狹義相對(duì)論與時(shí)空觀ppt課件

1、4.1 Galilean-Newtonian Relativity 4.2* The Michelson-Morley Experiment4.3 Postulates of the Special Theory Relativity 4.4 Simultaneity4.5 Time Dilation and the Twin Paradox4.6 Length Contraction4.7 Four-Dimensional Space-Time4.8 Galilean and Lorentz Transformations 4.9 Relativistic Momentum and Mass

2、 4.10 The Ultimate Speed4.11 Energy and Mass; E = mc24.12* Doppler Shift for Light 狹義相對(duì)論與時(shí)空觀狹義相對(duì)論與時(shí)空觀Special Theory of RelativityFor inertial reference frames.General Theory of RelativityFor non-inertial reference frames.(1916)cv Albert Einstein ( 1879 1955 )1921: Nobel prize(1905)Quantum of Light(1

3、905) 愛因斯坦的哲學(xué)觀念：自然界該當(dāng)是調(diào)和而簡(jiǎn)單的愛因斯坦的哲學(xué)觀念：自然界該當(dāng)是調(diào)和而簡(jiǎn)單的. 實(shí)際特征：實(shí)際特征： 出于簡(jiǎn)單而歸于深?yuàn)W出于簡(jiǎn)單而歸于深?yuàn)W. 4.1 Galilean-Newtonian Relativity In two inertial frames A and B,which relative velocity is Inertial frame is one in which Newtons law holdconstant BAvpBpAaa The particles velocity isThe acceleration is BApBpArrrBApBpA

4、vvvpBpAamam pBpAFF According to Newtons second law 經(jīng)典力學(xué)的相對(duì)性原理經(jīng)典力學(xué)的相對(duì)性原理 Observers in different inertial framed agree on the net force acting on an object.Newtons second law Galilean-Newtonian Relativity to MechanicspApAamF pBpBamF Galilean-Newtonian Relativity to Mechanics : that the basic laws of p

5、hysics are the same in all inertial reference frames.經(jīng)典力學(xué)的相對(duì)性原理經(jīng)典力學(xué)的相對(duì)性原理:對(duì)于任何慣性參照系對(duì)于任何慣性參照系 , 牛頓力學(xué)牛頓力學(xué)的規(guī)律都具有一樣的方式的規(guī)律都具有一樣的方式 . All inertial reference frames are equivalent for the description of mechanical phenomena.伽利略變換伽利略變換當(dāng)當(dāng) 時(shí)時(shí)0tt oo與與 重合重合txxvyy zz tt 位置坐標(biāo)變換公式位置坐標(biāo)變換公式經(jīng)典力學(xué)以為經(jīng)典力學(xué)以為 1空間的量度是絕對(duì)的空間的

6、量度是絕對(duì)的, 與參考系無(wú)關(guān)；與參考系無(wú)關(guān)； 2時(shí)間的量度也是絕對(duì)的時(shí)間的量度也是絕對(duì)的, 與參考系無(wú)關(guān)與參考系無(wú)關(guān) .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-Timezzaayyaa xxaa加速度變換公式加速度變換公式aaamF amFvxxuuyyuu zzuu 伽利略速度變換公式伽利略速度變換公式 在兩相互作勻速直線運(yùn)動(dòng)的慣性在兩相互作勻速直線運(yùn)動(dòng)的慣性系中，牛頓運(yùn)動(dòng)定律具有一樣的方式系中，牛頓運(yùn)動(dòng)定律具有一樣的方式.x xy yvo

