狭义相对论与时空观

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 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)cv albert einstein ( 1879 1955 )1921: nobel prize(1905)quantum of light(1

3、905) 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自然界应当是和谐而简单的简单的. 理论特色：理论特色： 出于简单而归于出于简单而归于深奥深奥. 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 经典力学的相对性原理经典力学的相对性原理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.经典力学的相对性原理经典力学的相对性原理:对于任何惯性参照对于任何惯性参照系系 , 牛顿力学的规律都具有相同的形式牛顿力学的规律都具有相同的形式 . all inertial reference frames are equivalent for the description of mechanical phenomena.伽利略变换伽利略变换当当 时时0tt oo与与 重重合合txxvyy zz tt 位置坐标变换公位置坐标变换公式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

6、的量度是绝对的, 与参与参考系无关；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-timezzaayyaa xxaa加速度变换公加速度变换公式式aaamf amfvxxuuyyuu zzuu伽利略速度变换公伽利略速度变换公式式 在两相互作匀速直线运在两相互作匀速直线运动的惯性系中，牛顿运动定律动的惯性系中，牛顿运动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伽利略变换伽利略变换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长度和时间的测量结果是一样的吗果是一样的吗? 绝对时空概念：时间和空间的量度和绝对时空概念：时间和空间的量度和参考系无关参考系无关 , 长度和时间的测量是绝对的长度和时间的测量是绝对的.牛顿的绝对时牛顿的绝对时空观空观牛顿力学的相对性牛顿力学的相对性原理原理二二 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，在牛顿力学的相对性原理，在宏观、低速的范围内，是与实宏观、低速的范围内，是与实验结果相一致的验结果相一致

8、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的. 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电磁现象基本规律的形式是一样吗？式是一样吗？真空中的光速真空中的光速m/s10998. 21800c 对于两个不同的惯性对于两个不同的惯性参考系参考系 , 光速满足伽利光速满足伽利略变换吗略变换吗 ？?v ccx xy yvo oz z ssc球球投投出出前前cdcdt 112tt v cdt2结果结果:观察者先看到投出后的球，后看到投观察者先看到投出后的球，后看到投出前的球出前的球. 试计算球被投出前后的瞬间，球所发试计算球被投出前后的瞬间，球所发出的光波达到观

9、察者所需要的时间出的光波达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发超新星爆发， 这次爆发的残骸形成这次爆发的残骸形成了著名的金牛星座的蟹状星云。北宋天文了著名的金牛星座的蟹状星云。北宋天文学家记载从公元学家记载从公元 1054年年 1056年均能用年均能用肉眼观察肉眼观察, 特别是开始的特别是开始的 23 天天, 白天也能白天也能看见看见 .km/s1500v物质飞散速度物质飞散速度l = 5000 光光年年cvcab 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

10、发时, 它它的外围物质向四面八方飞散的外围物质向四面八方飞散, 即有些抛射物即有些抛射物向着地球运动向着地球运动, 现研究超新星爆发过程中现研究超新星爆发过程中光线传播引起的疑问光线传播引起的疑问 .实际持续时间约为实际持续时间约为 22 个月个月, 这怎么解这怎么解释释 ?年25abttt理论计算观察到超新性爆发的强光的时间理论计算观察到超新性爆发的强光的时间持续约持续约l = 5000 光光年年cvckm/s1500v物质飞散速度物质飞散速度abvclta a 点光线点光线到达地球所到达地球所需时间需时间cltbb 点光线点光线到达地球到达地球所需时间所需时间 4.2 the michel

11、son-morley experimentmichelsons interferometer 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年他与莫雷以更高的精度重新做了此类实验此类实验,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“以以太太”的运动的运动 .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设设“以太以太”参考系为参考系为s系，实系，实验室为验室为 系系 s s（从（从 系看）系看）2222cln v m/s103,nm500,m104vl4 . 0n 人们为维护人们为维护“以太以太”观念作了种种努观念作

13、了种种努力，力， 提出了各种理论提出了各种理论 ，但这些理论或与，但这些理论或与天文观察，或与其它的实验相矛盾，最后天文观察，或与其它的实验相矛盾，最后均以均以失败失败告终告终 .仪器可测量精度仪器可测量精度01. 0n 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. 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：物理定爱因斯坦相对性原理：物理定律在律在所有所有的惯性系中都具有相同的表达的惯性系中都具有相同的表达形式形式 . 2）光速不变原理：光速不变原理： 真空中的光真空中的光速是常量，它与光源或观察者的运动无速是常量，它与光源或观察者的运动无关，即不依赖于惯性系的选择关，即不依赖于惯性系的选择. 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相对性原理是自然界的普遍规律律. 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狭义相对论的基本

