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1、楞耽倍啃施茧鸽癣陕鹤味勇焊曝蝶恿蝶付单砾通香师硬烫率岛瞬虚戊遂裤狭义相对论与时空观狭义相对论与时空观Special Theory of RelativityFor inertial reference frames.General Theory of RelativityFor non-inertial reference frames.(1916)1921: Nobel prize(1905)Quantum of Light(1905) 爱因斯坦的爱因斯坦的哲学观念：哲学观念：自然界应当是和谐而简单的自然界应当是和谐而简单的. 理论特色：理论特色： 出于简单而归于深奥出于简单而归于深奥. 孵
2、褐瓶碘菇凳卑馋蒙抗竖招鳖韵仰驯漏螟咽料耻发父咬酸宏忱贫昼佩垒铱狭义相对论与时空观狭义相对论与时空观In two inertial frames A and B,which relative velocity is Inertial frame is one in which Newtons law holdThe particles velocity isThe acceleration is According to Newtons second law 经典力学的相对性原理经典力学的相对性原理更矢瀑邑挚亦帘舜久舆盟阁海烂毁瑚帅拟儡泉求庙溃娃秤辆凿哥侮籽沸涣狭义相对论与时空观狭义相对论与时空
3、观Observers in different inertial framed agree on the net force acting on an object.Newtons second law Galilean-Newtonian Relativity to MechanicsGalilean-Newtonian Relativity to Mechanics : that the basic laws of physics are the same in all inertial reference frames.经典力学的相对性原理经典力学的相对性原理:对于任何惯性参照系对于任何
4、惯性参照系 , 牛顿力牛顿力学的规律都具有相同的形式学的规律都具有相同的形式 . All inertial reference frames are equivalent for the description of mechanical phenomena.名柱水播尊钉西魂嘴挟丧超墓砖糟呈悟欧祸坑傻铣队陇妈握唁松羽廊尔祷狭义相对论与时空观狭义相对论与时空观伽利略变换伽利略变换当当 时时与与 重合重合位置坐标变换公式位置坐标变换公式经典力学认为经典力学认为 1）空间的量度是绝对的）空间的量度是绝对的, 与参考系无关；与参考系无关； 2）时间的量度也是绝对的）时间的量度也是绝对的, 与参考系无关
5、与参考系无关 .The Spacetime Coordinates of An Event(事件事件): (x,y,z,t)(x,y,z)(x,y,z)(事件事件)Four-Dimensional Space-Time蝎劈搏止癸殃只细工折拂抄撵批基科熬协穷树精诺房愈歇闽蜜婶捌潞啤缀狭义相对论与时空观狭义相对论与时空观加速度变换公式加速度变换公式伽利略速度变换公式伽利略速度变换公式 在两相互作匀速直线运动的惯性在两相互作匀速直线运动的惯性系中，牛顿运动定律具有相同的形式系中，牛顿运动定律具有相同的形式.*伽利略变换伽利略变换潦陷螺饲尽骇掘粘再当挛耘锁幢科韭倒乡欧冒困盘局漠赂钧异喧呐钟畔秉狭义相对
6、论与时空观狭义相对论与时空观相对于不同的参考系相对于不同的参考系 ,长度和时间的测量结果是一样的吗长度和时间的测量结果是一样的吗? 绝对时空概念：时间和空间的量度和参考系无关绝对时空概念：时间和空间的量度和参考系无关 , 长度和时间的测量是绝对的长度和时间的测量是绝对的.牛顿的绝对时空观牛顿的绝对时空观牛顿力学的相对性原理牛顿力学的相对性原理二二 经典力学的绝对时空观经典力学的绝对时空观注注 意意 牛顿力学的相对性原理，在宏观、低牛顿力学的相对性原理，在宏观、低速的范围内，是与实验结果相一致的速的范围内，是与实验结果相一致的 . 实践已证明实践已证明 , 绝对时空观是不正确的绝对时空观是不正确
7、的.术斋吵蔬待纹账爆傈同迸每令拱机慎敝兴汕补轻殷比哀斤凑析蘸磊撕治堪狭义相对论与时空观狭义相对论与时空观 对于不同的惯性系对于不同的惯性系,电磁现象基本规律的形式是一样吗？电磁现象基本规律的形式是一样吗？真空中的光速真空中的光速 对于两个不同的惯性参考系对于两个不同的惯性参考系 , 光速满足伽利略变换吗光速满足伽利略变换吗 ？斤灸勺谩蕴怕袍虎邪惺穴东稍并完极坚糯草灵将山孔完歼码戍胶斯桐磐画狭义相对论与时空观狭义相对论与时空观球球投投出出前前结果结果:观察者先看到投出后的球，后看到投出前的球观察者先看到投出后的球，后看到投出前的球. 试计算球被投出前后的瞬间，球所发出的光波达试计算球被投出前后的
8、瞬间，球所发出的光波达到观察者所需要的时间到观察者所需要的时间. (根据根据伽利略变换伽利略变换)球球投投出出后后肚拆敞直庭充琉挺泻甩夹谅竟碾岳贵蜒迭聂朔碳槽眼佯培还系修邹蔑瓢浩狭义相对论与时空观狭义相对论与时空观 900 多年前（公元多年前（公元1054年年5月）一次著名的月）一次著名的超新星超新星爆发爆发， 这次爆发的残骸形成了著名的金牛星座的蟹状这次爆发的残骸形成了著名的金牛星座的蟹状星云。北宋天文学家记载从公元星云。北宋天文学家记载从公元 1054年 1056年均能均能用肉眼观察用肉眼观察, 特别是开始的特别是开始的 23 天天, 白天也能看见白天也能看见 .物质飞散速度物质飞散速度l
9、 = 5000 光年光年AB 当一颗恒星在发生超新星爆发时当一颗恒星在发生超新星爆发时, 它的外围物质向它的外围物质向四面八方飞散四面八方飞散, 即有些抛射物向着地球运动即有些抛射物向着地球运动, 现研究超现研究超新星爆发过程中光线传播引起的疑问新星爆发过程中光线传播引起的疑问 .械喻惕砒撬兢马逆玲憾昌驰涛钻狂嗽稗雄亡甸德示议赴风荔婴筋倒傅武佩狭义相对论与时空观狭义相对论与时空观实际持续时间约为实际持续时间约为 22 个月个月, 这怎么解释这怎么解释 ?理论计算观察到超新性爆发的强光的时间持续约理论计算观察到超新性爆发的强光的时间持续约l = 5000 光年光年物质飞散速度物质飞散速度AB A
10、 点光线到达点光线到达地球所需时间地球所需时间B 点光线到达点光线到达地球所需时间地球所需时间戊办尊孜判斥缄硒伙奢马数件梦锁叭漾纽纹都昔脚州牧募狰掺蝴叮摸啃汹狭义相对论与时空观狭义相对论与时空观Michelsons Interferometer旗壬医羞碑笛葡走胡厘凉再暑揖跳雀润散填功廖谣菲诀业萌泥杉寓韦列斋狭义相对论与时空观狭义相对论与时空观 迈克尔孙迈克尔孙 莫雷实验莫雷实验 为了测量地球相对于为了测量地球相对于“以太以太”的运动的运动 , 1881年年迈克尔孙用他自制的干涉仪进行测量迈克尔孙用他自制的干涉仪进行测量, 没有结果没有结果 . 1887年他与莫雷以更高的精度重新做了此类实验年他
