广义相对论课堂5引力红移时间膨胀检验和推论课件

1、广义相对论课堂5引力红移/时间膨胀检验和推论分解=LorentzEinstein=运动学引力叠成乘综合效应实际钟v0推导钟固定v=0水平平移vs斜坡平移信号速度列表比较三种推导相同：固定？同步轨道近似？低速=弱场牛顿or SR在原理上唯一区别信号速度无限vs有限=Doppler辅助钟加速系信号光慢子光框架牛顿SR独特牛顿特点快清晰繁琐量纲分析dimensional analysisC信号速度GM、R活动1：快速说明无量纲。思考20秒、写下或解释给邻座记忆术能量比Action 2:推导比例=引力能/静质量能条件：球天体质量M、半径R、均匀密度1、什么叫束缚能？Binding energy?引力束

2、缚能=-牛顿（自）引力势能分解、2、用M、R=3、比例Martin Rees 7 Numbers in Universe结果：引力势能Martin Rees,Just Six Numbers The Deep Forces that Shape the UniverseN1036示范：走时率比例差异rate =N/TN=TAction 2: local law = global effects local law=equation+measure，globally compare and verify.三种推导讨论课1：FF (2)、auxiliary clock辅助钟推导=思想实验示范！dt

3、为什么相等？如何区分坐标时和固有时速度相对优点LPI思路图前半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.运动学力学其他物理LLI点质量SEPFFFpref

4、erred对应原理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：电磁精细结构常数测量速度相对性原理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何地引力红移实验GRE何时物理学常数上两者合起来时空position活动3：测试你对实验的理解时钟考题牛顿版本的EEPEEPMetric TheoryMetric theory1、Spacetime is endowed with a symmetric metric g. 2、测地线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怎么来的决定引力场的场方程不同Brans-Dicke scalar+tensorEinstein GR tensorVessot & Levine 1979 火箭引力红移实验UCR=Universal Clock R

7、ateHartle 10.110五大经典检验引力红移实验1979Classical tests 4-5-6Transponder异频雷达收发机一阶、二阶效应因子叠加 vs 叠乘火箭红移实验构造设计（自动）雷达异频收发机天才设计：自动异频收发固定？教材第221页第二段第一句: a transponder on the rocket， which then sends it back again at the frequency it was received.收（音、视）+发需要准确到Doppler效应二阶往返Doppler效应是叠乘，非叠加！k1+V+V2/2k2=(1+V)/(1-V)(1+

8、V)(1+V+V2)(1+V)2+V2(1+V)1+2V+2V2往返是否有二阶？教材错！有4倍的二阶思路图后半Einstein引力场=弯曲时空？四点引力时间膨胀=时间弯曲闵氏时空一体几何转盘非欧几何潮汐引力时空弯曲时间弯曲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!关键要有Minkowski观念Schilds ladder如何确定静止无穷远精度双曲加速常引力场倒数加速度vs平方反比范式paradigm作业：哪种推导超距与场Ohanian提及量子力学测量解释不相容推导时用的牛顿或狭义结果却没有全局平直时空=没有全局惯性系（钟尺）LIF弯曲时间弯曲时空类比地球球面弯曲直观=测地线减速偏离正曲率两次相交习题6.14潮汐引力径向拉伸+横向挤压三种摆法潮汐加速度=？测地线偏离加速度=曲率Einstein转盘(匀速V) ：数量杆数目L0=桌面测得外围周长L=转盘系测