【文章內(nèi)容簡(jiǎn)介】 Event: (x,y,z,t) FourDimensional SpaceTime AE ven t x=, y=, z=0m, t= The Galilean Transformation Equations Galilean and Lorentz Transformation 39。39。ttvtxx???y′= y, z′= z (Approximately valid at low speed) The Lorentz Transformation Equations cvxttzzyyvtxx)(39。39。39。)(39。2???????(valid at all physically possible speed) cvxttzzyyvtxx)39。39。(39。39。)39。39。(2????????The Galilean Transformation for Pair of Events t , t39。 , 12121212 ttxxxttxxx??????????? 39。39。39。39。39。Let label Event 1 for x1 , t1 and Event 2 for x2 , t2 , then 39。39。tttvxx???????? 39。39。ttvtxx???The Lorentz Transformation for Pair of Events cvxttzzyyvtxx)(39。39。39。)(39。2??????? cxvttzzyytvxx)(39。39。39。)(39。2????????????????? cxvttzzyytvxx)39。39。(39。39。)39。39。(2??????????????????The Lorentz Transformation ( 1’30” ) For each situation, if we choose the blue frame to be stationary, then is v in the equations of Table 382 a positive or negative quantity ? Solution: CP3.() (a) positive cxvtttvxx2 )(39。 2 39。.)(39。 1 39。.???????????? cxvtttvxx2 )39。39。( 2.)39。39。( .1????????????(b) negative (c) positive Table 382 Simultaneity Consequences of the Lorentz Transformation Equations cxvtt )39。39。(2????? ?If two events occur at difference places in S’: 039。?x?and the events are simultaneous in S’: 039。?t?211????cv?? (simultaneous in S ) In S： 039。?t?2cxvt 39。??? ? 0?? t 039。?x?( not simultaneous in S ) Simultaneity Consequences of the Lorentz Transformation Equations cxvtt )39。39。(2????? ?If two events occur at difference places in S’: 0?39。x?2cxvt 39。??? ?and the events are simultaneous in S’: 039。?t?In S： 0?t?211????cv?? 0?39。x?Time Dilation 039。?x? 0t39。t ?? ?In S’: 39。)39。39。( t c xvtt ??????? ??0tt ??? ?The Galilean Transformation for Pair of Events t , t39。 , 12121212 ttxxxttxxx??????????? 39。39。39。39。39。Let label Event 1 for x1 , t1 and Event 2 for x2 , t2 , then 39。39。tttvxx???????? 39。39。ttvtxx???The Lorentz Transformation for Pair of Events cvxttzzyyvtxx)(39。39。39。)(39。2??????? cxvttzzyytvxx)(39。39。39。)(39。2????????????????? cxvttzzyytvxx)39。39。(39。39。)39。39。(2??????????????????Length Constant in Galilean Transformation t39。ttvx39。x????????xx039。 Lx ??If we put 0 a n d ?? tLx ?? 0????xtvx39。x????x39。x ?? ?LL ?0The rod’s end points are measured simultaneously. 0?t?0?t?Length Contraction 039。 Lx ??If we put )(39。 tvxx ??? ?? ?0 a n d ?? tLx ??The rod’s end points are measured simultaneously. xx0?t?0?t?x)x(39。x???????? 0LL 0 ??200 11 ?? ??? LLL As the ship follows a straightline course first past the pla and then past the moon, it detects a highenergy microwave burst at the Reptulian moon base and then, later, an explosion at the Earth outpost, which is 108m from the Reptilian base as measured from the ship’s reference frame. The Reptulians have obviously attacked the Earth outpost, so the starship begins to prepare for a confrontation with them. Solution: SP4.() mxxx be ?????sttt be ????In S frame: Earth outpost (a) The speed of the ship relative to the pla and its moon is . What are the distance and time interval between the burst and the explosion as measured in the plamoon inertial frame? Solution: SP4.() sttt be ????In S frame: ??In S’ frame: cxvtttvxx)(39。)(39。2????????????mx 810863 ??? .39。st 39。 ???cv in f ?Solution: SP4.() 0101 ???? be?0041 ????? s.39。t39。t39。t be?(b)What is the meaning of the minus sigh in the value for ? 39。t?In S frame: f i r s tt,l a t e rt be ?? be tt ?39。39。 be tt ?In S’ frame: l a t e r39。t,f i r s t39。t be ?? (c) Does the burst cause the explosion, or vice versa? In S frame: sms mtxv / 88i n f ???????Impossible! The burst dosen’t cause the explosion, they are unrelated events! 02 ???? )xcut(t ????xcut ?? 2?uctx 2???時(shí)序不變 012 ???? ttt 即事件 1先發(fā)生 若 S 系中 則 系中： S?xcut ?? 2?uctx 2???02 ???? )xcut(t ????時(shí)序變化 討論 ： 1) 在某一慣性系中的同步鐘，在另一相對(duì)其運(yùn)動(dòng)的慣性系中是否是同步的 ? 2) 兩事件發(fā)生的時(shí)序與因果律 即在 系中觀測(cè)，事件 1有可能比事件 2先發(fā)生、同時(shí)發(fā)生、或后發(fā)生，時(shí)序有可能倒置。 s?與因果律是否矛盾？ 有因果關(guān)聯(lián)的事件之間的信號(hào)速率 uctxcu 2????滿足時(shí)序不變條件 有因果關(guān)聯(lián)的事件 時(shí)序不變， 無(wú)因果關(guān)聯(lián)的事件 才可能發(fā)生時(shí)序變化。 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 marshal39。s 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 gunfighter39。s frame of reference, who fired first? (b) How much earlier did he fire? (c) Who was struck first? 22() 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 marshal39。s 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