狭义相对论与时空观

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,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 Mass,4,.10,The Ultimate Speed,4,.11,Energy and Mass;,E = mc,2,4,.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 Light,(,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 different 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 inertial reference frames are equivalent for the description of mechanical phenomena.,伽利略变换,当 时,与 重合,位置坐标变换公式,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,),(x,y,z),(,x,y,z,),(事件),Four-Dimensional Space-Time,加速度变换公式,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考系无关,长度和时间的测量是绝对的,.,牛顿的绝对时空观,牛顿力学的相对性原理,二 经典力学的绝对时空观,注 意,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 ？,球投出,前,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,),球投出,后,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,均能用肉眼观察, 特别是开始的,23,天, 白天也能看见 .,物质飞散速度,l,=,5000,光年,A,B,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,l,=,5000,光年,物质飞散速度,A,B,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,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 .,L,G,1,G,2,Michelsons Interferometer,If,M,2,is moved by ,then and,the fringe pattern is shifted by one fringe,M,1,L,M,1,L,M,1,L,G,M,1,M,2,T,G,M,1,G,G,M,2,G,G,M,2,M,2,G,M,2,M,1,G,T,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,Michelsons 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 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 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,Event,2,Frame,S,(on Earth),Frame,S,(in train),Event,1,(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 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 run 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. Macroscopic 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 the,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,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 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),Event 1,: the start of the trip,at Earth,Event 2,: the end of the trip,at LP13,.,t,1,=0,t,1,=0,t,2,t,2,In your frame:,In Earth frame:,In Earth frame:,E,P,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,0.75,c,relativity to the,teacher. When,1,h,(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.3,For a student rests in the,teachers frame,S,:,For a moving clock with the student in frame,S,:,t,1,=0,t,1,=0,t,2,t,2,The Twins Paradox,(343”),A,B,L,0,Sally,Sally,The Proper Length (Rest Length),4.6 Length Contraction,The proper length,L,0,of the platform,measured by Sam:,The train moves through the,length,L,0,in a time:,A,B,For Sally,Length,L,of the platform,:,B,Sally,v,v,Sally,Length Contraction (,长度收缩,),(Contracted Length ),The relative motion causes a,length contraction,!,A,B,Sally,v,v,A,B,Sam :,L,0,In the figure, Sally (at point A) and,Sams,spaceship (of proper Length,L,0,=230m,) pass each other with,constant relative speed,v,.,Sally,measures a time interval of,3.57,s,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:,L,0,The relative speed:,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. 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,0.75,c,relativity to the,teacher. When,1,h,(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.,For a student rests in the teachers frame,S,:,For a moving clock with the student in frame,S,:,t,1,=0,t,1,=0,t,1,t,2,(a),C,1,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 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 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 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),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 . ）,注意,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 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,x,1,t,1,and Event 2 for,x,2,t,2, then,The Lorentz Transformation for Pair of Events,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 Transformation 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,simultaneous,in,S,:,In,S：,Time Dilation,In,S,:,The Galilean Transformation for Pair of Events,Let label Event 1 for,x,1,t,1,and Event 2 for,x,2,t,2, then,The Lorentz Transformation for Pair of Events,Length Constant,in Galilean Transformation,If we put,The rods end points are measured simultaneously.,Length Contraction,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,4.00,10,8,m,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 moon 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 the burst cause the explosion, or vice versa?,In S frame:,Impossible!,The,burst,dosent,cause,the explosion, they are,unrelated events,!,时序不变,即事件1先发生,若,S,系中,则 系中：,时序变化,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？,有因果关联的事件之间的信号速率,满足时序不变条件,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, 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 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,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 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),The Galilean Velocity Transformation,The Lorentz Velocity Transformation,The Lorentz Velocity Transformation,The Lorentz Velocity Transformation,(40),4.9 Relativistic Momentum and Mass,Classical Momentum,(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,C,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:,v = 0.99975c,Newtons 2nd Law in Relativity,4.11 Energy and Mass;,E = mc,2,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 Energy,Mass Energy (Rest Energy),Total Energy,Momentum and Kinetic Energy,爱因斯坦认为（1905）,懒惰性,惯性,( inertia ),活泼性,能量,( energy ),物体的懒惰性就,是物体活泼性的度量 .,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 ，每天用电,10 小时,，,年耗电量 ，可用约,33 年,。,例：,在一种热核反应中，各种粒子的静质量如下：,求：,反应释放的能量。,氘核,氚核,氦核,中子,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,理论计算和实验结果相符,实验测量,物理意义,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 的动能，足以克服两 之间的库仑排斥力.,氘核,氦核,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 separation),(,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:,f,0,proper,frequency,corresponding to motion away from us,corresponding to motion toward us,Transverse Doppler Effect,T,0,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,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:,corresponding 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 between,the passage of the front and back ends of the ship ?,Solution:,11P.(p.949),(a),The rest length of the spaceship:,L,0,= 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 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 clock in moving frame,S.,Clocks,C,1,and C,1,read zero when they pass each other. When clocks,C,1,and C,2,pass each other, (a) Which clock has the,smaller reading,? and (b) which clock measures a,proper time,?,Solution:,Q.2 (p.947),(b),C,1,t,1,=0,t,1,=0,t,1,t,2,(a),C,1,t,1, t,2,Solution:,(a),C,1 :,t,1, t,2,(b),C,1,Fig,.,b,shows two clocks in stationary frame S ( they are synchronized in that frame) and one clock in moving frame S. Clocks,C,1,and C,1,read zero when they pass each other. When clocks,C,1,and C,2,pass each other, (a),Which clock has the,smaller reading,? and (b),which clock measures a,proper time,?,Q.3(p.947),t,1,=0,t,1,=0,t,2,t,1,Quasars 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,10,41,W,. At what,rate is,the,mass,of,this quasar being reduced to supply this energy?,Solution:,37P.(p.950),Since the rest energy,E,0,and the mass,m,of the quasar are related by,E,0,=,mc,2,the rate,P,of energy radiation and the rate of mass loss are related by,P,=,dE,0,/dt,= (,dm/dt,),c,2,.,Thus,Since a solar mass is 2,.,0,10,30,kg and a year is 3,.,156,10,7,s,Show that when the kinetic energy of a particle equals its rest energy, the speed of the particle is about 0.866c,Solution:,35 (p.759),What is the momentum of a,7,50-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 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 Accelerator,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 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 seconds would she say elapsed,on your watch,when she saw,20.0s,pass,on her,?,Solution:,10(p.758),A stick of length,L,o, at rest in reference frame S, makes an angle,with the,x,axis. In reference frame S. which moves to the right with velocity,v =,vi,with respect to S, determine,(a),the length,L,of the stick, and (b) the angle,it makes with the,x,axis.,Solution:,21(p.759),The nearest star to Earth is Proxima Centauri,4.3 light-years,away,(a),At what constant velocity must a spacecraft travel from Earth if it is to reach the star in,4.0 years, as measured by travelers on the spacecraft?,(b),How long does the trip take according to Earth observers?,Solution:,62(p.761),In the old West, a marshal riding on a train traveling,50m/s,sees a duel between two men standing on