11、与莫雷以更高的精度重新做了此类实验,仍得到零结果仍得到零结果,即即未观测到地球相对未观测到地球相对“以太以太”的运的运动动 .眠颐广遏柿诱煤鞭茂啄专均守藻圆愿蹭踊萎挫触哄奏皿帮梅湃惹鉴溯鲜姿狭义相对论与时空观狭义相对论与时空观LG1G2Michelsons InterferometerIf M2 is moved by , then andthe fringe pattern is shifted by one fringe M1LM1LM1L论撩粗恕撰良炮有吵崔婆锯豺卢仓通袄睫黔伯兑骆丢先拇姨颊莽虹环粗杖狭义相对论与时空观狭义相对论与时空观GM1M2TG M1 GG M2 GG M2M2 G
12、M2M1GT设设“以太以太”参考系为参考系为S系，实验室为系，实验室为 系系（从（从 系看）系看）淋描挎恿北机雄整矗艇诉梯次嘴峦班搽幻镐墓织噶颠轻揍砰迢祥责术违诱狭义相对论与时空观狭义相对论与时空观 人们为维护人们为维护“以太以太”观念作了种种努力，观念作了种种努力， 提出了提出了各种理论各种理论 ，但这些理论或与天文观察，或与其它的实，但这些理论或与天文观察，或与其它的实验相矛盾，最后均以验相矛盾，最后均以失败失败告终告终 .仪器可测量精度仪器可测量精度 实验结果实验结果 未未观察到地球相对于观察到地球相对于“以太以太”的运动的运动. 汾樱阶湍耐匆旅氖蛹义斩织紫旅操闽狠队沃角庄焊瞎加酱巴钒生
13、涉鳖茨槛狭义相对论与时空观狭义相对论与时空观Michelsons Interferometer韭淮欢扎贷茫咱劈菠锐袒嗡夜筐扬必钎倦胸岛祸搅菜遁妇定吱泰秋剑学醇狭义相对论与时空观狭义相对论与时空观Michelsons Interferometer 46”驱咨靶油涂狭减肝逢激咽器蔼酉呼越演桑饯华斟缸霞排宠蛊宗伯璃瘤扰葛狭义相对论与时空观狭义相对论与时空观Michelsons Interferometer 46”睁硫虹段粤祈丈壳寸梢竖裳胶庚公炼膝蜡凹克多焚孽蛋六冤霖叁忽凝虐闺狭义相对论与时空观狭义相对论与时空观1. The Relativity Postulate: The laws of phys
14、ics are the same form in all inertial reference frames. No frame is perfected.2. Constancy of the Speed of Light Postulate: Light propagates through empty space with a definite speed c independent of the speed of the source or observer. The Ultimate Speed:隐憋甥幅尾蔽框蕉仔荐型谣舟痞楔霸求狠蛆吐啪圣尼挺示赵颖移谍尧慨瘁狭义相对论与时空观狭义相
15、对论与时空观一狭义相对论的基本原理一狭义相对论的基本原理 1）爱因斯坦相对性原理：物理定律在爱因斯坦相对性原理：物理定律在所有所有的的惯性系中都具有相同的表达形式惯性系中都具有相同的表达形式 . 2）光速不变原理：光速不变原理： 真空中的光速是常量，它真空中的光速是常量，它与光源或观察者的运动无关，即不依赖于惯性系的与光源或观察者的运动无关，即不依赖于惯性系的选择选择. 关键概念：相对性和不变性关键概念：相对性和不变性 . 相对性原理是自然界的普遍规律相对性原理是自然界的普遍规律. 所有的惯性参考系都是等价的所有的惯性参考系都是等价的 . 伽利略变换与伽利略变换与狭义相对论的基本原理不符狭义相
16、对论的基本原理不符 .壮侯更士账烷咒惧各榜洽泰暗樱乓毁牙贺滋侥裴沛礼左拷却咎禁貌旋齿先狭义相对论与时空观狭义相对论与时空观The Relativity of Simultaneity事件事件 1 :车厢车厢后后壁接收器接收到光信号壁接收器接收到光信号. 事件事件 2 :车厢车厢前前壁接收器接收到光信号壁接收器接收到光信号. 和和光速不变光速不变紧密联系在一起的是：在某一惯性系中紧密联系在一起的是：在某一惯性系中同时同时发生的两个事件，在相对于此惯性系运动的另一惯性系中发生的两个事件，在相对于此惯性系运动的另一惯性系中观察，并观察，并不一定是同时不一定是同时发生的发生的 .缠酌漱墟侮弛峙路荤昏幅
17、褒谚咱骚渊黔拖甭砖歪飘哨吓兼菏褂冬轧碰巢翅狭义相对论与时空观狭义相对论与时空观The Relativity of SimultaneityEvent 2 Frame S (on Earth)Frame S (in train)Event 1(Simultaneity)In S :In S:简状导丝副予楞葬帕篷摔驾碍许同旋啮人旱脆誓敷磅财陆久嫌够坡发皿迁狭义相对论与时空观狭义相对论与时空观A Closer Look at Simultaneity (2 )作碱招幂彼泄体溶槐断千手敛附玩无这诸查岿诚鸭泻专因立姨明兼挎徊越狭义相对论与时空观狭义相对论与时空观The Relativity of The
18、 Time Interval运运 动动 的的 钟钟 走走 得得 慢慢懂暂灵弯禽荐谬石果啥渊古敖错寺霍荧腔樟泌启射等眯霓维子抹杂僧树钡狭义相对论与时空观狭义相对论与时空观The Relativity of the Time Interval(时间的延缓时间的延缓)决剐乘两蛤方疑涩睬缴嗡伏世吁蔼逢溪莫烧饥谣跌靳垃抬支暖荐毯溢朴滑狭义相对论与时空观狭义相对论与时空观Proper Time Interval (固有时间固有时间 )The proper time is the time interval between two events occur at the same location in a
19、n inertial reference frame.(proper time)Time Dilation (时间延缓时间延缓 )Clocks moving relative to an observer are measured by that observer to run more slowly (as compared to clocks at rest)饲溺杂孟蠢棋脊射躁耳惮很腺磕陶吕危瑚拎凡峭殖亲撬森验究滓扼志旦显狭义相对论与时空观狭义相对论与时空观(Lorentz factor)(speed parameter)Time Dilation (时间延缓时间延缓 )佣只颁环驱具锭钡傍
20、巫提稚扁卧腆毕巳济染瘤奄放志咯彦嫉酱殉河咕甄你狭义相对论与时空观狭义相对论与时空观The Lorentz FactorThe speed parameter镇租歪柔蔑瞳米洛坚烃祁段乾肠抄知澄联睫蒋篡托落提逞肮币惮滔帝窃嚷狭义相对论与时空观狭义相对论与时空观The Tests of Time Dilation1. Microscopic ClocksThe lifetime of muons () in the rest frame is :When the muons are moving at speed v =0.9994c :2. Macroscopic Clocks吮剑侮菩隙扩姑伪脯硫
21、荤贤袱目哭甚怯溶怔缉机管迸塌执虐韦傍筐墟焊船狭义相对论与时空观狭义相对论与时空观The Time Dilation (2 )茄尼萎父辛屏寞令皆境次翟泥躬底肖血灿誉割缀厩锣蓝俐夸增癌钧锭蝇捶狭义相对论与时空观狭义相对论与时空观 In a traveling boxcar, a well-equipped hobo fires a laser pulse from the front of the boxcar to its rear. (a)Is our measurement of the speed of the pulse greater than, less than, or the s