16、原理不符原理不符 .the relativity of simultaneity 4.4 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：在某一紧密联系在一起的是：在某一惯性系中惯性系中同时同时发生的两个事件，在相对于此发生的两个事件，在相对于此惯性系运动的另一惯性系中观察，并惯性系运动的另一惯性系中观察，并不一定不一定是同时是同时发生的发生的 .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运运 动动 的的 钟钟 走走 得得 慢慢t

18、he relativity of the time intervalcdt20 clt2 0tt 2221dtvl (时间的延时间的延缓缓)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 an inertial reference frame.cdt20 (proper time)time dilation (时间延缓时间延缓 )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 (时间延缓时间延缓 )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 (长度收长度收缩缩)(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)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，两个事件在不同的惯性系看来，它们的空间关系是相对的，它们的空间关系是相对的， 时间关系也时间关系也是相对的，只有将空间和时间联系在一是相对的，只有将空间和时间联系在一起才有意义起才有意义. 2）时时空不互相独立，而是不可分空不互相独立，而是不可分割的整体割的整体. 3）光速

35、光速 c 是建立不同惯性系间时空是建立不同惯性系间时空变换的纽带变换的纽带. 3） 时，时， .cv tt1）时间延缓是一种相对效时间延缓是一种相对效应应 . 2）时间的流逝不是绝对的，时间的流逝不是绝对的，运动将改变时间的进程运动将改变时间的进程.（例如新（例如新陈代谢、放射性的衰变、寿命等陈代谢、放射性的衰变、寿命等 . ）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 时序不时序不变变012ttt即事件即事件1先发先发生生若若 s 系系中中则则 系中：系中：sxcut 2 uctx2 02 )xcut(t 时序变时序变化化：1) 在某一惯性系中的同步钟，在另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一相对其运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即在即在 系中观测，事件系中观测，事件1有可能比事有可能比事件件2先发生、同时发生、或后发生，时先发生、同时发生、或后发生，时序有可能倒置。序有可能倒置。s与因果律是否矛与因果

47、律是否矛盾？盾？有因果关联的事件之间的信有因果关联的事件之间的信号速率号速率uctxcu2 满足时序不变条满足时序不变条件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，无因果关联无因果关联的事件的事件才可能发生时序变化。才可能发生时序变化。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 牛顿定律与光速极限牛顿定律与光速极限的的矛盾矛盾tmtmtpfddddddv)v (mfa 物体在恒力作用下的物体在恒力作用下的运动运动att0vv经典力学中物体的质量与运动无经典力学中物体的质量与运动无关关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 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 ) 物体的懒惰物体的懒惰性就性就是物体活泼性的是物体活泼性

56、的度量度量 .质能关系质能关系预言预言：物质的质量就是能量的一：物质的质量就是能量的一种储藏种储藏 .电子的静质量电子的静质量 kg10911. 0300mmev511. 0j1019. 81420cm电子的静能电子的静能 mev938j10503. 11020cm质子的静能质子的静能 k202ecmmce相对论相对论质能质能关关系系 1千克千克的物体所包含的的物体所包含的静静能能 j109161千克汽油的燃烧值为千克汽油的燃烧值为 焦耳焦耳 .7106 . 4 静静能能 ：物体：物体静止静止时所具有时所具有的的能量能量 .20cm质子的静质量质子的静质量 kg10673. 1270m质能关系

57、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 j109161千克汽油的燃烧值为千克汽油的燃烧值为 焦耳焦耳 .7106 . 4例例：j109,kg1162000cmem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。 w1028j1072. 215例：例：在一种热核反应

58、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：反应释放的能反应释放的能量。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 反应质量亏损反应质量亏损j10799. 2122mce释放释放能量能量1 kg 核燃料释放能量核燃料释放能量(j/kg)103.3514td mme 锂原子的核反应锂原子的核反应hehebehli4242

59、841173两粒子所具有的总动两粒子所具有的总动能能mev3 .17ke0.01855ukg1008. 3292kcem两粒子质量比静质量两粒子质量比静质量增加增加0.01864um1.00783uhm7.01601ulim4.00260uhem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h11li37he42he42kg1066. 1u127k202ecmmce物理意义物理意义2mce 2mce 惯性质量的增加和能量的增加相联惯性质量的增加和能量的增加相联系，质量的系，质量的大小应标志着能量的大小，这是相对论大小应标志着能量的大小，这是相对论的又一极其的又一极其重要的推论重要

60、的推论 . 相对论的质能关系为开创原子能时代提供相对论的质能关系为开创原子能时代提供了理论基础了理论基础, 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 .四质能公式在原子核裂变和聚变中四质能公式在原子核裂变和聚变中的应用的应用n2srxenu109538139541023592u22.0m质量亏损质量亏损原子质量单位原子质量单位 kg1066. 1u127放出的能量放出的能量mev2002cmeq1g 铀铀 235 的原子裂变所释放的原子裂变所释放的能量的能量j105 . 810q1 核裂变核裂变我国于我国于 1958 年建成的首座重水反应堆年建成的首座重水反应堆2