狹義相對論與時空觀

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 狹義相對論與時空觀狹義相對論與時空觀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) 愛因斯坦的愛因斯坦的哲學(xué)觀念：哲學(xué)觀念：自然界應(yīng)當(dāng)是和諧而自然界應(yīng)當(dāng)是和諧而簡單的簡單的. 理論特色：理論特色： 出于簡單而歸于出于簡單而歸于深奧深奧. 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)的相對性原理經(jīng)典力學(xué)的相對性原理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 ph

5、ysics are the same in all inertial reference frames.經(jīng)典力學(xué)的相對性原理經(jīng)典力學(xué)的相對性原理:對于任何慣性參照對于任何慣性參照系系 , 牛頓力學(xué)的規(guī)律都具有相同的形式牛頓力學(xué)的規(guī)律都具有相同的形式 . 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) 時時0tt oo與與 重重合合txxvyy zz tt 位置坐標(biāo)變換公位置坐標(biāo)變換公式式經(jīng)典力學(xué)認(rèn)為經(jīng)典力學(xué)認(rèn)為 1）空間的量度是絕對的）空間

6、的量度是絕對的, 與參與參考系無關(guān)；考系無關(guān)； 2）時間的量度也是絕對的）時間的量度也是絕對的, 與參考系無關(guān)與參考系無關(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加速度變換公加速度變換公式式aaamf amfvxxuuyyuu zzuu伽利略速度變換公伽利略速度變換公式式 在兩相互作勻速直線運(yùn)在兩相互作勻速直線運(yùn)動的慣性系中，牛頓運(yùn)動定律動的慣性系中，牛頓運(yùn)動定律具有相同的形式具有相同的形式.x xy y

7、vo oz z ss*) , , (),(zyxzyxpx xt vz z yy伽利略變換伽利略變換相對于不同的參考系相對于不同的參考系 ,長度和時間的測量結(jié)長度和時間的測量結(jié)果是一樣的嗎果是一樣的嗎? 絕對時空概念：時間和空間的量度和絕對時空概念：時間和空間的量度和參考系無關(guān)參考系無關(guān) , 長度和時間的測量是絕對的長度和時間的測量是絕對的.牛頓的絕對時牛頓的絕對時空觀空觀牛頓力學(xué)的相對性牛頓力學(xué)的相對性原理原理二二 經(jīng)典力學(xué)的絕對時空觀經(jīng)典力學(xué)的絕對時空觀注注 意意 牛頓力學(xué)的相對性原理，在牛頓力學(xué)的相對性原理，在宏觀、低速的范圍內(nèi)，是與實(shí)宏觀、低速的范圍內(nèi)，是與實(shí)驗(yàn)結(jié)果相一致的驗(yàn)結(jié)果相一致

8、的 . 實(shí)踐已證明實(shí)踐已證明 , 絕對時空觀是不正確的絕對時空觀是不正確的. 對于不同的慣性系對于不同的慣性系,電磁現(xiàn)象基本規(guī)律的形電磁現(xiàn)象基本規(guī)律的形式是一樣嗎？式是一樣嗎？真空中的光速真空中的光速m/s10998. 21800c 對于兩個不同的慣性對于兩個不同的慣性參考系參考系 , 光速滿足伽利光速滿足伽利略變換嗎略變換嗎 ？?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:觀察者先看到投出后的球，后看到投觀察者先看到投出后的球，后看到投出前的球出前的球. 試計(jì)算球被投出前后的瞬間，球所發(fā)試計(jì)算球被投出前后的瞬間，球所發(fā)出的光波達(dá)到觀

9、察者所需要的時間出的光波達(dá)到觀察者所需要的時間. (根據(jù)根據(jù)伽利略變換伽利略變換)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）一次月）一次著名的著名的超新星爆發(fā)超新星爆發(fā)， 這次爆發(fā)的殘骸形成這次爆發(fā)的殘骸形成了著名的金牛星座的蟹狀星云。北宋天文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年均能用年均能用肉眼觀察肉眼觀察, 特別是開始的特別是開始的 23 天天, 白天也能白天也能看見看見 .km/s1500v物質(zhì)飛散速度物質(zhì)飛散速度l = 5000 光光年年cvcab 當(dāng)一顆恒星在發(fā)生超新星爆發(fā)時當(dāng)一顆恒星在發(fā)生超新星爆

