狭义相对论与时空观课件.ppt

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(1905)爱因斯坦

3、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.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 BApBpArrrBApBpAvvvpBpAamam

4、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 physics are the

5、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惯性参照系,牛顿力学牛顿力学的规律都具有相同的形式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 重合重合txxvyy zz tt 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

6、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加速度变换公式加速度变换公式aaamF amFvxxuuyyuu zzuu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.x xy yvo oz z ss*),(),(zyxzyx

7、Px 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

8、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m/s10998.21800c 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？?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

9、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.km/s1500v物质飞散速度物质飞散速度l=5000 光年光年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

10、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.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?年25ABttt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cvckm/s1500v物质飞散速度物质飞散速度ABvcltA A 点光线到达点光线到达地球所需时间地球所需时间cltBB 点光线到达点光线到达地球所需时间地球所需时间 4.2 The Michelson-Morley ExperimentMichelsons Interferometer 迈克尔孙迈克尔孙 莫雷

11、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.LG1G2Michelsons Interferometer2)12(2221221 mmLdd mL 221 Lm 221If M2 is moved by ,then andthe fringe pattern is shifted by one f

12、ringe 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，实验室为系，实验室为 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

13、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 Theory Relativity The laws of physics are the same form in all inertial refere

14、nce 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

15、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对论的基本原理不符.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

16、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.The Relativity of Simultaneityv x y o121236912369 x y o12xyov123691236912369Event 2),(111txP),(222txPFrame S(on Earth)Frame S(in train),(1

17、11txPEvent 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The Relativity of the Time IntervalcDt20 cLt2 0tt 2221DtvL (时间的延缓时间的延缓)Proper Time Interval(固有时间固有时间)

18、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 observer are measured by that observer to run more slowly(as compared to clocks at rest)20)(1cvtt 20222tc2

19、1tv21Dtv21L)()(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 Dilation27.289994.0111122 1.Microscopic ClocksThe lifetime of muons()in the rest frame is:st 200.20 When the muons

20、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.(a)Is our measurement of the speed of the pulse greater(b)than,less than,or the same as that measurement by th

21、e(c)hobo?(b)Is his measurement of the flight time of the(d)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 speed of postulate).(b)no.The proper time is the time interval between two events occur at the same locatio

22、n 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 travel back to Earth with the same relative speed.The trip back takes another 10.0y(your time).How long does the round t

23、rip 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 at EarthEvent 2:the end of the trip at LP13.t1=0t1=0t2t2yt0.100 In your frame:In Earth frame

24、: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 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 h

25、as 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 student in frame S:20)(1cvtt 0tt 21 tthh66.075.0112 t1=0t1=0t2t2The Twins Paradox (343”)ABL0SallySallyThe Proper Length(Rest Length)4.6

26、 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,Length L of the platform:(Sally)0tvL(Sally)vLt0BSallyvv0tvL SallyLength Contraction(长度收缩长度收缩)(Sam)0tvL(Sally)0tvL 0tt 1 00 ttLL2001 LLL 0L L(Con

27、tracted Length)The relative motion causes a length contraction!ABSallyvv0tvL ABSam:L0 0tvL In the figure,Sally(at point A)and Sams spaceship(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

28、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 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 m

29、oving at speed v=0.9994c:stt 51.630 2.Macroscopic Clocks0tt 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 of 0.75c relativity to the teacher.When 1h(one hour)has passed on the teachers clock,how much ti

30、me has passed on a clock that moves with the student,as measured by the teacher?Solution:Ex.h1t hhtt66075011122.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

31、.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 friend?(d)How many seconds would she say el

32、apsed on your watch when she saw 20.0s pass on her?Solution:10(p.758)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

33、 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)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

34、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，.cv tt1）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The Spacetime Coordinates of An Event:(x,y,z,t)4.7 Four-

35、Dimensional Space-Time AEvent x=3.7m,y=1.2m,z=0m,t=34.5sThe Galilean Transformation 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

36、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-cxvttzzyytvxx)()(2 The Lorentz Transformation(130”)For each situation,if we choos

37、e 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 cxvtttvxx2)(2.)(1.cxvtttvxx2)(2.)(.1 (b)negative(c)positive Table 38-2 SimultaneityConsequences of the Lorentz Transformation Equations cxvtt)(2 If two events oc

38、cur at difference places in S:0 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 simulta

39、neous in S:0t In S：0 t 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-c

40、xvttzzyytvxx)()(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(

41、x)t(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 Rept

42、ilian 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 and its mo

43、on 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.t t tbe(b)What

44、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 )xcut(t xcut

45、 2 uctx2 时序不变时序不变012ttt即事件即事件1先发生先发生若若 S 系中系中则则 系中：系中：Sxcut 2 uctx2 02 )xcut(t 时序变化时序变化：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。s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

46、的信号速率uctxcu2 满足时序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。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 fr

47、ame 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)Solution:In th

48、e 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 one the train passes(A)or the seco

49、nd 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 Velocity Transformation)cvdxdt(dt)vdtdx(dx2 ttvtxx dtdtvdtdxdxvdtdxdt

50、dxvuuxx 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 Classical Momentum(low speed)dtdxmvmp00 牛顿定律与光速极限的牛顿定律与光速极限的矛盾矛盾tmtmtpFddddd