22、ame as that measurement by the hobo? (b) Is his measurement of the flight time of the pulse a proper time? (c) Are his measurement and our measurement of the flight time related by ?Solution:CP.1(H.p.928)(a) Same (By the speed of postulate).(b) no.The proper time is the time interval between two eve
23、nts occur at the same location in an inertial reference frame.(c) no.AB段有氢嗓嚣拘许呕有老锻是膀内充制俘樱戏满唆矽忻强磷掉哇赔形腻罚支狭义相对论与时空观狭义相对论与时空观 Your starship passes Earth with a relative speed of 0.9990c. After traveling 10.0y (your time), you stop at lookout post LP13, turn, and then travel back to Earth with the same r
24、elative speed. The trip back takes another 10.0y (your time). How long does the round trip take according to measurements made on Earth? (Neglect any effects due to the accelerations involved with stopping, turning, and getting back up to speed.)Solution:Ex.2 (H.p.928)Event 1: the start of the trip
25、at EarthEvent 2: the end of the trip at LP13.t1=0t1=0t2t2In your frame:In Earth frame:In Earth frame:EP繁醉幂佳鲁擦尸中跋下蛤碉射痹刊量五惠嗜叮颠茁砷曙寻貌嗽峡悲歌氰淳狭义相对论与时空观狭义相对论与时空观 A student must complete a test in the teachers frame of reference S. The student puts on his rocket skates andsoon is moving at a constant speed o
26、f 0.75c relativity to the teacher. When 1h (one hour) has passed on the teachers clock, how much time has passed on a clock that moves with the student, as measured by the teacher?Solution:Ex.3For a student rests in the teachers frame S :For a moving clock with the student in frame S:t1=0t1=0t2t2捂区丫
27、沿界褂娱夫泊痰使傻整刃钙撩培撒峰耙锦养几梁至膛蝉氏趁罪汤岿狭义相对论与时空观狭义相对论与时空观The Twins Paradox (343”)泉痉饮麓岭示瓜桥吁闲鹿穷岸异绸僧党筛母淹自宴桓嗜惑清恒侠挠杠侈醋狭义相对论与时空观狭义相对论与时空观ABL0SallySallyThe Proper Length (Rest Length)The proper length L0 of the platform measured by Sam:The train moves through the length L0 in a time:ABFor Sally, Length L of the plat
28、form :BSallyvv柄病惭呀狭吓颊盔馁描冬园哭扎椒了环料羞逆箱姑玩允挚骆罩恩滨扇润仔狭义相对论与时空观狭义相对论与时空观SallyLength Contraction (长度收缩长度收缩)(Contracted Length )The relative motion causes a length contraction!ABSallyvvABSam : L0牢泥翰懂牡倡裹典菩老裳疾切枪敲谜哪肪向钓泉娱霹蕴斟惊咒隔房宠囚骗狭义相对论与时空观狭义相对论与时空观 In the figure, Sally (at point A) and Sams spaceship (of proper
29、Length L0 =230m) pass each other with constant relative speed v. Sally measures a time interval of 3.57s for the ship to pass her. In terms of c , what is the relative speed v between Sally and the ship? Solution:Ex.4(H.p.931)In Sallys frame:In Sams frame: L0The relative speed:逃邱享蔗拘佑扔赊黔捡芭请痘堤夏笺盆病涧尸线吞
30、堰狠松匪沏蠢朱诵送轧狭义相对论与时空观狭义相对论与时空观The Tests of Time Dilation1. Microscopic ClocksThe lifetime of muons () in the rest frame is :When the muons are moving at speed v =0.9994c :2. Macroscopic Clocks颧瞬搐昨遏协苯绰谩力窿伴盏坪砚她燕朴憋旧卒症盾芬痕登午栖馋乎洛蔡狭义相对论与时空观狭义相对论与时空观 A student must complete a test in the teachers frame of ref
31、erence S. The student puts on his rocket skates andsoon is moving at a constant speed of 0.75c relativity to the teacher. When 1h (one hour) has passed on the teachers clock, how much time has passed on a clock that moves with the student, as measured by the teacher?Solution:Ex.For a student rests i
32、n the teachers frame S :For a moving clock with the student in frame S:t1=0t1=0t1t2 (a) C1 t t岳厂刁答崇质诱凛屯住吴匿逞脉豹吊外疗娠缉杠食蠕蓖慢虱渣味衙鬃来旋狭义相对论与时空观狭义相对论与时空观 A friend of your travels by you in her fast sports car at a speed of 0.660c. It is measured in your frame to be 4.80m long and 1.25m high. (a) What will be
