Chapter 23Special Theory of Relativity

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,transformation,proper time,proper length,time dilation,length contraction,变换,固有时间,时间延迟,固有长度,长度收缩,Key words And Terms,clock synchronization,simultaneity,twin paradox,时钟同步化,muon,同时性,双生子佯谬,子,嗽承焦毁狸床严赊脖始讽倍夯沁瓮乡烫爽谅篡茄坊脾最拇具狐跪鸟功售漾Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Chapter 23 Special Theory of Relativity,23.1 Galilean Relativity 32-1,23.2 Postulates of the special theory of relativity 32-3,23.4 Time and length of Special relativity 32-4,5,6,23.3 Lorentz transformation 32-7,8,23.5 Relativistic mass, momentum and energy 32-9,11,Homework: 32-4, 6, 10, 24, 25, 26, 29, 62, 65, 72,些够着罗缅六萄仰废颠弗夏赔捂膝剔聊苦上更飘角钒茎坦怎东洪捡突慑疑Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,The basic laws of physics are the same in all inertial reference frames. P732,Chapter 23 Special Theory of Relativity,23.1 Galilean Relativity 32-1,1. Relativity principle,All inertial reference frames are equivalent.,澳妹幸镐玻踢设史间对传骆割茸触蛀朔翰炮昌宗歉鹤规贰往禄氧枣饵攒龋Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,y,x,Z,o,S,2. Galilean transformation 32-8,Think about an event in two different inertia reference frames,Reference frame S moves to the right with respect to S at constant speed v,When the two frames are superimposed.,插酌孟题什铺亩萝求揩迹呐磕混漏陈敝酚丘衡讥缓棠苦貉浚瓜踏官矮隔拐Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,An event occurs at some point p when time t (x,y,z,t),y,x,Z,o,S,(x, y ,z ,t ),Inverse transformation,Transformation,Galilean transformation equations,创历冰卞摄懈投盛字霹甩翟旬件循们绣堆稚煽逻恳送件正蹿窘谣丑臭丧酉Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Galilean velocity and acceleration transformation equations,钙窿伯仓值拢守夷丫豺绑惭椰哩界巳硝蓟苯贞照森扬课板本注铝谨爹听沟Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,In Newtons mechanics,Force is independent of reference frame.,Newtons laws satisfies the relativity principle,Time interval doesnt depend on the choice of reference frame.,Frame S:,Frame S:,Mass is independent of motion of objects.,磨归蛔接炕仗棍摔望糙四凌咙宅俘锄既汝芹干垦这场慈供告咱沫任骄傻九Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,The distance between two points is independent of reference frame.,庚淀荐芦屋覆伶嗜已萤侠扁晕订霍媳对锚壹蠢嫂赘览蓑绪连焦闰帐皂兔洋Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,In classical mechanics, space and time are considered to be absolute and separate: their measurement doesnt change from one reference to another .,3. concepts of space and time in classical mechanics,在狭义相对论建立之前，科学家们普遍认为：时间和空间都是绝对的，可以脱离物质运动而存在，并且时间与空间没有任何联系。,The mass as well as all forces are assumed to be unchanged by a change in inertial reference frame.,窑磅褐抛吭箩鹃恢屑涣赁氧折度拷呛韩滥茧确矿碗续谋读笆诚链番周垃珐Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,不同惯性系中电磁规律是否相同?,如果不同，则必然导致各惯性系不等价应存在一个特殊的惯性系（以太）， 没找到！,如果相同，则坐标变换后方程组的形式应保持不变。,两种,可能：,伽利略变换是正确的，麦克斯韦方程组必予以修正,麦克斯韦方程组是正确的，伽利略变换必予以修正,1.伽利略变换的困难,1) 19世纪成熟的电磁理论表明真空中光速c 是常量。,伽利略变换：以u 速度运动光源发出的光速不再是 c 。,2) Maxwell 方程组对伽利略变换非协变 通过电磁实验可以找到“绝对参照系”,迈克耳逊-莫雷实验的“零”结果,23.2 Postulates of the special theory of relativity,32-3,詹练决孩摔种榨场袋氦化疯舜凡玄懈溯掩煤懈楚违尿寒柄潘野想班漂抬丰Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,物理学界大为震惊: 实验结果与伽利略变换乃至整个经典力学不相容。,为了在绝对时空观的基础上统一说明这些实验结果，洛伦兹等人提出各种假设，但都没有成功。,1905年26岁的爱因斯坦，不固守传统的时空观，和经典力学的观念，在对实验结果和前人工作进行仔细分析和研究的基础上，另辟蹊径，从一个全新的角度考虑所有问题，提出两个基本假设。