狭义相对论与时空观

1、4.1 Galilean-Newtonian Relativity 4.2* The Michelson-Morley Experiment 4.3 Postulates of the Special Theory Relativity 4.4 Simultaneity 4.5 Time Dilation and the Twin Paradox 4.6 Length Contraction 4.7 Four-Dimensional Space-Time 4.8 Galilean and Lorentz Transformations 4.9 Relativistic Momentum and

2、 Mass 4.10 The Ultimate Speed 4.11 Energy and Mass; E = mc2 4.12* Doppler Shift for Light,狭义相对论与时空观,Special Theory of Relativity,For inertial reference frames.,General Theory of Relativity,For non-inertial reference frames.,(1916),Albert Einstein ( 1879 1955 ),1921: Nobel prize,(1905),Quantum of Lig

3、ht,(1905),爱因斯坦的哲学观念：自然界应当是和谐而简单的. 理论特色： 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 hold,The particles velocity is,The acceleration is,According to Newtons second law,经典力学的相对性原理,Observers in differe

4、nt inertial framed agree on the net force acting on an object.,Newtons second law,Galilean-Newtonian Relativity to Mechanics,Galilean-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:对于任何惯性参照系 , 牛顿力学的规律都具有相同的形式 .,All inertia

5、l reference frames are equivalent for the description of mechanical phenomena.,伽利略变换,经典力学认为 1）空间的量度是绝对的, 与参考系无关； 2）时间的量度也是绝对的, 与参考系无关 .,The Spacetime Coordinates of An Event(事件): (x,y,z,t),Four-Dimensional Space-Time,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.,伽利略变换,相对于不同的参考系 ,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

6、考系无关 , 长度和时间的测量是绝对的.,二 经典力学的绝对时空观,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 .,实践已证明 , 绝对时空观是不正确的.,对于不同的惯性系,电磁现象基本规律的形式是一样吗？,真空中的光速,对于两个不同的惯性参考系 , 光速满足伽利略变换吗 ？,结果: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，球所发出的光波达到观察者所需要的时间. (根据伽利略变换),900 多年前（公元1054年5月）一次著名的超新星爆发， 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 1054年 1056年均能用肉眼观

7、察, 特别是开始的 23 天, 白天也能看见 .,物质飞散速度,当一颗恒星在发生超新星爆发时, 它的外围物质向四面八方飞散, 即有些抛射物向着地球运动, 现研究超新星爆发过程中光线传播引起的疑问 .,实际持续时间约为 22 个月, 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,A 点光线到达地球所需时间,B 点光线到达地球所需时间,4.2 The Michelson-Morley Experiment,Michelsons Interferometer,迈克尔孙 莫雷实验,为了测量地球相对于“以太”的运动 , 1881年 迈克尔孙用他自制的干涉仪进行测量, 没有结果 . 1887

8、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,即未观测到地球相对“以太”的运动 .,Michelsons Interferometer,If M2 is moved by , then and the fringe pattern is shifted by one fringe,设“以太”参考系为S系，实验室为 系,（从 系看）,人们为维护“以太”观念作了种种努力， 提出了各种理论 ，但这些理论或与天文观察，或与其它的实验相矛盾，最后均以失败告终 .,仪器可测量精度,实验结果 未观察到地球相对于“以太”的运动.,Michelsons Interferometer,Michelson

9、s 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 reference frames. No frame is perfected.,2. Constancy of the Speed of Light Postulate:,Light propagates through empty

10、space with a definite speed c independent of the speed of the source or observer.,The Ultimate Speed:,一狭义相对论的基本原理,1）爱因斯坦相对性原理：物理定律在所有的惯性系中都具有相同的表达形式 .,2）光速不变原理： 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选择.,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.,所有的惯性参考系都是等价的 .,伽利略变换与狭义相对论的基本原理不符 .,The Relativity of Simultaneity,4.4

11、 Simultaneity,事件 1 :车厢后壁接收器接收到光信号. 事件 2 :车厢前壁接收器接收到光信号.,和光速不变紧密联系在一起的是：在某一惯性系中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观察，并不一定是同时发生的 .,The Relativity of Simultaneity,(Simultaneity),In S :,In S:,A Closer Look at Simultaneity (2 ),The Relativity of The Time Interval,4.5 Time Dilation and the Twin Paradox,运 动 的 钟 走

12、得 慢,The Relativity of the Time Interval,(时间的延缓),Proper Time Interval (固有时间 ),The proper time is the time interval between two events occur at the same location in an inertial reference frame.,(proper time),Time Dilation (时间延缓 ),Clocks moving relative to an observer are measured by that observer to r

13、un more slowly (as compared to clocks at rest),(Lorentz factor),(speed parameter),Time Dilation (时间延缓 ),The Lorentz Factor,The speed parameter,The Tests of Time Dilation,1. Microscopic Clocks,The lifetime of muons () in the rest frame is :,When the muons are moving at speed v =0.9994c :,2. Macroscop

