Action Free fall vs accelerating frame Hartle 6

例子—Action!

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

Hartle 6. 4

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

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").

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

Eovtos Dicke Eöt-Wash group @Washington Univ. @Seattle 注意精度提升！

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

locality! time！ • local——space+ time! – tidal effects – 例题 6. 1、Problem 6. 4 • 3种摆法

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

光线偏折 • Two viewpoints切换 – 图左 2：习题 6. 4 – 图右 2： • Curved – vs 直线 Aberation French

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 Cases Frequency relative to shift each other Static 0 Motion with k uniform speed γ acceleratin ? g

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

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

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 dr 2 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).

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.

2、viewpoint 2 nd • Nonrel牛顿运动学 enough

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