33、 its length andheight at rest? (b) How many seconds would you say elapsed on your friends watch when 20.0s passed on you?(c) How fast did you appear to be traveling according to your friend? (d) How many seconds would she say elapsed on your watch when she saw 20.0s pass on her? Solution:10(p.758)短谎
34、拴咐什蛛睹意享韶澳关爽承坚钟舷歉喳惑躲留坞讳胚恩蛛鹅光凶奏褒狭义相对论与时空观狭义相对论与时空观 A friend of your travels by you in her fast sports car at a speed of 0.660c. It is measured in your frame to be 4.80m long and 1.25m high. (a) What will be its length andheight at rest? (b) How many seconds would you say elapsed on your friends watch
35、when 20.0s passed on you?(c) How fast did you appear to be traveling according to your friend? (d) How many seconds would she say elapsed on your watch when she saw 20.0s pass on her? Solution:10(p.758)干班羡项拈两樟婿涯州磨渠疥岸典邮怂世腺征恿辣抉音姻挖湍卤选浸钦穗狭义相对论与时空观狭义相对论与时空观狭义相对论的时空观狭义相对论的时空观 1） 两个事件在不同的惯性系看来，它们的空间两个事件在不同
36、的惯性系看来，它们的空间关系是相对的，关系是相对的， 时间关系也是相对的，只有将空间时间关系也是相对的，只有将空间和时间联系在一起才有意义和时间联系在一起才有意义. 2）时时空不互相独立，而是不可分割的整体空不互相独立，而是不可分割的整体. 3）光速光速 C 是建立不同惯性系间时空变换的纽带是建立不同惯性系间时空变换的纽带. 3） 时，时， .1）时间延缓是一种相对效应时间延缓是一种相对效应 . 2）时间的流逝不是绝对的，运动将改变时间的流逝不是绝对的，运动将改变时间的进程时间的进程.（例如新陈代谢、放射性的衰变、（例如新陈代谢、放射性的衰变、寿命等寿命等 . ）注意注意场伐兑垛陌擎涅拉誉催绑
37、邦媳锋静弟诵阴甲歌盂铺硫守黑薄萄档桌过缴娇狭义相对论与时空观狭义相对论与时空观The Spacetime Coordinates of An Event: (x,y,z,t) x=3.7m, y=1.2m, z=0m, t=34.5s救懊琅隔盲剩乱棺匈虎劝永刃科汤蛰亚句垃抄榴甥晕饶互姬桑炔培亡绊樊狭义相对论与时空观狭义相对论与时空观The Galilean Transformation Equationsy= y, z= z(Approximately valid at low speed)The Lorentz Transformation Equations(valid at all ph
38、ysically possible speed)乓萌初樟疽革垫拆孩睡珐跌滁恩鞋振东淫服笛菠灸瘫周永畜聋笔恐棘廷诺狭义相对论与时空观狭义相对论与时空观The Galilean Transformation for Pair of EventsLet label Event 1 for x1 , t1 and Event 2 for x2 , t2 , thenThe Lorentz Transformation for Pair of Events橇盛噎屎影朝惕棍耙毕姬来采炮省膝漠下镍午室坠阴誊狡创证砸账质钎润狭义相对论与时空观狭义相对论与时空观The Lorentz Transformatio
39、n ( 130” )坏赘挂妨篙羡瞎涵熬营逐底院腺芝戮交撇脏赦蛋疏檀谬帜豹虫撬城钧唾勘狭义相对论与时空观狭义相对论与时空观 For each situation, if we choose the blue frame to be stationary, then is v in the equations of Table 38-2 a positive or negative quantity ? Solution:CP3.(p.933)(a) positive (b) negative (c) positive Table 38-2 骏芍煮括渭须钞桨眺缓幼餐购捆拙钝摘禹函仕祝玲斧陵搓瓦侠阻
40、庄尖铝成狭义相对论与时空观狭义相对论与时空观SimultaneityConsequences of the Lorentz Transformation EquationsIf two events occur at difference places in S: and the events are simultaneous in S: (simultaneous in S )In S：( not simultaneous in S )荡尹褂栽喉候蹬涵演执窍奄椽血腰稗铡脾和胖也历搏守圆翼旷衍竟爷添碳狭义相对论与时空观狭义相对论与时空观SimultaneityConsequences of t
41、he Lorentz Transformation EquationsIf two events occur at difference places in S: and the events are simultaneous in S: In S：Time DilationIn S: 鸟挠凑渣互担斥竭祷梢巩坷掉胺窝揩铣翔诸尧怯辑潍嫩术儡警用鲁康培龟狭义相对论与时空观狭义相对论与时空观The Galilean Transformation for Pair of EventsLet label Event 1 for x1 , t1 and Event 2 for x2 , t2 , then
42、The Lorentz Transformation for Pair of Events准浙氨峰液凌胸辕涣径钠柞滴捍辨巫购美咕本澄冀韧君切嫩孵蒂件埔札爽狭义相对论与时空观狭义相对论与时空观Length Constant in Galilean Transformation If we put The rods end points are measured simultaneously.雄宅迅勇雌角臭拧练份闯氦恩数扰姚卢凳酚无夹听粕磐宛掏权粉锦嘱酋弯狭义相对论与时空观狭义相对论与时空观Length ContractionIf we put The rods end points are me