10、發(fā)時, 它它的外圍物質(zhì)向四面八方飛散的外圍物質(zhì)向四面八方飛散, 即有些拋射物即有些拋射物向著地球運(yùn)動向著地球運(yùn)動, 現(xiàn)研究超新星爆發(fā)過程中現(xiàn)研究超新星爆發(fā)過程中光線傳播引起的疑問光線傳播引起的疑問 .實(shí)際持續(xù)時間約為實(shí)際持續(xù)時間約為 22 個月個月, 這怎么解這怎么解釋釋 ?年25abttt理論計(jì)算觀察到超新性爆發(fā)的強(qiáng)光的時間理論計(jì)算觀察到超新性爆發(fā)的強(qiáng)光的時間持續(xù)約持續(xù)約l = 5000 光光年年cvckm/s1500v物質(zhì)飛散速度物質(zhì)飛散速度abvclta a 點(diǎn)光線點(diǎn)光線到達(dá)地球所到達(dá)地球所需時間需時間cltbb 點(diǎn)光線點(diǎn)光線到達(dá)地球到達(dá)地球所需時間所需時間 4.2 the michel

11、son-morley experimentmichelsons interferometer 邁克爾孫邁克爾孫 莫雷實(shí)驗(yàn)?zāi)讓?shí)驗(yàn) 為了測量地球相對于為了測量地球相對于“以太以太”的運(yùn)動的運(yùn)動 , 1881年年邁克爾孫用他自制的干涉儀進(jìn)行測量邁克爾孫用他自制的干涉儀進(jìn)行測量, 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年他與莫雷以更高的精度重新做了此類實(shí)驗(yàn)此類實(shí)驗(yàn),仍得到零結(jié)果仍得到零結(jié)果,即即未觀測到地球相對未觀測到地球相對“以以太太”的運(yùn)動的運(yùn)動 .lg1g2michelsons interferometer2)12(2221221 mmldd ml 221 lm 221i

12、f m2 is 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)“以太以太”參考系為參考系為s系，實(shí)系，實(shí)驗(yàn)室為驗(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)“以太以太”觀念作了種種努觀念作

13、了種種努力，力， 提出了各種理論提出了各種理論 ，但這些理論或與，但這些理論或與天文觀察，或與其它的實(shí)驗(yàn)相矛盾，最后天文觀察，或與其它的實(shí)驗(yàn)相矛盾，最后均以均以失敗失敗告終告終 .儀器可測量精度儀器可測量精度01. 0n 實(shí)驗(yàn)結(jié)果實(shí)驗(yàn)結(jié)果 未未觀察到地球相對于觀察到地球相對于“以太以太”的運(yùn)動的運(yùn)動. 0nmichelsons interferometermichelsons interferometer 46”michelsons interferometer 46”1. the relativity postulate: 4.3 postulates of the special theo

14、ry relativity the 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 79

15、2 299一狹義相對論的基本原理一狹義相對論的基本原理 1）愛因斯坦相對性原理：物理定愛因斯坦相對性原理：物理定律在律在所有所有的慣性系中都具有相同的表達(dá)的慣性系中都具有相同的表達(dá)形式形式 . 2）光速不變原理：光速不變原理： 真空中的光真空中的光速是常量，它與光源或觀察者的運(yùn)動無速是常量，它與光源或觀察者的運(yùn)動無關(guān)，即不依賴于慣性系的選擇關(guān)，即不依賴于慣性系的選擇. 關(guān)鍵概念：相對性和不變性關(guān)鍵概念：相對性和不變性 . 相對性原理是自然界的普遍規(guī)相對性原理是自然界的普遍規(guī)律律. 所有的慣性參考系都是等價的所有的慣性參考系都是等價的 . 伽利略變換與伽利略變換與狹義相對論的基本狹義相對論的基本