7、 oz z ss*) , , (),(zyxzyxPx xt vz z yy伽利略變換伽利略變換相對(duì)于不同的參考系相對(duì)于不同的參考系 ,長(zhǎng)度和時(shí)間的丈量結(jié)果是一樣的嗎長(zhǎng)度和時(shí)間的丈量結(jié)果是一樣的嗎? 絕對(duì)時(shí)空概念：時(shí)間和空間的量度和參考系無(wú)關(guān)絕對(duì)時(shí)空概念：時(shí)間和空間的量度和參考系無(wú)關(guān) , 長(zhǎng)度和時(shí)間的丈量是絕對(duì)的長(zhǎng)度和時(shí)間的丈量是絕對(duì)的.牛頓的絕對(duì)時(shí)空觀牛頓的絕對(duì)時(shí)空觀牛頓力學(xué)的相對(duì)性原理牛頓力學(xué)的相對(duì)性原理二二 經(jīng)典力學(xué)的絕對(duì)時(shí)空觀經(jīng)典力學(xué)的絕對(duì)時(shí)空觀注注 意意 牛頓力學(xué)的相對(duì)性原理，在宏觀、低牛頓力學(xué)的相對(duì)性原理，在宏觀、低速的范圍內(nèi)，是與實(shí)驗(yàn)結(jié)果相一致的速的范圍內(nèi)，是與實(shí)驗(yàn)結(jié)果相一致的

8、. 實(shí)際已證明實(shí)際已證明 , 絕對(duì)時(shí)空觀是不正確的絕對(duì)時(shí)空觀是不正確的. 對(duì)于不同的慣性系對(duì)于不同的慣性系,電磁景象根本規(guī)律的方式是一樣嗎？電磁景象根本規(guī)律的方式是一樣嗎？真空中的光速真空中的光速m/s10998. 21800c 對(duì)于兩個(gè)不同的慣性參考系對(duì)于兩個(gè)不同的慣性參考系 , 光速滿足伽利略變換嗎光速滿足伽利略變換嗎 ？?v ccx xy yvo oz z ssc球球投投出出前前cdcdt 112tt v cdt2結(jié)果結(jié)果:察看者先看到投出后的球，后看到投出前的球察看者先看到投出后的球，后看到投出前的球. 試計(jì)算球被投出前后的瞬間，球所發(fā)出的光波到試計(jì)算球被投出前后的瞬間，球所發(fā)出的光波

9、到達(dá)察看者所需求的時(shí)間達(dá)察看者所需求的時(shí)間. (根據(jù)伽利略變換根據(jù)伽利略變換)球球投投出出后后vcv 900 多年前公元多年前公元1054年年5月一次著名的超新星迸發(fā)，月一次著名的超新星迸發(fā)， 這次迸發(fā)的殘骸構(gòu)成了著名的金牛星座的蟹狀星云。北宋天文這次迸發(fā)的殘骸構(gòu)成了著名的金牛星座的蟹狀星云。北宋天文學(xué)家記載從公元學(xué)家記載從公元 1054年年 1056年均能用肉眼察看年均能用肉眼察看, 特別是開場(chǎng)特別是開場(chǎng)的的 23 天天, 白天也能看見白天也能看見 .km/s1500v物質(zhì)飛散速度物質(zhì)飛散速度l = 5000 光年光年cvcAB 當(dāng)一顆恒星在發(fā)生超新星迸發(fā)時(shí)當(dāng)一顆恒星在發(fā)生超新星迸發(fā)時(shí), 它

10、的外圍物質(zhì)向它的外圍物質(zhì)向四面八方飛散四面八方飛散, 即有些拋射物向著地球運(yùn)動(dòng)即有些拋射物向著地球運(yùn)動(dòng), 現(xiàn)研討超現(xiàn)研討超新星迸發(fā)過(guò)程中光線傳播引起的疑問(wèn)新星迸發(fā)過(guò)程中光線傳播引起的疑問(wèn) .實(shí)踐繼續(xù)時(shí)間約為實(shí)踐繼續(xù)時(shí)間約為 22 個(gè)月個(gè)月, 這怎樣解釋這怎樣解釋 ?年25ABttt實(shí)際計(jì)算察看到超新性迸發(fā)的強(qiáng)光的時(shí)間繼續(xù)約實(shí)際計(jì)算察看到超新性迸發(fā)的強(qiáng)光的時(shí)間繼續(xù)約l = 5000 光年光年cvckm/s1500v物質(zhì)飛散速度物質(zhì)飛散速度ABvcltA A 點(diǎn)光線到達(dá)點(diǎn)光線到達(dá)地球所需時(shí)間地球所需時(shí)間cltBB 點(diǎn)光線到達(dá)點(diǎn)光線到達(dá)地球所需時(shí)間地球所需時(shí)間 4.2 The Michelson-M

