广义相对论课堂2 牛顿引力与SR不相容 自由落体思想及推论

1. 广义相对论课堂2牛顿引力与SR不相容自由落体思想及推论广义相对论课堂2牛顿引力与SR不相容自由落体思想及推论 2012.9.13

2. 一、牛顿万有引力定律不符合Lorentz不变性 不相容于SR

3. 引力万有——惯性系 Einstein1907年底评述 Thorne P.77--

4. Lorentz不变× • 瞬时反应、超距作用（等价于场Ohanian第2章末节） • Poisson方程 • 引力势——源 • Lorentz力——场——速度+B的变换

5. 同是平方反比力荷只正不负、只吸引不排斥论文项目同是平方反比力荷只正不负、只吸引不排斥论文项目 • 引力波带走能量为负——》辐射源自身能量+——》辐射强度增大 • 标量、矢量、对称张量场MTW §7习题 • 严重缺陷与实验结果不符 • 或不自洽且无精确解 • 1950-60s相对论场论修正回到GR • Ohanian • Zeldovich

6. 二、Einstein自由落体思想：如果一个人自由下落，他将感受不到自己的重量。二、Einstein自由落体思想：如果一个人自由下落，他将感受不到自己的重量。 活动：回忆3-5个自由落体情景 ——亲身或眼见

7. 失重——太空舱 • 代入——身感+想像——思想实验 • 失重——引力消除——相对于谁？ • 自由漂浮 • 不漂浮的教室? • 完美惯性

9. Reference frame=参考系 • 自由、惯性 • 颠倒了牛顿力学观念——表格 • “下落”——类似加速包含了减速

10. 例子—Action!

11. 理论上优先性Free fall vs accelerating frame □ □ □ □

12. Hartle 6.4

13. 二=》三、Weak Equivalence PrincipleGalileo原理Universal Free Fall 万有=不依赖于组分（本性）

14. 多种表述wikipedia • The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition. • All test particles at the alike spacetime point in a given gravitational field will undergo the same acceleration, independent of their properties, including their rest mass.[2] • All local centers of mass vacuum free fall along identical (parallel-displaced, same speed) minimum action trajectories independent of all observable properties. • The vacuum world line of a body immersed in a gravitational field is independent of all observable properties. • The local effects of motion in a curved space (gravitation) are indistinguishable from those of an accelerated observer in flat space, without exception. • Mass (measured with a balance) and weight (measured with a scale) are locally in identical ratio for all bodies (the opening page to Newton's "Principia").

15. 质荷比——组分=本性nature深刻！未尽？量子场论多体质荷比——组分=本性nature深刻！未尽？量子场论多体 • 引力 • 电磁学

16. tests • Year Investigator Sensitivity Method • 500? Philoponus [8] "small" Drop Tower • 1585 Stevin [9] 5x10-2 Drop Tower • 1590? Galileo [10] 2x10-2 Pendulum, Drop Tower • 1686 Newton [11] 10-3 Pendulum • 1832 Bessel [12] 2x10-5 Pendulum • 1910 Southerns [13] 5x10-6 Pendulum • 1918 Zeeman [14] 3x10-8 Torsion Balance • 1922 Eötvös [15] 5x10-9 Torsion Balance • 1923 Potter [16] 3x10-6 Pendulum • 1935 Renner [17] 2x10-9 Torsion Balance • 1964 Dicke,Roll,Krotkov [18] 3x10-11 Torsion Balance • 1972 Braginsky,Panov [19] 10-12 Torsion Balance • 1976 Shapiro, et al.[20] 10-12 Lunar Laser Ranging • 1981 Keiser,Faller [21] 4x10-11 Fluid Support • 1987 Niebauer, et al.[22] 10-10 Drop Tower • 1989 Heckel, et al.[23] 10-11 Torsion Balance • 1990 Adelberger, et al.[24] 10-12 Torsion Balance • 1999 Baeßler, et al.[25] 5x10-13 Torsion Balance • cancelled? MiniSTEP 10-17Earth Orbit • 2015? MICROSCOPE 10-16 Earth Orbit

17. EovtosDickeEöt-Wash group @Washington Univ. @Seattle 注意精度提升！

18. 弱等效原理“等效” ≠ 等同FFF=LIF 1、locally, exactly a point, no frame 2、globally, G cannot be canceled out • 加速系∞有效----“不等效”！----引力场∞消失

19. locality!time！ • local——space+ time! • tidal effects • 例题6.1、Problem 6.4 • 3种摆法

20. 四、Two deductions 1、light ray deflection, curved! 2、gravitational time dilation or clocks slow down

21. 光线偏折 • Two viewpoints切换 • 图左2：习题6.4 • 图右2： • Curved • vs 直线AberationFrench

22. 引力时间膨胀引力红移 最基本的引力效应 frequency<time=duration N=VT

23. 引力时间膨胀 • 1、FF viewpoint——fastest derivation • （1）gravitational redshift——from viewers on Earth • Doppler effect • v= g(h/c) • k=1+v/c—+O(2) 一阶效应

24. 讨论twin paradox (Kleppner 12) • 最早？ • 赵凯华

25. Doppler效应源-接收器相对运动起因不同 Doppler、SR 引力 宇宙学

26. Physics unclear • how to measure proper time along any worldline that belongs to a particle in free fall？ • a nearby geometrodynamic clock =Marzke-Wheeler coordinates Problem 4.6 • By means of the geometrodynamic clock and the radar-ranging procedure outlined in Fig. 5.5 we can measure the spacetime interval between these points. close enoughlatticework

27. (2)、auxiliary clock辅助钟推导 • t坐标时，固有时 • 两条世界线——套 • 平移=静态

28. Physical meaning课外作业阅读笔记 • Signals! • This shows that if clock II is at the higher potential (ДФ > 0), then dr2 is larger than drx. The signals sent out from clock I at one-second intervals arrive at clock II with intervals larger than one second. Clock I, which is deeper in the gravitational potential, runs slow. This effect does not depend on the type of signal that is used (light flashes, cannonballs, messenger rockets, periodic radio wave, etc.). It is only important that each signal have exactly the same motion as the preceding one (same shape of worldline).

29. Result conditions: • 1、 valid to lowest order in the gravitational field strength. • 2、 if the potential Ф is time dependent and changes appreciably in the time needed to send the signal from one clock to the other, then fails.

30. 2、viewpoint 2nd • Nonrel牛顿运动学 enough

31. 引力场等效加速系为什么引入加速系？自学笔记预习、讨论引力场等效加速系为什么引入加速系？自学笔记预习、讨论 □ □ □ □

32. 时空弯曲 • 时间弯曲warped/curved • Ohanian: runs slowgeodesicwarp • Similar on Earth • In diagram: since curved depicted in flat plane