1、Chapter 20 The special theory of relativityAlbert Einstein (1879 1955)20-1 Troubles with classical physicsThe kinematics developed by Galileo and the mechanics developed by Newton,which form the basis of what we call“classical physics”,had many triumphs.However,a number of experimental phenomena can
2、 not be understoodwith these otherwise successful classical theories.1.Troubles with our ideas about timeThe pions(or )created at rest are observed+to decay(to other particles)with an average lifetime of only .In one particular experiment,pions were created in motion at a speed of.In this case they
3、were observed to travel in the laboratory an average distance of before decaying,from which we conclude that they decay in a time given by,much larger than the lifetime measured for pions at rest.This effect,called“time dilation”,which cannot be explained by Newtonian physics.In Newtonian physics ti
4、me is a universal coordinate having identical values for all observers.ns0.26cv913.0=nsvD7.63=mD4.17=2.Trouble with our ideas about lengthSuppose an observer in the above laboratory placed one marker at the location of the pions formation and another at the location of its decay.The distance between
5、 the markers is measured to be 17.4m.Now consider the observer who is traveling along with the pion at a speed of u=0.913c.This observer,to whom the pion appear to be at rest,measures its lifetime to be 26.0ns,and the distance between the markers is Thus two observers measure different value for the
6、 same length interval.mc1.7)100.26)(913.0(9=3.Troubles with our ideas about light20-2 The postulates of special relativity1.Einstein offered two postulates that form the basis of his special theory of relativity.(I)The principle of relativity:“The laws of physics are the same in all inertial referen
7、ce frames.”(II)The principle of the constancy of the speed oflight:“The speed of light in free space has the same value c in all inertial reference frames.”2.The first postulate declares that the laws of physics are absolute,universal,and same for all inertial observers.The Second postulate is much
8、more difficult to accept,because it violates our“common sense”,which is firmly grounded in the Galilean kinematics that we have learned from everyday experiences.It implies that“it is impossible to accelerate a particle to a speed greater than c”.20-3 Consequences of Einsteins postulates1.The relati
9、vity of timeWe consider two observers:S is at rest on the ground,and S is in a train moving on a long straight track at constant speed u relative to S.The observers carry identical timing devices,illustrated in Fig 20-4,consisting of a flashing light bulb F attached to a detector D and separated by
10、a distance from a mirror M.The bulb emits a flash of light that travels to the mirror,when the reflected light returns to D,the clock ticks and another flash is triggered.0LThe time interval between ticks is:(20-1)The interval is observed by either S or S when the clock is at rest respect to that ob
11、server.MFDFig 20-40L0tcLt002=0tWe now consider the situation when one observer looks at a clock carried by the other.Fig 20-5 shows that S observes on the clock carried by S on the moving train.F DSABCLLSSStuFig 20-5FFDDAccording to S,the flash is emitted at A,reflected at B,and detected at C.This i
12、nterval is(20-20)Substituting for from Eq(20-1)and solving Eq(20-2)for gives(20-3)ctuLcLt220)2(22+=20)(1cutt=tt0LThe time interval measured by the observer(S)relative to whom the clock is at rest is called the“proper time(正确时间)”,and .That is,the observer relative to whom the clock is in motion measu
13、res a greater interval between ticks.This effect is called“time dilation”.All observer in motion relative to the clock measure“longer intervals”.0ttt0Eq(20-3)is valid for any direction of the relative motion of S and S.2.The relativity of lengthFig 20-6 shows the sequence of events as observed by S
14、for the moving clock which is on the train sideway,so that the light now travels along the direction of motion of the train.According to S the length of the clock is L,which is different from the length measured by S,relative to whom the clock is at rest.0L(A)(B)LS(C)SSSuu1tu2tu2tc22tuLtc=11tctuL=+F
15、ig 20-6uMFD0LFDFDFDIn the process from A,B to C,the total time taken is(20-6)From Eq(20-3),setting(20-7)Setting Eqs(20-6)and(20-7)equal to one another and solving,we obtain(20-8)221)(112cucLucLucLttt=+=+=2020)(112)(1cucLcutt=cLt002=20)(1cuLL=Eq(20-8)summarizes the effect known as“length contraction”
16、.(a)The lengthmeasured by an observer who is at rest with respect to the object being measured is called the“rest length”or“proper length”.(b)All observers in motion relative to S measure a shorter length,but only for dimensions along the direction of motion;length measurement transverse to the direction of motion are unaffected.0L(c)Under ordinary circumstances,and the effects of length contraction are too small to be observed.cu3 The relativistic addition of velocities Let us now modify our ti