11、orley ExperimentMichelsons Interferometer 邁克爾孫邁克爾孫 莫雷實(shí)驗(yàn)?zāi)讓?shí)驗(yàn) 為了丈量地球相對(duì)于為了丈量地球相對(duì)于“以太的運(yùn)動(dòng)以太的運(yùn)動(dòng) , 1881年年邁克爾孫用他自制的干涉儀進(jìn)展丈量邁克爾孫用他自制的干涉儀進(jìn)展丈量, 沒有結(jié)果沒有結(jié)果 . 1887年他與莫雷以更高的精度重新做了此類實(shí)驗(yàn)?zāi)晁c莫雷以更高的精度重新做了此類實(shí)驗(yàn),仍得到零結(jié)果仍得到零結(jié)果,即未觀測(cè)到地球相對(duì)即未觀測(cè)到地球相對(duì)“以太的運(yùn)動(dòng)以太的運(yùn)動(dòng) .LG1G2Michelsons Interferometer2)12(2221221 mmLdd mL 221 Lm 221If M2 is

12、 moved by , then andthe fringe pattern is shifted by one fringe 2 L 211 mN2 NL N 21M1LM1LM1LvsGM1M2TG M1 Gvvclclt1G M2 G22212ccltv22cltcv2222clN v G M2c22vcv-M2 Gcv-22vcvsM2M1l12GMGMGT設(shè)設(shè)“以太參考系為以太參考系為S系，實(shí)驗(yàn)室為系，實(shí)驗(yàn)室為 系系 s s從從 系看系看2222clN v m/s103,nm500,m104vl4 . 0N 人們?yōu)榫S護(hù)人們?yōu)榫S護(hù)“以太觀念作了種種努力，以太觀念作了種種努力， 提出了各

13、種實(shí)際提出了各種實(shí)際 ，但這些實(shí)際或與天文察看，或與其它的實(shí)驗(yàn)相矛盾，最后均以但這些實(shí)際或與天文察看，或與其它的實(shí)驗(yàn)相矛盾，最后均以失敗告終失敗告終 .儀器可丈量精度儀器可丈量精度01. 0N 實(shí)驗(yàn)結(jié)果實(shí)驗(yàn)結(jié)果 未察看到地球相對(duì)于未察看到地球相對(duì)于“以太的運(yùn)動(dòng)以太的運(yùn)動(dòng). 0NMichelsons InterferometerMichelsons Interferometer 46Michelsons Interferometer 46 1. The Relativity Postulate: 4.3 Postulates of the Special Theory Relativity Th

14、e laws of physics 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:cv smcv/458 792 299一狹義相對(duì)論的根本原

15、理一狹義相對(duì)論的根本原理 1愛因斯坦相對(duì)性原理：物理定律在一切的愛因斯坦相對(duì)性原理：物理定律在一切的慣性系中都具有一樣的表達(dá)方式慣性系中都具有一樣的表達(dá)方式 . 2光速不變?cè)恚汗馑俨蛔冊(cè)恚?真空中的光速是常量，它真空中的光速是常量，它與光源或察看者的運(yùn)動(dòng)無(wú)關(guān)，即不依賴于慣性系的與光源或察看者的運(yùn)動(dòng)無(wú)關(guān)，即不依賴于慣性系的選擇選擇. 關(guān)鍵概念：相對(duì)性和不變性關(guān)鍵概念：相對(duì)性和不變性 . 相對(duì)性原理是自然界的普遍規(guī)律相對(duì)性原理是自然界的普遍規(guī)律. 一切的慣性參考系都是等價(jià)的一切的慣性參考系都是等價(jià)的 . 伽利略變換與狹義相對(duì)論的根本原理不符伽利略變換與狹義相對(duì)論的根本原理不符 . The Re