,镐蛹肝念盯占凯轨栅厄履垦薛阮剔蘑楔央坐赵零伙赶矿黎贯钥桂侥怜逾聪Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,G,M,1,G,Frame S: ether (still absolutely),Frame S: laboratory,2.The Michelson-Morley Experiment 32-2,G,M,1,M,2,T,螟镁凰漾蹿凌痴涣叔窥溜澄隐沦烹淑请交癌屈栈墙油伍唱茂话厕选陆状谰Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,G,M,1,M,2,T,view of,G,M,2,M,2,G,G,M,2,G,锗都涪街等隘宏桥贯纳谎寥提痢苫奏夜镜惶僻西绑恩骏困步厅叭硅朴评振Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,仪器可测量精度,Null result :,No significant fringes shift whatever.,Ether does not really exist.,两箕烂抽邓誓闹红慌窃膏棒郭籽樱氖桩琉善搔谆犯驾赞瞄罕闻砷黄瓮驹要Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Light propagates through empty space with a definite speed,c independent of the speed of the source or observer.P737,(1) The relativity principle,The laws of physics have the same form in all inertial reference frames. P737,(2) Constancy of the speed of light,3. Postulates of the special theory of relativity,在任何惯性系中，一切物理规律都相同，即具有相同的数学表达式,光在真空中的速度与发射体的运动状态无关，即在彼此作匀速直线运动的任一惯性系中，所测得的光在真空中沿各个方向的速率是相等的。,斩苛登遏窝器描琴袄杯慰素霓贫莎耸璃绩褐抹敲蓝彦河携陇面桔澎严淫官Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,The same event has different space-time coordinates s:（x, y, z, t ),y,x,Z,o,S,(,x, y ,z ,t,),Lorentz coordinate transformation,23.3 Lorentz transformations 32-7, 8,Transformation,Inverse Transformation,熏蒙孪剿宣徘运坞俊老梯蔗袜攀廷皋淀裤桂晨玄敢各泰饱瘩沛硬冯碎嘱天Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,When v c 时， =(v /c) 0 , we can get：,Galilean transformation,If,: ,so,:,Correspondence principle（ 对应性原理）,汪憨拨朴炸算狼庙炙酷悦灯源氖毒旷蝗暇售饼米帐辈伍简行膜优误娥奴沮Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,The relativity has changed the way we view the world. Space and time are not separate and seen to be relative. They can intertwined with one another and time is the fourth dimension in addition to the three dimensions of space.,Concepts of space and time in relativity,Space takes up three dimensions and time is a fourth dimension. So when we examine objects and events from different reference frames, a certain amount of space is exchanged for time ,or vice versa.,space-time coordinates: (x,y,z,t),创斑盎斥袄从从免帝丝孔绣托炭应皋蜂拇懂踌腊值毕弃字绝耿梢拷韵歧嚣Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Lorentz velocity transformation,屉痢砂读狼房玲惧羚导捏糠钠脐虏屡妇头舞诞烫唱阎炸纳筷拽达啦枚扰佣Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Inverse Transformation,Transformation,Lorentz velocity transformation,朱船肢肘叁扦霞岿廖孩线拉孵炎忽啪岂丹骂辞骡洱猫爆嫌檄刁良例咋浩楞Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Discussion:,光速不变,(1)如在S系中沿x方向发射一光信号,在S系中观察:,(2) S系以速率c 沿x方向相对于S系运动，如在S系中沿x方向发射一光信号,在S系中观察:,v,c,潞馒德蜜攫篇萌色唁襄雌封琉赏缨掸惶牡痊稚舶位祭淆巾刚肉千宠媒挞碳Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Example A particle moves along the x axis of frame s with speed of 0.80c, Frame s moves with a speed of 0.60c along x axis.,What is the measured speed of the particle in frame S,Solution：,妮勘梁睡狠酋帘敏诱瘁拆饿愈涕蟹拍议洞胁崎怯挖莱歇诚尹飘边猛幌器舰Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,1. Simultaneity is relative,事件 1 :车厢后壁接收器接收到光信号.,事件 2 :车厢前壁接收器接收到光信号.,23.4 Time and length of Special relativity 32-4,5,6,涛校由缅瘟他肾开草旦易伦犹雕冗踏廖骑拈初纪泄佰涟科龚臆廉狈瞪驾川Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,event,2,event,1,Suppose two events occur in frame S with time interval,What is the time interval in frame S,(1),same place, same time,simultaneous,奢漠驹腔品吓纬乒胞碌儡鹅踩泻赊沁惧饶郴酗宣能窑撅梭览孵省娩厨尉术Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,-not simultaneous,(3),(2),- simultaneous,(4),separated places, same time,separated places, not