16、原理不符原理不符 .the relativity of simultaneity 4.4 simultaneity事件事件 1 :車廂車廂后后壁接收器接收到光信號壁接收器接收到光信號. 事件事件 2 :車廂車廂前前壁接收器接收到光信號壁接收器接收到光信號. 和和光速不變光速不變緊密聯(lián)系在一起的是：在某一緊密聯(lián)系在一起的是：在某一慣性系中慣性系中同時同時發(fā)生的兩個事件，在相對于此發(fā)生的兩個事件，在相對于此慣性系運(yùn)動的另一慣性系中觀察，并慣性系運(yùn)動的另一慣性系中觀察，并不一定不一定是同時是同時發(fā)生的發(fā)生的 .the relativity of simultaneityv x y o12123691

17、2369 x y o12xyov123691236912369event 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) 動動 的的 鐘鐘 走走 得得 慢慢t

18、he relativity of the time intervalcdt20 clt2 0tt 2221dtvl (時間的延時間的延緩緩)proper time interval (固有時間固有時間 )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 (時間延緩時間延緩 )clt2 0tt clocks moving relative to an ob

19、server are 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 (時間延緩時間延緩 )cdt20 the lorentz factor211 cv the speed parameter1 cv 0tt the tests of time dilation

20、27.289994.0111122 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 the time dilation (2 ) in a traveling boxcar, a well-equipped hobo fires a laser pulse from the front of the boxcar to i

21、ts rear. (a)is 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

22、) same (by the 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,

23、and then travel 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:

24、ex.2 (h.p.928)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 skat

25、es 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.3h1t for a student rests in the teachers frame s :for a moving clo

26、ck with the student in frame s:20)(1cvtt 0tt 21 tthh66. 075. 0112 t1=0t1=0t2t2the twins paradox (343”)abl0sallysallythe 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 f

27、or sally, length l of the platform :(sally) 0tvl (sally) vlt0bsallyvv0tvl sallylength contraction (長度收長度收縮縮)(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 s

28、paceship (of 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 r

29、elative speed: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

30、 reference 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.h1t hhtt660750111

31、22. for a student 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

32、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) a friend of your travels b

33、y 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 when 20.0s passed on you?(c) how fast did you appear to be traveling accord

34、ing 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)狹義相對論的時空觀狹義相對論的時空觀 1） 兩個事件在不同的慣性系看來，兩個事件在不同的慣性系看來，它們的空間關(guān)系是相對的，它們的空間關(guān)系是相對的， 時間關(guān)系也時間關(guān)系也是相對的，只有將空間和時間聯(lián)系在一是相對的，只有將空間和時間聯(lián)系在一起才有意義起才有意義. 2）時時空不互相獨(dú)立，而是不可分空不互相獨(dú)立，而是不可分割的整體割的整體. 3）光速

35、光速 c 是建立不同慣性系間時空是建立不同慣性系間時空變換的紐帶變換的紐帶. 3） 時，時， .cv tt1）時間延緩是一種相對效時間延緩是一種相對效應(yīng)應(yīng) . 2）時間的流逝不是絕對的，時間的流逝不是絕對的，運(yùn)動將改變時間的進(jìn)程運(yùn)動將改變時間的進(jìn)程.（例如新（例如新陳代謝、放射性的衰變、壽命等陳代謝、放射性的衰變、壽命等 . ）注意注意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=34.5sthe galilean tr

36、ansformation equations 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 ttxx

37、xttxxx let label event 1 for x1 , t1 and event 2 for x2 , t2 , then tttvxx ttvtxxthe 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 i

38、n the equations of 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

39、 x and the events are 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

40、 211 cv 0 x time dilation 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 ttvtxxthe lorentz transformation for pair of events cvxttzzyyvtxx)()(2- cxvttzzyytvxx)()(2- cxvttzzyy

41、tvxx)() (2 length 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

42、 (xxab 00 )()(01ltxtxxab 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 r