14、ic Clocks,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 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 t

15、he 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 events occur at the same location in an inertial reference frame.,(c) no.,A,B,You

16、r 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 trip take according to measurements mad

17、e 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 Earth Event 2: the end of the trip at LP13.,t1=0,t1=0,In your frame:,In Earth frame:,In Earth frame:,E,P,A student must

18、 complete a test in the teachers frame of reference S. The student puts on his rocket skates and soon 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

19、 the teacher?,Solution:,Ex.3,For a student rests in the teachers frame S :,For a moving clock with the student in frame S:,t1=0,t1=0,The Twins Paradox (343”),Sally,Sally,The Proper Length (Rest Length),4.6 Length Contraction,The proper length L0 of the platform measured by Sam: The train moves throu

20、gh the length L0 in a time:,For Sally, Length L of the platform :,Sally,Length Contraction (长度收缩),(Contracted Length ),The relative motion causes a length contraction!,In the figure, Sally (at point A) and Sams spaceship (of proper Length L0 =230m) pass each other with constant relative speed v. Sal

21、ly 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: L0,The relative speed:,The Tests of Time Dilation,1. Microscopic Clocks,The lifetime of muons () in the rest

22、 frame is :,When the muons are moving at speed v =0.9994c :,2. Macroscopic Clocks,A student must complete a test in the teachers frame of reference S. The student puts on his rocket skates and soon is moving at a constant speed of 0.75c relativity to the teacher. When 1h (one hour) has passed on the

23、 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 in the teachers frame S :,For a moving clock with the student in frame S:,t1=0,t1=0,(a) C1 t t,A friend of your travels by you in her fast sports car at a s

24、peed 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 friend? (d) How many

25、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 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 and height at rest? (b) How many seco

26、nds 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),狭义相对论的时空观 1） 两个事件在不同的惯性系看来，它们的空间关系是相对的， 时间关系也是相

27、对的，只有将空间和时间联系在一起才有意义. 2）时空不互相独立，而是不可分割的整体. 3）光速 C 是建立不同惯性系间时空变换的纽带.,3） 时， .,1）时间延缓是一种相对效应 .,2）时间的流逝不是绝对的，运动将改变时间的进程.（例如新陈代谢、放射性的衰变、寿命等 . ）,The Spacetime Coordinates of An Event: (x,y,z,t),4.7 Four-Dimensional Space-Time,x=3.7m, y=1.2m, z=0m, t=34.5s,The Galilean Transformation Equations,4.8 Galilean

28、 and Lorentz Transformation,y= y, z= z (Approximately valid at low speed),The Lorentz Transformation Equations,(valid at all physically possible speed),The Galilean Transformation for Pair of Events,Let label Event 1 for x1 , t1 and Event 2 for x2 , t2 , then,The Lorentz Transformation for Pair of E

29、vents,The Lorentz Transformation ( 130” ),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,Simultaneity,Consequences of the Lorentz Tran

30、sformation Equations,If two events occur at difference places in S:,and the events are simultaneous in S:,(simultaneous in S ),In S：,( not simultaneous in S ),Simultaneity,Consequences of the Lorentz Transformation Equations,If two events occur at difference places in S:,and the events are simultane

31、ous in S:,In S：,Time Dilation,In S:,The Galilean Transformation for Pair of Events,Let label Event 1 for x1 , t1 and Event 2 for x2 , t2 , then,The Lorentz Transformation for Pair of Events,Length Constant in Galilean Transformation,If we put,The rods end points are measured simultaneously.,Length C

32、ontraction,If we put,The rods end points are measured simultaneously.,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 4.0010

33、8m from the Reptilian base as measured from the ships reference frame. The Reptulians have obviously attacked the Earth outpost, so the starship begins to prepare for a confrontation with them.,Solution:,SP4.(p.935),In S frame:,Earth outpost,(a) The speed of the ship relative to the planet and its m

34、oon is 0.980c. What are the distance and time interval between the burst and the explosion as measured in the planet-moon inertial frame?,Solution:,SP4.(p.935),In S frame:,In S frame:,Solution:,SP4.(p.935),(b)What is the meaning of the minus sigh in the value for ?,In S frame:,In S frame:,(c) Does t

35、he burst cause the explosion, or vice versa?,In S frame:,Impossible!,The burst dosent cause the explosion, they are unrelated events!,讨论：1) 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? 2) 两事件发生的时序与因果律,即在 系中观测，事件1有可能比事件2先发生、同时发生、或后发生，时序有可能倒置。,与因果律是否矛盾？,有因果关联的事件时序不变，无因果关联的事件 才可能发生时序变化。,Solution:,In the old West,