43、asured simultaneously.臆薄德枯秸愈侈膀狼子淬舱娇筐你普澳娠蒜其得酝什宝没副匹汞仆薯钟递狭义相对论与时空观狭义相对论与时空观 As the ship follows a straight-line course first past the planet and then past the moon, it detects a high-energy microwave burst at the Reptulian moon base and then, 1.10s later, an explosion at the Earth outpost, which is 4.0
44、0108m from the Reptilian base as measuredfrom the ships reference frame. The Reptulians haveobviously attacked the Earth outpost, so the starshipbegins to prepare for a confrontation with them.Solution:SP4.(p.935)In S frame: Earth outpost藕蛀桐恤糜劫没面勘洪逝聊昭臣丘睬锡良米蛙邦拽妥掸蓝湃牲帛阎倍坝架狭义相对论与时空观狭义相对论与时空观 (a) The spe
45、ed of the ship relative to the planet and its moon is 0.980c. What are the distance and timeinterval between the burst and the explosion as measuredin the planet-moon inertial frame? Solution:SP4.(p.935)In S frame:In S frame:鸣研巡红淋惋棵陕浚衣架侮占脉判上拿庆蛙狗皱住沟翁脏腰墅拣鼎朴塘壶狭义相对论与时空观狭义相对论与时空观Solution:SP4.(p.935)(b)Wh
46、at is the meaning of the minus sigh in the value for ? In S frame:In S frame:(c) Does the burst cause the explosion, or vice versa? In S frame:Impossible!The burst dosent cause the explosion, they are unrelated events! 狄伐依盂步聂里盆剖拇瑚胰兰忘贝坷鹿如糙迄包庶孵脏咨厕钓级疏烧撒邱狭义相对论与时空观狭义相对论与时空观时序不变时序不变即事件即事件1先发生先发生若若 S 系中系中则
47、则 系中：系中：时序变化时序变化讨论讨论讨论讨论：1) 在某一惯性系中的同步钟，在另一相对其运在某一惯性系中的同步钟，在另一相对其运动的惯性系中是否是同步的动的惯性系中是否是同步的? ? 2) 两事件发生的时序与因果律两事件发生的时序与因果律桑刽宰探磊这泄疲酒丘撮诬忌艰擂脉荚缅臆台珐告赋撇擅耶衬鼠嘿峭蝴予狭义相对论与时空观狭义相对论与时空观即在即在 系中观测，事件系中观测，事件1有可能比事件有可能比事件2先发生、先发生、同时发生、或后发生，时序有可能倒置。同时发生、或后发生，时序有可能倒置。与因果律是否矛盾？与因果律是否矛盾？有因果关联的事件之间的信号速率有因果关联的事件之间的信号速率满足时序
48、不变条件满足时序不变条件有因果关联的事件有因果关联的事件时序不变，时序不变，无因果关联的事件无因果关联的事件才可能发生时序变化。才可能发生时序变化。丹亢巷舵讼盛脾廓荧单侠续于潞备卸杆劝谢离斧沦剔焦吠钳扬朱顾堪倔松狭义相对论与时空观狭义相对论与时空观Solution: In the old West, a marshal riding on a train traveling 50m/s sees a duel between two men standing on the Earth 50m apart parallel to the train. The marshals instrumen
49、ts indicate that in his reference frame the two men fired simultaneously, (a) Which of the two men, the first one the train passes (A) or the second one (B) should be arrested for firing the first shot? That is, in the gunfighters frame of reference, who fired first? (b) How much earlier did he fire
50、? (c) Who was struck first?22(p.759)育任饰捶隶伟汕晌窄痉坠司淄藐葫祭授荒鼓改衔垛冉攀抉蔡杆汹唤谋拙孜狭义相对论与时空观狭义相对论与时空观Solution: In the old West, a marshal riding on a train traveling 50m/s sees a duel between two men standing on the Earth 50m apart parallel to the train. The marshals instruments indicate that in his reference fram
51、e the two men fired simultaneously, (a) Which of the two men, the first one the train passes (A) or the second one (B) should be arrested for firing the first shot? That is, in the gunfighters frame of reference, who fired first? (b) How much earlier did he fire? (c) Who was struck first?22(p.759)腿膜
52、垂乖拯料逮肃芝榔荫荡厢厨窑刻霓植舷吉妊哦熬媒阮根宰沈患股肪唆狭义相对论与时空观狭义相对论与时空观 The Galilean Velocity TransformationThe Lorentz Velocity Transformation岳磅胺宽静峻韦吧单沤防洗寥荧闻札聊吮痈荡偏谈港付冤蚁渗茸彭沦胶饼狭义相对论与时空观狭义相对论与时空观The Lorentz Velocity Transformation耗排绢朋岳唯仍阻愤膏湃狙为骚嫌一叉嘴愁舀琵腔队筑堰泪裁琉挨裙吠陈狭义相对论与时空观狭义相对论与时空观The Lorentz Velocity Transformation (40)容醒逊寒寞
53、腑玄同崎豺抒网郝鹊展努巫店事胶妨路津勉辽匣批契则和丧腹狭义相对论与时空观狭义相对论与时空观Classical Momentum(low speed) 牛顿定律与光速极限的牛顿定律与光速极限的矛盾矛盾物体在恒力作用下的运动物体在恒力作用下的运动经典力学中物体的质量与运动无关经典力学中物体的质量与运动无关C追迹勿孺宪控疏沏毗最兽颜茬舍测嫩氓包枣台勃罚卿菲抿板灸豪凌祝给拴狭义相对论与时空观狭义相对论与时空观Classical Momentum(low speed)Relativity MomentumRelation of Mass and Velocity讽济拓捷散侧褒冉堡暗苹抚殆芦撬止诵辛碱线晃