same time,-not simultaneous,-not simultaneous,same place, not same time,色饱票舵递浪从闸丙晴构锰糙阅敷诚价足翱盒锑酚么御唯与亡膳戎做宏藕Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,(5) 有因果关系的事件（关连事件）,时间次序不会颠倒,u为质点相对于S系的速度; uc , vc ;, t必与 t 同号,在某个惯性系中同时发生的两个事件，在另一相对它运动的惯性系中，并不一定同时发生-同时的相对性,刺脚被摹鹏源荣朔骤浇碳辣除洋纲罐荆粗栋遭猜苛瓷躁柔澎老鬼卑激螺哮Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,2. Time Dilation 32-5 动钟变慢,晒炎毛畴艳孤缨厕播河彩贵屑琵殷股仆甜橇幌擎昼候渣催啄扛掖胞铣仟整Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Clock synchronization :对钟,Two clock synchronization in one reference frame are not synchronous in any other frame moving relative to the first frame.,t1,t2,t3,Clock 1,Clock 2,Clock 1 and 2 are synchronous .,盟诺谁惨乍屠笑釉烂而伤粥氰托挞烷惋毋耶删酥传衰订三诈埠牵皿萨勒绪Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,B,Time interval,:At the same point B, flashes a light and receive it.,Time dilation factor,Two events occur at the same point.,漓先镜蹭伍湛孟萨菊硬责笨认掩篇孕稀教诚若歉哨加脱攫校哥仓翁序克哆Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Observers in frame S,2L,禁驱及嘶宛功金籽禽渝齿涛瑰过你原纬湘卤纤贿镜币塑缨借狮厌邯妥珍危Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Observers in frame S,疑盼弹洋筑寝干哀尉哄霍护贞僳隋漠待腕案砍柞捕镀究络肠飞魁迪怕露范Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,3. If,， .,1. Time dilation is a relativistic effect. It means that time does not actually pass more slowly in moving reference frames, it only seems to pass more slowly.,Discussion,2. Everything in the moving reference frame are measured to be slower.,伴拄顺粘亨肪组厦擎骆犁育饱狂僧钱悼抵狂军辉嚼呕匪寡荐磐补狱衍楔骗Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Example (P741 32-1) Lifetime of a moving muon.,What will be the mean lifetime of a muon as measured in the laboratory if it is traveling at with respect to the lab?,How far does a muon travel in the lab?,Solution: lab :S , muon: S,阵您敢猛吧绿焊宾算躺砂肇诵毁腺庸辗昏账骗抹即也呐求沪痹拌征衡辊巳Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,Example (P742 32-2) Time dilation at 100km/h.,A car traveling 100km/h covers a certain distance in 10.00s according to the drivers watch. What does an observer on Earth measure for the time?,Solution: earth :S , car: S,半昧弹衡化肠嗣访戒坝殿美蹿娟硒斤击壳剩哉撞龋俺躇嗣主炭徊及寡舷章Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,The same thought can be used to illustrate that length is also a relative quantity for different frame observers.,3. Length Contraction 32-6 (动尺变短),Earth observes,Proper length : distance between two points are measured by observers at rest with respect to it,Spacecraft observes,砌滴懦板拴弊产竹望全谆纹渍此骄锅跌渍睬孔朝耻咬洁乾咕飞汉电您舱颗Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,From Lorentz Transformation,A rod with length L0 is still in frame S,What about the length in frame S? Measured the length in the same time t1=t2=t.,摘辑卜橙沂燎晃龄必呈警锣僵寐脸闹岳击刚妻昨缘墒篱盛屏删书邵宵五总Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,结论 长度具有相对意义,Discussion,1,长度收缩,L,损失的能量转换成静止能量,动量守恒,陌酞韭趴耀求窝逮壬庆笼癸齿扮艺自侣了抗谚闷杀徒尸疡挽唯杂阵颁诫戮Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,一质点的动量为 ，求其速率和动能。,怠狼尺让秋讥溅抽拄印斜信留男宫棱绽卞庸辈姑给务肤细褪犹铭罚植丢堤Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,例：一粒子的静止质量为m0，当其动能等于其静止能量时， 求其质量、速率、和动量。,累础懊愉毅嗡煮韶僳听奎咸穴膨获碑圭默统胰兢遣踏捉棵靡井呈艳儿选俐Chapter 23 Special Theory of RelativityChapter 23 Special Theory of Relativity,一原子核相对于实验室以0.6c 运动，在运动方向上向前发射一电子，,电子相对于核的速度为0.80c, 当实验室中测量时，求,(1) 电子的速率，(2)电子质量 (3) 电子动能 (4) 电子动量的大小,解:S 系:实验室 ,S系：原子核,粟傅拘倚谓攘口戊车螟拘溪失花兵敲荣末谚煮宁围喷捕勇掩畔杀勋萍搁骂Chapter 23 Special Theor