36、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 second on

37、e (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 sees a duel between two men standing on th

38、e 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

39、of reference, who fired first? (b) How much earlier did he fire? (c) Who was struck first?,22(p.759),The Galilean Velocity Transformation,The Lorentz Velocity Transformation,The Lorentz Velocity Transformation,The Lorentz Velocity Transformation (40),4.9 Relativistic Momentum and Mass,Classical Mome

40、ntum,(low speed),牛顿定律与光速极限的矛盾,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,Classical Momentum,(low speed),Relativity Momentum,Relation of Mass and Velocity,4.10 The Ultimate Speed,The Ultimate Speed,No entity that carries energy or information can exceed the limit c.,Testing the speed of light postulate,Neutral pion

41、: v = 0.99975c,Newtons 2nd Law in Relativity,4.11 Energy and Mass; E = mc2,The Relativistic Kinetic Energy,For a particle,Using the work- energy theorem,The Relativistic Kinetic Energy,The Relativistic Kinetic Energy,(classical kinetic energy),(Relativistic kinetic energy),The Relativistic Kinetic E

42、nergy,Mass Energy (Rest Energy),Total Energy,Momentum and Kinetic Energy,质能关系预言：物质的质量就是能量的一种储藏 .,电子的静质量,电子的静能,质子的静能,相对论质能关系,1千克的物体所包含的静能,1千克汽油的燃烧值为 焦耳 .,静能 ：物体静止时所具有的能量 .,质子的静质量,质能关系预言：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统一的物理规律。,1千克的物体所包含的静能,1千克汽油的燃烧值为 焦耳 .,例：,现有 100 座楼，每楼 200 套房，每套房用电功率 10000 W ，总功率 ，每天用

43、电 10 小时 ， 年耗电量 ，可用约 33 年。,反应质量亏损,释放能量,1 kg 核燃料释放能量,锂原子的核反应,两粒子所具有的总动能,两粒子质量比静质量增加,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，这是相对论的又一极其 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, 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的应用,质量亏损,原子质量单位,放出的能量,1g 铀 235 的原子裂变所释放的能量,1 核裂变,我国于 1958 年建成的首座重水反应堆,2 轻核聚变,释放能量,质量亏损,轻核聚变条件 温度要达到 时，使 具有

44、 的动能，足以克服两 之间的库仑排斥力.,例1 设一质子以速度 运动. 求其总能量、动能和动量.,解 质子的静能,也可如此计算,例2 已知一个氚核 和一个氘核 可聚变成一氦核 , 并产生一个中子 , 试问这个核聚变中有多少能量被释放出来 .,解 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,Energy,The Doppler Effect for Light,4.12 Doppler Shift for Light,(source and detector separation),Low-Speed Doppler Effect,(source and detector sepa

45、ration),(v is the relative velocity between source and detector ),Astronomical Doppler Effect,- corresponding to motion away from us + corresponding to motion toward us,radial speed of light source, vc,Doppler Shift,Red Shift:,Blue Shift:,f0 proper frequency,corresponding to motion away from us corr

46、esponding to motion toward us,Transverse Doppler Effect,T0 proper period,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 the galaxy at

47、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 us 499.8nm: correspon

48、ding to motion toward us,Proper wavelength:,The speed of the gas:,The Doppler shift :,A spaceship of rest length 130m races past a timing station at a speed of 0.740c. (a) What is the length of the spaceship as measured by the timing station? (b) What time interval will the station clock record betw

49、een 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 L Therefore, L = 87.4m. (b) The time interval for the passage of the spaceship is,(a) Is the spatial separation x between

50、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) positive,Fig.a shows two clocks in stationary frame S( they are synchronized in that frame) and one

51、 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 reading ? and (b) which clock measures a proper time?,Solution:,Q.2 (p.947),(b) C1,t1=0,t1=0,(a) C1 t1 t2,Solution:,(a) C1 : t1 t2,(b) C1,Fig.b shows

52、 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 reading ? and (b) which clock measures a proper time?,Q.3(p.947),Quas

53、ars are thought to be the nuclei of action galaxies in the early stages of their formation. A typical quasar 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

54、are related by E0 = mc2, the rate P of energy radiation and the rate of mass loss are related by P = dE0/dt = (dm/dt)c2. Thus,Since a solar mass is 2.0 1030 kg and a year is 3.156 107s,Show that when the kinetic energy of a particle equals its rest energy, the speed of the particle is about 0.866c,S

55、olution:,35 (p.759),What is the momentum of a 750-MeV proton (that is, its kinetic energy is 750MeV)?,Solution:,39 (p.759),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

56、 is the 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),(a) What is the speed of an electron whose kinetic energy is 10,000 times its rest energy? Such speeds are reached in the Stanford Linear Accelerat

57、or, 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),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 l