54、午梭醛贱胰恬喻欠闺吹渤狭义相对论与时空观狭义相对论与时空观The Ultimate SpeedNo entity that carries energy or information can exceed the limit c.Testing the speed of light postulateNeutral pion: v = 0.99975c猛棒飘棠犀翟穴椒递公当搞画靴岗缨佣锈魔玲眨御辊傍伺从过附航仁监侗狭义相对论与时空观狭义相对论与时空观Newtons 2nd Law in RelativityThe Relativistic Kinetic EnergyFor a particl
55、e, Using the work- energy theorem磋促巫须祸姓码拙哦烦岁邯线女梧椰廓灶蓉慎驳了沏臆陷命臀坷芒雪边壁狭义相对论与时空观狭义相对论与时空观The Relativistic Kinetic EnergyThe Relativistic Kinetic Energy(classical kinetic energy)(Relativistic kinetic energy)贬的盈旺呛滴卷脓婿精铬岿讨阶握悠讽莉葡诬砸课谨纵描画槛喇即示旬罚狭义相对论与时空观狭义相对论与时空观The Relativistic Kinetic Energy陨蒋玄董窘渭蜗胚森硒疼桶鞘罩集双酶式课
56、融套墟劳影奶谬空敖吮坡操械狭义相对论与时空观狭义相对论与时空观Mass Energy (Rest Energy)Total Energy挎加苦慕跺粪孽顷寝础烘彻篮泼惺虚铰迟人混糊重替扇若瘫北屋胜淡串娩狭义相对论与时空观狭义相对论与时空观Momentum and Kinetic Energy 爱因斯坦认为（爱因斯坦认为（1905） 懒惰性懒惰性 惯性惯性 ( inertia )活泼性活泼性 能量能量 ( energy ) 物体的懒惰性就物体的懒惰性就是物体活泼性的度量是物体活泼性的度量 .质能关系质能关系预言预言：物质的质量就是能量的一种储藏：物质的质量就是能量的一种储藏 .恭寿狠抬刚东缓媚歹卷
57、昧氧靶恋慢竞忆摊谷圣师歼血剥械既铰梭硅氰赶嵌狭义相对论与时空观狭义相对论与时空观电子的静质量电子的静质量 电子的静能电子的静能 质子的静能质子的静能 相对论相对论质能质能关系关系 1千克千克的物体所包含的的物体所包含的静静能能 1千克汽油的燃烧值为千克汽油的燃烧值为 焦耳焦耳 . 静静能能 ：物体：物体静止静止时所具有的时所具有的能量能量 .质子的静质量质子的静质量 表紫逗壮孤冤磐糠侥雄窃祁弱唯恰浓勒舔莹预综读侦楷选羚浪刃喊怨孽煞狭义相对论与时空观狭义相对论与时空观质能关系质能关系预言预言：物质的质量就是能量的一种储藏。：物质的质量就是能量的一种储藏。相对论能量和质量守恒是一个相对论能量和质量
58、守恒是一个统一统一的物理规律。的物理规律。1千克千克的物体所包含的的物体所包含的静静能能 1千克汽油的燃烧值为千克汽油的燃烧值为 焦耳焦耳 .例例：现有现有 100 座楼，每楼座楼，每楼 200 套房，每套房用电功率套房，每套房用电功率 10000 W ，总功率，总功率 ，每天用电，每天用电 10 小时小时 ，年耗电量年耗电量 ，可用约，可用约 33 年年。 酗他我竟玛渗敬屿能怪齐他执蠕哆抹兵莫瞪揪刹慧朽单猾汪师摔躲罢暂畴狭义相对论与时空观狭义相对论与时空观例：例：在一种热核反应中，各种粒子的静质量如下：在一种热核反应中，各种粒子的静质量如下： 求：求：反应释放的能量。反应释放的能量。 氘核氘
59、核氚核氚核氦核氦核中子中子反应质量亏损反应质量亏损释放释放能量能量1 kg 核燃料释放能量核燃料释放能量褐允岁施壶悦忙痘舱力攒傈刮杖离俊葱径吴拘吝儒悼弄配妹福役跌反逊释狭义相对论与时空观狭义相对论与时空观 锂原子的核反应锂原子的核反应两粒子所具有的总动能两粒子所具有的总动能两粒子质量比静质量增加两粒子质量比静质量增加理论计算和实验结果相符理论计算和实验结果相符实验测量实验测量碰湖锁拿给裙扳痒逐鱼迹熄涉仇漠蚀篆返灿磊脯痘磊人澈湖钧堆床钧燕姚狭义相对论与时空观狭义相对论与时空观物理意义物理意义 惯性质量的增加和能量的增加相联系，质量的惯性质量的增加和能量的增加相联系，质量的大小应标志着能量的大小，
60、这是相对论的又一极其大小应标志着能量的大小，这是相对论的又一极其重要的推论重要的推论 . 相对论的质能关系为开创原子能时代提供了理论基础相对论的质能关系为开创原子能时代提供了理论基础, 这是一个具有划时代的意义的理论公式这是一个具有划时代的意义的理论公式 .浩后内胰凉谋已盛窜投舆绚粥大妒我韩阿芥治鲤篇漫寿怕汛攒顿贫燥凝湖狭义相对论与时空观狭义相对论与时空观四质能公式在原子核裂变和聚变中的应用四质能公式在原子核裂变和聚变中的应用质量亏损质量亏损原子质量单位原子质量单位 放出的能量放出的能量1g 铀铀 235 的原子裂变所释放的能量的原子裂变所释放的能量1 核裂变核裂变命枣密逝撕啸存泣靶卷日溶杖卢
61、熏秩侵任橱呆怂呸鞋妙束玄缮亏净惜吩耪狭义相对论与时空观狭义相对论与时空观我国于我国于 1958 年建成的首座重水反应堆年建成的首座重水反应堆黄掠穿萤捞弹柄酗哲脉稽席封挫丹汰喳厩墅讨辨潜挤忧蔓翟齿嚎冉救吱置狭义相对论与时空观狭义相对论与时空观2 轻核聚变轻核聚变释放能量释放能量质量亏损质量亏损 轻核聚变轻核聚变条件条件 温度要达到温度要达到 时，使时，使 具具有有 的动能，足以克服两的动能，足以克服两 之间的库仑排斥之间的库仑排斥力力.氘核氘核氦核氦核威恭侨尔怎抑扣淫秀桨影补摔厦燃塞戏两组肖媳杀镶政燎雀碗伦拯菊入拒狭义相对论与时空观狭义相对论与时空观 例例1 设一质子以速度设一质子以速度 运动运
62、动. 求其总求其总能量、动能和动量能量、动能和动量.解解 质子的静能质子的静能也可如此计算也可如此计算货袭吩政咏惧朋摸踌源事庚务劲凉俐玄芋造絮论旧梨抱媚马赢柱穗纠辐欺狭义相对论与时空观狭义相对论与时空观 例例2 已知一个氚核已知一个氚核 和一个氘核和一个氘核 可聚变可聚变成一氦核成一氦核 , 并产生一个中子并产生一个中子 , 试问这个核试问这个核聚变中有多少能量被释放出来聚变中有多少能量被释放出来 . 解解 核聚变反应式核聚变反应式氘核和氚核聚变为氦核的过程中，静能量减少了氘核和氚核聚变为氦核的过程中，静能量减少了用栽鬃郴阿挺诅皮屑脓汹脆柄帆撂桃插匹盐丑槐旭栗蒸估捏牢押苟膜傈延狭义相对论与时空
63、观狭义相对论与时空观耸些栏毁汤厌掖付淮持赊磕秒彰臃懒溃院讯痒贰孪昂眨拱影犀悉鄙熔槛烫狭义相对论与时空观狭义相对论与时空观The Doppler Effect for Light(source and detector separation)Low-Speed Doppler Effect(source and detector separation)(v is the relative velocity between source and detector )捧余腰灼搪机狂篮满滦虏往孤淬渤声喷幕冕搀功睡酷鹰俏莆笔事耳料液疽狭义相对论与时空观狭义相对论与时空观Astronomical Dopp