16、lativity of Simultaneity 4.4 Simultaneity事件事件 1 :車廂后壁接納器接納到光信號(hào)車廂后壁接納器接納到光信號(hào). 事件事件 2 :車廂前壁接納器接納到光信號(hào)車廂前壁接納器接納到光信號(hào). 和光速不變嚴(yán)密聯(lián)絡(luò)在一同的是：在某一慣性系中同時(shí)發(fā)生的兩和光速不變嚴(yán)密聯(lián)絡(luò)在一同的是：在某一慣性系中同時(shí)發(fā)生的兩個(gè)事件，在相對(duì)于此慣性系運(yùn)動(dòng)的另一慣性系中察看，并不一定是個(gè)事件，在相對(duì)于此慣性系運(yùn)動(dòng)的另一慣性系中察看，并不一定是同時(shí)發(fā)生的同時(shí)發(fā)生的 . The Relativity of Simultaneityv x y o121236912369 x y o12xyo

17、v123691236912369Event 2 ),(111txP),(222txPFrame S (on Earth)Frame S (in train),(111txPEvent 1),(222txP12tt (Simultaneity)012 tttIn S :12tt 012 tttIn S:12xx A Closer Look at Simultaneity (2 ) The Relativity of The Time Interval 4.5 Time Dilation and the Twin Paradox運(yùn)運(yùn) 動(dòng)動(dòng) 的的 鐘鐘 走走 得得 慢慢 The Relativity

18、 of the Time IntervalcDt20 cLt2 0tt 2221DtvL (時(shí)間的延緩時(shí)間的延緩) Proper Time Interval (固有時(shí)間固有時(shí)間 )The proper time is the time interval between two events occur at the same location in an inertial reference frame.cDt20 (proper time) Time Dilation (時(shí)間延緩時(shí)間延緩 )cLt2 0tt Clocks moving relative to an observer are

19、measured by that observer to run more slowly (as compared to clocks at rest)20)(1cvtt 20222tc21tv21Dtv21L)()(0tt cv 112(Lorentz factor)(speed parameter)cL2t 2tcL 2022)()()(tctvtc Time Dilation (時(shí)間延緩時(shí)間延緩 )cDt20 The Lorentz Factor211 cv The speed parameter1 cv 0tt The Tests of Time Dilation27.289994.0

20、111122 1. Microscopic ClocksThe lifetime of muons () in the rest frame is :st 200. 20 When the muons are moving at speed v =0.9994c :stt 51.630 2. Macroscopic Clocks0tt The Time Dilation (2 ) In a traveling boxcar, a well-equipped hobo fires a laser pulse from the front of the boxcar to its rear. Is

21、 our measurement of the speed of the pulse greater than, less than, or the same 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)0tt (a) Same (By the

22、 speed of postulate).(b) no.The proper time is the time interval between two events occur at the same location in an inertial reference frame.(c) no.cAB 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 trave

23、l back to Earth with the same relative 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)

24、Event 1: the start of the trip at EarthEvent 2: the end of the trip at LP13.t1=0t1=0t2t2yt0 .100 In your frame:In Earth frame:yycvtt224999. 0110)(1220 In Earth frame:ytttotal4482 EP A student must complete a test in the teachers frame of reference S. The student puts on his rocket skates andsoon is

25、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.3h1t For a student rests in the teachers frame S :For a moving clock with the st

26、udent in frame S:20)(1cvtt 0tt 21 tthh66. 075. 0112 t1=0t1=0t2t2 The Twins Paradox (343)ABL0SallySally The Proper Length (Rest Length) 4.6 Length ContractionThe proper length L0 of the platform measured by Sam:The train moves through the length L0 in a time:(Sam) 0tvL AB(Sam) 0vLt Sam For Sally, Len