43、eptilian 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)mxxxbe81000. 4 stttbe10. 1 in s frame: earth outpost (a) the speed of the ship relative to the planet a

44、nd 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)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

45、. t t tbe (b)what 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 unrel

46、ated events! 02 )xcut(t xcut 2 uctx2 時序不時序不變變012ttt即事件即事件1先發(fā)先發(fā)生生若若 s 系系中中則則 系中：系中：sxcut 2 uctx2 02 )xcut(t 時序變時序變化化：1) 在某一慣性系中的同步鐘，在另在某一慣性系中的同步鐘，在另一相對其運(yùn)動的慣性系中是否是同步的一相對其運(yùn)動的慣性系中是否是同步的? ? 2) 兩事件發(fā)生的時序與因果律兩事件發(fā)生的時序與因果律即在即在 系中觀測，事件系中觀測，事件1有可能比事有可能比事件件2先發(fā)生、同時發(fā)生、或后發(fā)生，時先發(fā)生、同時發(fā)生、或后發(fā)生，時序有可能倒置。序有可能倒置。s與因果律是否矛與因果

47、律是否矛盾？盾？有因果關(guān)聯(lián)的事件之間的信有因果關(guān)聯(lián)的事件之間的信號速率號速率uctxcu2 滿足時序不變條滿足時序不變條件件有因果關(guān)聯(lián)的事件有因果關(guān)聯(lián)的事件時序不變，時序不變，無因果關(guān)聯(lián)無因果關(guān)聯(lián)的事件的事件才可能發(fā)生時序變化。才可能發(fā)生時序變化。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 instrumen

48、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

49、? (c) who was struck first?22(p.759)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 t

50、he 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)0108214 stttab.ababtttt 0,ababtttt 0 the galilean ve

51、locity transformation )cvdxdt(dt)vdtdx(dx2 ttvtxx dtdtvdtdxdxvdtdxdtdxvuuxx the lorentz velocity transformation21 cvuvuuxxx/ vuucvxx the lorentz velocity transformation21c/vuvuuxxx 2(1 /)yyxuuuv c2(1 /)zzxuuu v cthe lorentz velocity transformation (40)cvuvuu/1 4.9 relativistic momentum and mass clas

52、sical momentum(low speed)dtdxmvmp00 牛頓定律與光速極限牛頓定律與光速極限的的矛盾矛盾tmtmtpfddddddv)v (mfa 物體在恒力作用下的物體在恒力作用下的運(yùn)動運(yùn)動att0vv經(jīng)典力學(xué)中物體的質(zhì)量與運(yùn)動無經(jīng)典力學(xué)中物體的質(zhì)量與運(yùn)動無關(guān)關(guān)tvc0vo tvclassical momentum(low speed)dtdxmvmp00 relativity momentummvp relation of mass and velocity201 mmm0 0 1mmcvv ,. 0mconstm1cv2light0v, , , , . 4.10 the

53、ultimate speedthe ultimate speedsmcv/458 792 299no entity that carries energy or information can exceed the limit c.testing the speed of light postulate 0neutral pion: v = 0.99975cnewtons 2nd law in relativity 4.11 energy and mass; e = mc2dtpdfvmp0 2001 mmmthe relativistic kinetic energyfor a partic

54、le, using the work- energy theoremkenergykineticvvelocity-0 : ,0 :fwk v0llfvdpdsdtdpfdswkthe relativistic kinetic energythe relativistic kinetic energy2020222020220200200 1 1 cmmccvcmmvcvvdvmmvmvdvmvmvvdvdpkvvvvvv /)(2001 mmm202cmmck cv20vm21k (classical kinetic energy)(relativistic kinetic energy)t

55、he relativistic kinetic energy2001 mmm202cmmck 00mass energy (rest energy)2001 mmm202cmmck 200cmekcmmc 202total energykcmkee 2002mce momentum and kinetic energy2001 mmm202cmmck 202222ckmkcp422220cmcpekcme 20 愛因斯坦認(rèn)為愛因斯坦認(rèn)為（1905） 懶惰性懶惰性 慣性慣性 ( inertia )活潑性活潑性 能量能量 ( energy ) 物體的懶惰物體的懶惰性就性就是物體活潑性的是物體活潑性