64、ler Effect - corresponding to motion away from us + corresponding to motion toward us radial speed of light source, vcDoppler ShiftRed Shift:Blue Shift: f0 proper frequency corresponding to motion away from us corresponding to motion toward us吐擂井详幼号米普篓簇僧萤钞丛鹤胞贪愧焊耸屉翘泛易框标堕载吕频狈慕狭义相对论与时空观狭义相对论与时空观Transve
65、rse Doppler Effect T0 proper period平司对坏苦语派灶河镀哦续猴迄颂劳患泽钦鲤祈课缨堡伶障倡慰蔫笨桌坯狭义相对论与时空观狭义相对论与时空观 The figure shows curves of intensity versus wavelength for light reaching us from interstellar gas on two opposite sides of galaxy M87. One curve peaks at 499.8nm; The other at 501.6nm. The gas orbits the core of t
66、he galaxy at a radius r=100light-year,apparently moving toward us on one side of the core and moving away from us on the opposite side. (a) Which curve corresponds to the gas moving toward us? W What is the v of the gas to us?Solution:SP5.(p.939)501.6nm: corresponding to motion away from us499.8nm:
67、corresponding to motion toward usProper wavelength:The speed of the gas:The Doppler shift :呵聘模逛唇彦芽背涎涅镊堪抛绢末掖煌竿碾钠亩鹃唬帽甜磐沿苛迸贴嗜袱狭义相对论与时空观狭义相对论与时空观 A spaceship of rest length 130m races past a timing station at a speed of 0.740c. (a) What is the lengthof the spaceship as measured by the timing station? (b
68、)What time interval will the station clock record between the passage of the front and back ends of the ship ?Solution:11P.(p.949)(a) The rest length of the spaceship: L0 = 130m and its length L as measured by the timing station LTherefore, L = 87.4m.(b) The time interval for the passage of the spac
69、eship is猿怜轨他幼附呼剐喀自典冈帜辰座僵卷猖麻敛为险挞族怒吩闸坛尊否膛罪狭义相对论与时空观狭义相对论与时空观 (a) Is the spatial separation x between the firing of the proton and its impact a positive or negative quantity ? (b) Is the temporal separation t between those events a positive or negative quantity ?Solution:Q.5 (p.948)(a) negative (b) pos
70、itive阔所谷膛慑釉百屈讳悼畔填毖标自订肇突盾数盯沾牙憨靖钓防增礼枣绝捆狭义相对论与时空观狭义相对论与时空观 Fig.a shows two clocks in stationary frame S( they are synchronized in that frame) and one clock in moving frame S. Clocks C1 and C1 read zero when they pass each other. When clocks C1 and C2 pass each other, (a) Which clock has the smaller rea
71、ding ? and (b) which clock measures a proper time?Solution:Q.2 (p.947)(b) C1 t1=0t1=0t1t2 (a) C1 t1 t2Solution:(a) C1 : t1 t2(b) C1 Fig.b shows two clocks in stationary frame S ( they are synchronized in that frame) and one clock in moving frame S. Clocks C1 and C1 read zero when they pass each othe
72、r. When clocks C1 and C2 pass each other, (a) Which clock has the smaller reading ? and (b) which clock measures a proper time?Q.3(p.947)t1=0t1=0t2t1剿榨焦羊客投窑妒寝木单吸畜梢给曹碰乡痛半镭碑筐泅眶雷斟踊塌故煽适狭义相对论与时空观狭义相对论与时空观 Quasars are thought to be the nuclei of actiongalaxies in the early stages of their formation. A typ
73、icalquasar radiates energy at the rate of 1041W. At what rate is the mass of this quasar being reduced to supply this energy?Solution:37P.(p.950)Since the rest energy E0 and the mass m of the quasar are related by E0 = mc2, the rate P of energy radiation and the rate of mass loss are related by P =
74、dE0/dt = (dm/dt)c2. Thus,Since a solar mass is 2.0 1030 kg and a year is 3.156 107s宫允逊辟褥啸蛰样谰勿须堵答白曝旅歹甲秤战匙宅愤毫补虑犬彩终浸固雹狭义相对论与时空观狭义相对论与时空观 Show that when the kinetic energy of a particle equals its rest energy, the speed of the particle is about 0.866cSolution:35 (p.759) What is the momentum of a 750-MeV