27、gth L of the platform :(Sally) 0tvL (Sally) vLt0BSallyvv0tvL Sally Length Contraction (長(zhǎng)度收縮長(zhǎng)度收縮)(Sam) 0tvL (Sally) 0tvL 0tt 1 00 ttLL2001 LLL 0L L(Contracted Length )The relative motion causes a length contraction!ABSallyvv0tvL ABSam : L0 0tvL In the figure, Sally (at point A) and Sams spaceship (of

28、 proper 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)tvL In Sallys frame:In Sams frame: L0201 )(cvLtv The relative spee

29、d:201LL cLtccLv210.0)(2020 The Tests of Time Dilation27.289994.0111122 1. Microscopic ClocksThe lifetime of muons () in the rest frame is :st 200. 20 When the muons are moving at speed v =0.9994c :stt 51.630 2. Macroscopic Clocks0tt A student must complete a test in the teachers frame of reference S

30、. 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.h1t hhtt66075011122. For a st

31、udent rests in the teachers frame S :For a moving clock with the student in frame S:t1=0t1=0t1t2 (a) C1 t t 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) Ho

32、w 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) A friend of your travels by you in her

33、 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 when 20.0s passed on you?(c) How fast did you appear to be traveling according to your

34、friend? (d) How many seconds would she say elapsed on your watch when she saw 20.0s pass on her? Solution:10(p.758)狹義相對(duì)論的時(shí)空觀狹義相對(duì)論的時(shí)空觀 1 兩個(gè)事件在不同的慣性系看來(lái)，它們的空間兩個(gè)事件在不同的慣性系看來(lái)，它們的空間關(guān)系是相對(duì)的，關(guān)系是相對(duì)的， 時(shí)間關(guān)系也是相對(duì)的，只需將空間時(shí)間關(guān)系也是相對(duì)的，只需將空間和時(shí)間聯(lián)絡(luò)在一同才有意義和時(shí)間聯(lián)絡(luò)在一同才有意義. 2時(shí)時(shí)空不相互獨(dú)立，而是不可分割的整體空不相互獨(dú)立，而是不可分割的整體. 3光速光速 C 是建立不同慣性系間時(shí)

35、空變換的紐帶是建立不同慣性系間時(shí)空變換的紐帶. 3 時(shí)，時(shí)， .cv tt1時(shí)間延緩是一種相對(duì)效應(yīng)時(shí)間延緩是一種相對(duì)效應(yīng) . 2時(shí)間的流逝不是絕對(duì)的，運(yùn)動(dòng)將改動(dòng)時(shí)間的流逝不是絕對(duì)的，運(yùn)動(dòng)將改動(dòng)時(shí)間的進(jìn)程時(shí)間的進(jìn)程.例如新陳代謝、放射性的衰變、例如新陳代謝、放射性的衰變、壽命等壽命等 . 留意留意The Spacetime Coordinates of An Event: (x,y,z,t)4.7 Four-Dimensional Space-Time AEvent x=3.7m, y=1.2m, z=0m, t=34.5s The Galilean Transformation Equatio

36、ns 4.8 Galilean and Lorentz Transformation ttvtxxy= y, z= z(Approximately valid at low speed) The Lorentz Transformation Equations cvxttzzyyvtxx)()(2- (valid at all physically possible speed) cvxttzzyyvtxx)() (2 The Galilean Transformation for Pair of Events -t , t , 12121212 ttxxxttxxx Let label Ev

37、ent 1 for x1 , t1 and Event 2 for x2 , t2 , then tttvxx ttvtxx The Lorentz Transformation for Pair of Events cvxttzzyyvtxx)()(2- cxvttzzyytvxx)()(2- cxvttzzyytvxx)() (2 The Lorentz Transformation ( 130 ) For each situation, if we choose the blue frame to be stationary, then is v in the equations of

38、Table 38-2 a positive or negative quantity ? Solution:CP3.(p.933)(a) positive cxvtttvxx2)( 2.)( 1. cxvtttvxx2)( 2.) ( . 1 (b) negative (c) positive Table 38-2 SimultaneityConsequences of the Lorentz Transformation Equations cxvtt)(2 If two events occur at difference places in S: 0 x and the events a

