【正文】 stant relative speed v. Sally measures a time interval of for the ship to pass her. In terms of c , what is the relative speed v between Sally and the ship? Solution: () tvL ??In Sally’s frame: In Sam’s frame: L0 20 1 )( cvLtv ????The relative speed: 20 1LL ??? cLtccLv )( 2020 ???? The Tests of Time Dilation 9 99 11122???????1. Microscopic Clocks The lifetime of muons (μ) in the rest frame is : st ?2 0 ??When the muons are moving at speed v = : stt ?? ?? ??2. Macroscopic Clocks 0tt ?? ? A student must plete a test in the teacher’s frame of reference S. The student puts on his rocket skates and soon is moving at a constant speed of relativity to the teacher. When 1h (one hour) has passed on the teacher’s clock, how much time has passed on a clock that moves with the student, as measured by the teacher? Solution: Ex. h1t ??hhtt 660750111 22 ..39。 ????? tthh 2 ???t139。2 t2 yt ??In your frame: In Earth frame: yycvtt 2 2 49 9 10)(1220 ???????In Earth frame: ytt t o t a l 4 4 82 ??? ??E P A student must plete a test in the teacher’s frame of reference S. The student puts on his rocket skates and soon is moving at a constant speed of relativity to the teacher. When 1h (one hour) has passed on the teacher’s clock, how much time has passed on a clock that moves with the student, as measured by the teacher? Solution: h1t ??For a student rests in the teacher’s frame S : For a moving clock with the student in frame S’: 20)(1cvtt????039。 xx ?A Closer Look at Simultaneity (2’ ) The Relativity of The Time Interval Time Dilation and the Twin Paradox 運(yùn) 動(dòng) 的 鐘 走 得 慢 The Relativity of the Time Interval cDt 20 ??cLt 2??0tt ?? ?2221 DtvL ??????? ??(時(shí)間的延緩 ) Proper Time Interval (固有時(shí)間 ) The proper time is the time interval between two events occur at the same location in an inertial reference frame. cDt 20 ??(proper time) Time Dilation (時(shí)間延緩 ) cLt 2??0tt ?? ?Clocks moving relative to an observer are measured by that observer to run more slowly (as pared to clocks at rest) 20)(1cvtt????20222tc21tv21Dtv21L )()( ??????????? ??0tt ?? ?? cv?????? 112 (Lorentz factor) (speed parameter) cL2t ??2tcL ??2022 )()()( tctvtc ?????Time Dilation (時(shí)間延緩 ) cDt 20 ??The Lorentz Factorγ 211????cv?? The speed parameter 1 ??cv ?0tt ?? ??The Tests of Time Dilation 9 99 11122???????1. Microscopic Clocks The lifetime of muons (μ) in the rest frame is : st ?2 0 ??When the muons are moving at speed v = : stt ?? ?? ??2. Macroscopic Clocks 0tt ?? ?The Time Dilation (2’ ) In a traveling boxcar, a wellequipped 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 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: () 0tt ?? ??(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. c? A B Your starship passes Earth with a relative speed of . After traveling (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 (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: () Event 1: the start of the trip at Earth Event 2: the end of the trip at LP13. t139。 : 12 tt ?012 ???? tttIn S: 12 39。39。 tt ?(Simultaneity) 039。( 222 txP12 39。 (in train) ),( 111 txPEvent 1 )39。,39。y39。o1 2123691236939。x39。s39。ssc?球投出前 c?dcdt ??112 tt ???v??? cdt2結(jié)果 :觀察者先看到投出后的球，后看到投出前的球 . 試計(jì)算球被投出前后的瞬間，球所發(fā)出的光波達(dá)到觀察者所需要的時(shí)間 . (根據(jù) 伽利略變換 ) 球投出后 v???cv? 900 多年前（公元 1054年 5月）一次著名的 超新星爆發(fā) ， 這次爆發(fā)的殘骸形成了著名的金牛星座的蟹狀星云。oz 39。xy 39。yy伽利略變換 相對(duì)于不同的參考系 ,長(zhǎng)度和時(shí)間的測(cè)量結(jié)果是一樣的嗎 ? 絕對(duì)時(shí)空概念：時(shí)間和空間的量度和參考系無(wú)關(guān) , 長(zhǎng)度和時(shí)間的測(cè)量是絕對(duì)的 . 牛頓的絕對(duì)時(shí)空觀 牛頓力學(xué)的相對(duì)性原理 二 經(jīng)典力學(xué)的絕對(duì)時(shí)空觀 注 意 牛頓力學(xué)的相對(duì)性原理，在宏觀、低速的范圍內(nèi)，是與實(shí)驗(yàn)結(jié)果相一致的 . 實(shí)踐已證明 , 絕對(duì)時(shí)空觀是不正確的 . 對(duì)于不同的慣性系 ,電磁現(xiàn)象基本規(guī)律的形式是一樣嗎？ 真空中的光速 m / 800??? ??c 對(duì)于兩個(gè)不同的慣性參考系 , 光速滿足伽利略變換嗎 ？ ?v??? ?? cc 39。xtvz 39。,39。ss* )39。oz 39。xy 39。zz uu ?39。amF ?? ?v?? xx uu 39。加速度變換公式 39。yy aa ?39。tt ?39。yy ?39。?? tt39。 GalileanNewtonian Relativity * The MichelsonMorley Experiment Postulates of the Special Theory Relativity Simultaneity Time Dilation and the Twin Paradox Length Contraction FourDimensional SpaceTime Galilean and Lorentz Transformations Relativistic Momentum and Mass The Ultimate Speed Energy and Mass。 E = mc2 * Doppler Shift for Light 狹義相對(duì)論與時(shí)空觀 Special Theory of Relativity For inertial reference frames. General Theory of Relativity For noninertial reference frames. (1916) cv ?Albert Einstein ( 1879 – 1955 ) 1921: Nobel prize (1905) Quantum of Light (1905) 愛(ài)因斯坦的 哲學(xué)觀念： 自然界應(yīng)當(dāng)是和諧而簡(jiǎn)單的 . 理論特色： 出于簡(jiǎn)單而歸于深?yuàn)W . GalileanNewtonian Relativity In two inertial frames A and B,which relative velocity is Inertial frame is one in which Newton’s law hold c o n s t a n t?BAv?pBpA aa?? ?The particle’s velocity is The acceleration is BApBpA rrr??? ??BApBpA vvv