是关键时刻力挽狂澜的作用，说白了，姚明没有能给对手带来真正的杀伤力，而这正是一名真正的超级巨星所应该体现的。

所以，姚明说，这个夏天他要找回自己的速度。“自从受伤后，我的速度再也不像赛季初期那样了。你们都看到了，在现在的比赛里，速度就是一切。没有速度，你什么都没有。这就是我夏天要做到的事。”

远离失误更加稳定

作为一名被球队所倚重的内线核心，本赛季的姚明，在篮板和失误方面，表现得并不尽如人意。

常规赛中，姚明场均篮板数为9.4个，比上赛季少了0.8个。尽管季后赛中，他的场均篮板数一下提高到10.2个，但几个极为关键的却没有拿到，这也令他十分自责。“我就是恨自己……最后三个后场篮板球，三个关键的篮板球没拿下来。如果拿下来一个，一切都不一样了，那都是我应该拿来的篮板球。”姚明说道。

另一方面，姚明还需要在争夺篮板时提高自己的稳定性。常规赛倒数第三场，在与黄蜂比赛中他只抢下两个篮板后，范甘迪话中连嘲带讽：“姚真不容易，他下半场居然也抢到一个篮板。”作为一名中锋，无论单场比赛砍下多少分，但只有两个篮板入账，是无论如何也说不过去的。

失误，则成为姚明本赛季最尴尬的地方。常规赛48场下来，他场均失误3.7次；季后赛中，他场均失误次数飙升到4.71次，更是有两场失误高达8次！对此，范甘迪坦言：“姚的失误太多了。他应该减少自己的失误，否则就会拖累自己的表现，事实上他一直就是一个高失误率的球员。这一点必须克服，否则就无法找到进攻节奏。”

而这点和姚明的内线统治力还不够强大有着直接的关系，如果他能将那些转身跳投，都变成在禁区里更加强力的移动、直接攻击篮下，那么他就不仅能够得到更多的分，还会减少在外围移动时所造成的失误。更重要的是，强力的得分可以变成激励球队前进的动力，这样的作用，远远大于简单的两分。【陈敏盘点姚明赛季之一：姚明曾猜想挑选四强对手 受伤影响季后赛发挥】

周三中国股市交易量超过亚洲其他国家之和

据统计数据表明,周三中国股市又创下了一个新的记录,那就是中国的股市交易量等于亚洲其他国家的总和。

昨天的交易量数据中,中国股市的总成交(行情论坛)量为3769亿人民币(合约490亿美元),其中上交所成交金额为2553亿元人民币（合约332亿美元），深交所成交金额为1216亿元人民币（合约158亿美元），比4月末创下的前一个历史纪录高出21%。

而亚洲其他国家的总成交量仅为434亿美元,其中日本为269亿美元,包括澳大利亚、香港、泰国、新加坡、马来西亚、韩国、印度、台湾、印尼、新西兰和越南等地的股市，当天的成交额之和约为165亿美元。这些全加起来还比中国的交易量小。

放眼全球,中国股市的交易量也是相当之惊人,美国股市周二成交量也只不过是1220亿美元,伦敦才为294亿美元。

考虑到中国股市尚不允许“T+0”交易（当日买即可当日卖），而其他某些地方被许可，这一创纪录的成交金额尤为令人感觉到恐怖

美华裔市长：中国人有教育没教养 影响奥运成功

美国首位华裔市长黄锦波在穗直批

新快报讯（记者陈红艳通讯员吴新再）“很多中国人受过教育，但没有教养……有教养比拿到文凭更重要。”昨天，美国首位华裔市长、医学博士黄锦波做客广东药学院，直批中国的国民素质不高，号召大学生提高自己的素养，以期成才、成功。

“教养比取得文凭更重要”

黄锦波的头发向后梳得一丝不苟，戴着招牌式的墨镜，黑色西服搭配鲜艳印花领带，左手无名指上是一个“硕大”的黄金戒指。他一上讲台，就开宗明义：“很多清华、北大的毕业生为什么找不到工作？因为他们态度不好。”