39、re simultaneous in S: 0t 211 cv (simultaneous in S )In S： 0t 2cxvt 0 t 0 x ( not simultaneous in S ) SimultaneityConsequences of the Lorentz Transformation Equations cxvtt)(2 If two events occur at difference places in S: 0 x 2cxvt and the events are simultaneous in S: 0t In S： 0 t 211 cv 0 x Time D

40、ilation 0 x 0t t In S: )(t cxvtt 0tt The Galilean Transformation for Pair of Events -t , t , 12121212 ttxxxttxxx Let label Event 1 for x1 , t1 and Event 2 for x2 , t2 , then tttvxx ttvtxx The Lorentz Transformation for Pair of Events cvxttzzyyvtxx)()(2- cxvttzzyytvxx)()(2- cxvttzzyytvxx)() (2 Length

41、 Constant in Galilean Transformation L)t (x)t (xxAB 00 )()(01LtxtxxAB t ttvx x xx0Lx If we put 0 and tLx 0 xtvx x x x LL 0The rods end points are measured simultaneously.0 t 0 t Length Contraction0Lx If we put )(tvxx 0 and tLx The rods end points are measured simultaneously.L)t (x)t (xxAB 00 )()(01L

42、txtxxAB xx0 t 0 t x)x( x 0LL0 20011 LLL 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 4.00108m from the Reptilian base as

43、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)mxxxbe81000. 4 stttbe10. 1 In S frame: Earth outpost (a) The speed of the ship relative to the planet and its moon is 0.

44、980c. What are the distance and timeinterval between the burst and the explosion as measuredin the planet-moon inertial frame? Solution:SP4.(p.935)mxxxbe81000. 4 stttbe10. 1 In S frame:0252. 5 In S frame: cxvtttvxx)()(2 mx810863 .st04. 1 cvinf Solution:SP4.(p.935)0101 s.tttbe 0041 s. t t tbe (b)What

45、 is the meaning of the minus sigh in the value for ? t In S frame:firstt,latertbe bett bett In S frame:later t,first tbe (c) Does the burst cause the explosion, or vice versa? In S frame:smsmtxv/1064. 310. 11000. 488inf Impossible!The burst dosent cause the explosion, they are unrelated events! 02 )

46、xcut(t xcut 2 uctx2 時(shí)序不變時(shí)序不變012ttt即事件即事件1先發(fā)生先發(fā)生假設(shè)假設(shè) S 系系中中那么那么 系中：系中：Sxcut 2 uctx2 02 )xcut(t 時(shí)序變化時(shí)序變化即在即在 系中觀測(cè)，事件系中觀測(cè)，事件1有能夠比事件有能夠比事件2先發(fā)生、先發(fā)生、同時(shí)發(fā)生、或后發(fā)生，時(shí)序有能夠倒置。同時(shí)發(fā)生、或后發(fā)生，時(shí)序有能夠倒置。s與因果律能否矛盾？與因果律能否矛盾？有因果關(guān)聯(lián)的事件之間的信號(hào)速率有因果關(guān)聯(lián)的事件之間的信號(hào)速率uctxcu2 滿足時(shí)序不變條件滿足時(shí)序不變條件有因果關(guān)聯(lián)的事件時(shí)序不變，無(wú)因果關(guān)聯(lián)的事件有因果關(guān)聯(lián)的事件時(shí)序不變，無(wú)因果關(guān)聯(lián)的事件才能夠發(fā)生時(shí)

47、序變化。才能夠發(fā)生時(shí)序變化。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 frame the two men fired simultaneously, (a) Which of the two men, the first

48、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)Solution: In the old West, a marshal riding on a train traveling 50m/s see

49、s 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 s

50、hot? 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)0108214 stttAB.ABABTTTT 0,ABABTTTT 0 The Galilean Velocity Transformation )cvdxdt(dt)vdtdx(dx2 ttvtxx dtdtvdtdxdxvdtdxdtdxvuuxx The Lorentz Velocity Transformatio