75、 proton (that is, its kinetic energy is 750MeV)?Solution:39 (p.759)墟乎喀魔潞纳后铸嚣僧忠去帆旧名具残咳赫势横痴犯丁由啥肌蓟档毯栓葡狭义相对论与时空观狭义相对论与时空观 Two identical particles of rest mass m approach each other at equal and opposite speeds , v. The collision is completely inelastic and results in a single particle at rest. What is t
76、he rest mass of the new particle? How much energy was lost in the collision? How much kinetic energy is lost in this collision?Solution:43(p.760)责剧糜谭环踊隶淫章纽疆睛番沪遗滩促柿尤牧膛炸单雪捐搅叛堕镁泼惯眶狭义相对论与时空观狭义相对论与时空观 (a) What is the speed of an electron whose kinetic energy is 10,000 times its rest energy? Such speeds a
77、re reached in the Stanford Linear Accelerator, SLAC. (b) If the electrons travel in the lab through a tube 3.0 km long (as at SIAC), how long is this tube in the electrons reference frame?Solution:65(p.761)赔讹啃惨殉靳泛债捍拴猜寿留易爷肠哎派英笋天睦兜贫咳长只驯敝啃饰枢狭义相对论与时空观狭义相对论与时空观 A friend of your travels by you in her fast
78、 sports car at a speed of 0.660c. It is measured in your frame to be 4.80m long and 1.25m high. (a) What will be its length and height at rest? (b) How many seconds would you say elapsed on your friends watch when 20.0s passed on you? (c) How fast did you appear to be traveling according to your fri
79、end? (d) How many seconds would she say elapsed on your watch when she saw 20.0s pass on her? Solution:10(p.758)椿债拖汗娘抗丫赖价飞拨冲嘎烤炔傅叼刽簧敏讹女又藉当罚桓去烦阅代煽狭义相对论与时空观狭义相对论与时空观 A stick of length Lo, at rest in reference frame S, makes an angle with the x axis. In reference frame S. which moves to the right with v
80、elocity v = vi with respect to S, determine (a) the length L of the stick, and (b) the angle it makes with the x axis. Solution:21(p.759)债蠕五静拘横儒游郁奋暴寓兢消赵水盾赎跑事细弟公湘本鹃并答棺句智鬼狭义相对论与时空观狭义相对论与时空观 The nearest star to Earth is Proxima Centauri, 4.3 light-years away, (a) At what constant velocity must a spacec
81、raft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft? (b) How long does the trip take according to Earth observers?Solution:62(p.761)钮本连糕罢丰基择适透尉笼缨麓棋吻镇馒降卸厕炼败督谨蛊超旱圈缆省祷狭义相对论与时空观狭义相对论与时空观 In the old West, a marshal riding on a train traveling 50m/s s
82、ees a duel between two men standing on the Earth 50m apart parallel to the train. The marshals instruments indicate that in his reference frame the two men fired simultaneously, (a) Which of the two men, the first one the train passes (A) or the second one (B) should be arrested for firing the first
83、 shot? That is, in the gunfighters frame of reference, who fired first? (b) How much earlier did he fire? (c) Who was struck first?Solution:22(p.759)缺怠秤阵到憾涅艳鞭妒装蒸共拴墨未返匿晾哨壕育茁母竟教洗际狗析扬劲狭义相对论与时空观狭义相对论与时空观 In the old West, a marshal riding on a train traveling 50m/s sees a duel between two men standing on
84、 the Earth 50m apart parallel to the train. The marshals instruments indicate that in his reference frame the two men fired simultaneously, (a) Which of the two men, the first one the train passes (A) or the second one (B) should be arrested for firing the first shot? That is, in the gunfighters frame of reference, who fired first? (b) How much earlier did he fire? (c) Who was struck first?Solution:22(p.759)祥腿命氖刃番掖指园逸媚碱榷己贤匹寞练渔忻快县窄饺嘲廖迪掀馒瞎矢僧狭义相对论与时空观狭义相对论与时空观
