廣義相對論課堂5引力紅移時間膨脹檢驗(yàn)和推論課件

1、廣義相對論課堂5引力紅移/時間膨脹檢驗(yàn)和推論分解=LorentzEinstein=運(yùn)動學(xué)引力疊成乘綜合效應(yīng)實(shí)際鐘v0推導(dǎo)鐘固定v=0水平平移vs斜坡平移信號速度列表比較三種推導(dǎo)相同：固定？同步軌道近似？低速=弱場牛頓or SR在原理上唯一區(qū)別信號速度無限vs有限=Doppler輔助鐘加速系信號光慢子光框架牛頓SR獨(dú)特牛頓特點(diǎn)快清晰繁瑣量綱分析dimensional analysisC信號速度GM、R活動1：快速說明無量綱。思考20秒、寫下或解釋給鄰座記憶術(shù)能量比Action 2:推導(dǎo)比例=引力能/靜質(zhì)量能條件：球天體質(zhì)量M、半徑R、均勻密度1、什么叫束縛能？Binding energy?引力束

2、縛能=-牛頓（自）引力勢能分解、2、用M、R=3、比例Martin Rees 7 Numbers in Universe結(jié)果：引力勢能Martin Rees,Just Six Numbers The Deep Forces that Shape the UniverseN1036示范：走時率比例差異rate =N/TN=TAction 2: local law = global effects local law=equation+measure，globally compare and verify.三種推導(dǎo)討論課1：FF (2)、auxiliary clock輔助鐘推導(dǎo)=思想實(shí)驗(yàn)示范！dt

3、為什么相等？如何區(qū)分坐標(biāo)時和固有時速度相對優(yōu)點(diǎn)LPI思路圖前半Einstein Equivalence Principle=EEP WEPLLI=Local Lorentz InvarianceLPI=Local Position InvarianceWEP The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition.運(yùn)動學(xué)力學(xué)其他物理LLI點(diǎn)質(zhì)量SEPFFFpref

4、erred對應(yīng)原理LIFLLI=Local Lorentz InvarianceThe outcome of any local non-gravitational experiment is independent of the velocity of the freely-falling reference frame in which it is performed.local非引力=失重自由下落FFFSEP例：電磁精細(xì)結(jié)構(gòu)常數(shù)測量速度相對性原理SRLPI=Local Position InvarianceThe outcome of any local non-gravitationa

5、l experiment is independent of where and when in the universe it is performed.局域非引力同LLIEEP vs SEP何地引力紅移實(shí)驗(yàn)GRE何時物理學(xué)常數(shù)上兩者合起來時空position活動3：測試你對實(shí)驗(yàn)的理解時鐘考題牛頓版本的EEPEEPMetric TheoryMetric theory1、Spacetime is endowed with a symmetric metric g. 2、測地線The trajectories of freely falling test bodies are geodesics

6、 of that metric. 3、local SR = LLI In local freely falling reference frames, the non-gravitational laws of physics are those written in the language of special relativity. 不同Metric theory不同在于 1怎么來的決定引力場的場方程不同Brans-Dicke scalar+tensorEinstein GR tensorVessot & Levine 1979 火箭引力紅移實(shí)驗(yàn)UCR=Universal Clock R

7、ateHartle 10.110五大經(jīng)典檢驗(yàn)引力紅移實(shí)驗(yàn)1979Classical tests 4-5-6Transponder異頻雷達(dá)收發(fā)機(jī)一階、二階效應(yīng)因子疊加 vs 疊乘火箭紅移實(shí)驗(yàn)構(gòu)造設(shè)計(jì)（自動）雷達(dá)異頻收發(fā)機(jī)天才設(shè)計(jì)：自動異頻收發(fā)固定？教材第221頁第二段第一句: a transponder on the rocket， which then sends it back again at the frequency it was received.收（音、視）+發(fā)需要準(zhǔn)確到Doppler效應(yīng)二階往返Doppler效應(yīng)是疊乘，非疊加！k1+V+V2/2k2=(1+V)/(1-V)(1+

8、V)(1+V+V2)(1+V)2+V2(1+V)1+2V+2V2往返是否有二階？教材錯！有4倍的二階思路圖后半Einstein引力場=彎曲時空？四點(diǎn)引力時間膨脹=時間彎曲閔氏時空一體幾何轉(zhuǎn)盤非歐幾何潮汐引力時空彎曲時間彎曲warped/curvedOhanian: runs slowgeodesicwarpSimilar on Earth范式In diagram: illusion because curved depicted in flat plane; curved/warp spacetime as a wholeflat spacetime curved!關(guān)鍵要有Minkowski觀念Schilds ladder如何確定靜止無窮遠(yuǎn)精度雙曲加速常引力場倒數(shù)加速度vs平方反比范式paradigm作業(yè)：哪種推導(dǎo)超距與場Ohanian提及量子力學(xué)測量解釋不相容推導(dǎo)時用的牛頓或狹義結(jié)果卻沒有全局平直時空=沒有全局慣性系（鐘尺）LIF彎曲時間彎曲時空類比地球球面彎曲直觀=測地線減速偏離正曲率兩次相交習(xí)題6.14潮汐引力徑向拉伸+橫向擠壓三種擺法潮汐加速度=？測地線偏離加速度=曲率Einstein轉(zhuǎn)盤(勻速V) ：數(shù)量桿數(shù)目L0=桌面測得外圍周長L=轉(zhuǎn)盤系測