51、n21 cvuvuuxxx/ vuucvxx The Lorentz Velocity Transformation21c/vuvuuxxx 2(1 /)yyxuuu v c2(1 /)zzxuuu v c The Lorentz Velocity Transformation (40)cvuvuu/1 4.9 Relativistic Momentum and Mass Classical Momentum(low speed)dtdxmvmp00 牛頓定律與光速極限的矛盾牛頓定律與光速極限的矛盾tmtmtpFddddddv)v (mFa 物體在恒力作用下的運(yùn)動(dòng)物體在恒力作用下的運(yùn)動(dòng)att0

52、vv經(jīng)典力學(xué)中物體的質(zhì)量與運(yùn)動(dòng)無(wú)關(guān)經(jīng)典力學(xué)中物體的質(zhì)量與運(yùn)動(dòng)無(wú)關(guān)tvC0vo tv Classical Momentum(low speed)dtdxmvmp00 Relativity Momentummvp Relation of Mass and Velocity201 mmm0 0 1mmcvv ,. 0mconstm1cv2light0v, , , , . 4.10 The Ultimate Speed The Ultimate Speedsmcv/458 792 299 No entity that carries energy or information can exceed t

53、he limit c.Testing the speed of light postulate 0Neutral pion: v = 0.99975c Newtons 2nd Law in Relativity 4.11 Energy and Mass; E = mc2dtpdFvmp0 2001 mmm The Relativistic Kinetic EnergyFor a particle, Using the work- energy theoremKenergykineticvvelocity-0 : ,0 :FWK v0LLFvdpdsdtdpFdsWK The Relativis

54、tic Kinetic EnergyThe Relativistic Kinetic Energy2020222020220200200 1 1 cmmccvcmmvcvvdvmmvmvdvmvmvvdvdpKvvvvvv /)(2001 mmm202cmmcK cv20vm21K (classical kinetic energy)(Relativistic kinetic energy) The Relativistic Kinetic Energy2001 mmm202cmmcK 00 Mass Energy (Rest Energy)2001 mmm202cmmcK 200cmEKcm

55、mc 202 Total EnergyKcmKEE 2002mcE Momentum and Kinetic Energy2001 mmm202cmmcK 202222cKmKcp422220cmcpEKcmE 20 愛因斯坦以為愛因斯坦以為1905 懶惰性懶惰性 慣性慣性 ( inertia )活潑性活潑性 能量能量 ( energy ) 物體的懶惰性就物體的懶惰性就是物體活潑性的度量是物體活潑性的度量 .質(zhì)能關(guān)系預(yù)言：物質(zhì)的質(zhì)量就是能量的一種貯藏質(zhì)能關(guān)系預(yù)言：物質(zhì)的質(zhì)量就是能量的一種貯藏 .電子的靜質(zhì)量電子的靜質(zhì)量 kg10911. 0300mMeV511. 0J1019. 81420cm

56、電子的靜能電子的靜能 MeV938J10503. 11020cm質(zhì)子的靜能質(zhì)子的靜能 k202EcmmcE相對(duì)論質(zhì)能關(guān)系相對(duì)論質(zhì)能關(guān)系 1千克的物體所包含的靜能千克的物體所包含的靜能 J109161千克汽油的熄滅值為千克汽油的熄滅值為 焦耳焦耳 .7106 . 4 靜能靜能 ：物體靜止時(shí)所具有的能量：物體靜止時(shí)所具有的能量 .20cm質(zhì)子的靜質(zhì)量質(zhì)子的靜質(zhì)量 kg10673. 1270m質(zhì)能關(guān)系預(yù)言：物質(zhì)的質(zhì)量就是能量的一種貯藏。質(zhì)能關(guān)系預(yù)言：物質(zhì)的質(zhì)量就是能量的一種貯藏。 相對(duì)論能量和質(zhì)量守恒是一個(gè)一致的物理規(guī)律。相對(duì)論能量和質(zhì)量守恒是一個(gè)一致的物理規(guī)律。1千克的物體所包含的靜能千克的物體所