56、的度量度量 .質(zhì)能關(guān)系質(zhì)能關(guān)系預(yù)言預(yù)言：物質(zhì)的質(zhì)量就是能量的一：物質(zhì)的質(zhì)量就是能量的一種儲藏種儲藏 .電子的靜質(zhì)量電子的靜質(zhì)量 kg10911. 0300mmev511. 0j1019. 81420cm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相對論相對論質(zhì)能質(zhì)能關(guān)關(guān)系系 1千克千克的物體所包含的的物體所包含的靜靜能能 j109161千克汽油的燃燒值為千克汽油的燃燒值為 焦耳焦耳 .7106 . 4 靜靜能能 ：物體：物體靜止靜止時所具有時所具有的的能量能量 .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

57、質(zhì)能關(guān)系預(yù)言預(yù)言：物質(zhì)的質(zhì)量就是能量的一種儲藏。：物質(zhì)的質(zhì)量就是能量的一種儲藏。相對論能量和質(zhì)量守恒是一個相對論能量和質(zhì)量守恒是一個統(tǒng)一統(tǒng)一的物理規(guī)律。的物理規(guī)律。1千克千克的物體所包含的的物體所包含的靜靜能能 j109161千克汽油的燃燒值為千克汽油的燃燒值為 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 小時小時 ，年耗電量年耗電量 ，可用約，可用約 33 年年。 w1028j1072. 215例：例：在一種熱核反應(yīng)

58、中，各種粒子的靜質(zhì)量如下：在一種熱核反應(yīng)中，各種粒子的靜質(zhì)量如下： 求：求：反應(yīng)釋放的能反應(yīng)釋放的能量。量。 nhehh10423121 kg103.3437h)(27d21 mkg105.0449h)(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 反應(yīng)質(zhì)量虧損反應(yīng)質(zhì)量虧損j10799. 2122mce釋放釋放能量能量1 kg 核燃料釋放能量核燃料釋放能量(j/kg)103.3514td mme 鋰原子的核反應(yīng)鋰原子的核反應(yīng)hehebehli4242

59、841173兩粒子所具有的總動兩粒子所具有的總動能能mev3 .17ke0.01855ukg1008. 3292kcem兩粒子質(zhì)量比靜質(zhì)量兩粒子質(zhì)量比靜質(zhì)量增加增加0.01864um1.00783uhm7.01601ulim4.00260uhem理論計(jì)算和實(shí)驗(yàn)結(jié)果相符理論計(jì)算和實(shí)驗(yàn)結(jié)果相符實(shí)驗(yàn)測量實(shí)驗(yàn)測量h11li37he42he42kg1066. 1u127k202ecmmce物理意義物理意義2mce 2mce 慣性質(zhì)量的增加和能量的增加相聯(lián)慣性質(zhì)量的增加和能量的增加相聯(lián)系，質(zhì)量的系，質(zhì)量的大小應(yīng)標(biāo)志著能量的大小，這是相對論大小應(yīng)標(biāo)志著能量的大小，這是相對論的又一極其的又一極其重要的推論重要

60、的推論 . 相對論的質(zhì)能關(guān)系為開創(chuàng)原子能時代提供相對論的質(zhì)能關(guān)系為開創(chuàng)原子能時代提供了理論基礎(chǔ)了理論基礎(chǔ), 這是一個具有劃時代的意義的理論公式這是一個具有劃時代的意義的理論公式 .四質(zhì)能公式在原子核裂變和聚變中四質(zhì)能公式在原子核裂變和聚變中的應(yīng)用的應(yīng)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 鈾鈾 235 的原子裂變所釋放的原子裂變所釋放的能量的能量j105 . 810q1 核裂變核裂變我國于我國于 1958 年建成的首座重水反應(yīng)堆年建成的首座重水反應(yīng)堆2