黄锦波告诫说：“找得到工作的人，是懂得做人的人，有教养的人。很多中国人接受了教育，但是不一定有教养。”他认为，大学生做人最重要的是要有教养，“有教养比拿到文凭更重要”。

这位口口声声表示“中国才是我的生母，美国是我的养母”的美籍华裔，昨天毫不客气地批评很多中国人的素质太差，影响了中国人的形象。

他说，在美国，凌晨两三点的红绿灯处，马路两边漆黑一片，周边没有警察也没有摄像头，但是几乎90％的美国民众都会自觉地停下车来等红灯，这被人叫做教养或者修养，中国人可能说这是笨蛋。然而在中国，情况则相反，下午两三点，看到红灯照样冲，除非旁边就有警察。

“此外，美国的塞车多发生在高速公路或车祸现场，而中国的塞车多发生在三岔路口，白云宾馆附近就是这样，大家都不肯礼让，导致塞车。”他表示。

“奥运成功取决于国民素质”

他还告诉大家一个故事：他有个朋友从中国携带巨资到美国做生意，虽然刚开张需要客源，但是这个老板宁愿用专机从韩国和日本接送客人，也不愿做中国人的生意。为何？原来韩国和日本客人离开后，1名员工1个小时内就能收拾完6个间房，而中国客人离开后，2名员工人1小时内只能收拾3个间房，并且客房的牙刷、毛巾之类的用品也被“洗劫一空”。

“有钱买不到庄重，金钱不代表文明。”黄锦波称，“特别是2008年奥运会的到来，很多外国人会来中国，以此为窗口来了解一个国家，因此每个人都是一张城市名片。奥运会办得成不成功，不是你中国拿了多少块金牌，而是取决中国人民的素质。”

Gold separation point

About 0.618 points to 0.618:1 is at the forefront of two parts. make the original line with the longer length of that portion of the ratio of 0.618 points. Segment on the two points. The use of two lines 0.618 points can be made is five-pointed star, is pentagon. More than 2,000 years ago, ancient Athens, Greece's third-largest school mathematicians EU first proposed Texas Road 0.618. The so-called golden section that is the length of the L line is divided into two parts, so that part of the ratio for all, to the other part for the part now. 0.618 calculated on the most simple method is the calculation Feibeijie series 1,1,2,3,5,8,13,21. ... After two 2/3,3/5,4/8,8/13,13/21 ratio of the number, the approximate .... 0.618 before and after the Renaissance, after the Arabs into Europe, have been welcomed by the Europeans, They call it "the law", 17th century Europe a mathematician, even nicknamed it "the algorithms can be the most valuable algorithm." This algorithm in India known as the "three rate" or "three rules", we often talk about the ratio method. In fact, the "golden section", China is also recorded. Although no ancient Greece early, but it is ancient China to create an independent mathematician, but later came to India. After verification. Europe's share algorithm is derived from China through India and into Europe by the Arab, and not directly into the ancient Greece. In the plastic arts because it has aesthetic value, arts and crafts and daily necessities Chang design, The ratio used to arouse people's sense of beauty, the real-life application is very extensive, Buildings certain segments than on the scientific use of the Golden Section, the arena is not a member of the narrator standing in the arcade before the stage, 35 in the side of the platform to stand on the stage length of 0.618 points on the most beautiful, the best voice transmission. Even the vegetable kingdom are still using the Golden Section, a softwood from the top down, will see the gold leaf is divided in accordance with the law with the ASEAN. In many scientific experiments, select the program used a .618 law, optimization, It allows us reasonable arrangements for the less number of tests to find reasonable and appropriate Western conditions. It is precisely because of the construction, cultural, industrial and agricultural production and scientific experiments which have extensive and important applications, So people were precious to call the "Golden Section."