57、包含的靜能 J109161千克汽油的熄滅值為千克汽油的熄滅值為 焦耳焦耳 .7106 . 4例：例：J109,kg1162000cmEm現(xiàn)有現(xiàn)有 100 座樓，每樓座樓，每樓 200 套房，每套房用電功率套房，每套房用電功率 10000 W ，總功率，總功率 ，每天用電，每天用電 10 小時(shí)小時(shí) ，年耗電量年耗電量 ，可用約，可用約 33 年。年。 W1028J1072. 215例：在一種熱核反響中，各種粒子的靜質(zhì)量如下：例：在一種熱核反響中，各種粒子的靜質(zhì)量如下： 求：反響釋放的能量。求：反響釋放的能量。 nHeHH10423121 kg103.3437H)(27D21 mkg105.044

58、9H)(27T31 mkg106.6425He)(27He42 mkg101.6750n)(27n10 m氘核氘核氚核氚核氦核氦核中子中子)kg(100311. 027)()(nHeTD0mmmmm 反響質(zhì)量虧損反響質(zhì)量虧損J10799. 2122mcE釋放能量釋放能量1 kg 核燃料釋放能量核燃料釋放能量(J/kg)103.3514TD mmE 鋰原子的核反響鋰原子的核反響HeHeBeHLi4242841173兩粒子所具有的總動(dòng)能兩粒子所具有的總動(dòng)能MeV3 .17kE0.01855ukg1008. 3292kcEm兩粒子質(zhì)量比靜質(zhì)量添加兩粒子質(zhì)量比靜質(zhì)量添加0.01864um1.00783

59、uHm7.01601uLim4.00260uHem實(shí)際計(jì)算和實(shí)驗(yàn)結(jié)果相符實(shí)際計(jì)算和實(shí)驗(yàn)結(jié)果相符實(shí)驗(yàn)丈量實(shí)驗(yàn)丈量H11Li37He42He42kg1066. 1u127k202EcmmcE物理意義物理意義2mcE 2mcE 慣性質(zhì)量的添加和能量的添加相聯(lián)絡(luò)，質(zhì)量的慣性質(zhì)量的添加和能量的添加相聯(lián)絡(luò)，質(zhì)量的大小應(yīng)標(biāo)志著能量的大小，這是相對(duì)論的又一極其大小應(yīng)標(biāo)志著能量的大小，這是相對(duì)論的又一極其重要的推論重要的推論 . 相對(duì)論的質(zhì)能關(guān)系為開創(chuàng)原子能時(shí)代提供了實(shí)際根底相對(duì)論的質(zhì)能關(guān)系為開創(chuàng)原子能時(shí)代提供了實(shí)際根底, 這是一個(gè)具有劃時(shí)代的意義的實(shí)際公式這是一個(gè)具有劃時(shí)代的意義的實(shí)際公式 .四質(zhì)能公式在原子

60、核裂變和聚變中的運(yùn)用四質(zhì)能公式在原子核裂變和聚變中的運(yùn)用n2SrXenU109538139541023592u22.0m質(zhì)量虧損質(zhì)量虧損原子質(zhì)量單位原子質(zhì)量單位 kg1066. 1u127放出的能量放出的能量MeV2002cmEQ1g 鈾 235 的原子裂變所釋放的能量J105 . 810Q1 核裂變核裂變我國(guó)于我國(guó)于 1958 年建成的首座重水反響堆年建成的首座重水反響堆2 輕核聚變輕核聚變HeHH42212124MeVJ1087. 3)(122cmEQ釋放能量釋放能量kg103 . 4u026. 029m質(zhì)量虧損質(zhì)量虧損 輕核聚變條件輕核聚變條件 溫度要到達(dá)溫度要到達(dá) 時(shí)，使時(shí)，使 具具有