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Extra resources for Elementary general relativity
10. Show that the difference between the clocks due to the gravitational redshift is ∆sa − ∆sr = gh∆t. Suppose that h = 10 km. 6 × 10−7 sec. 0 × 10−7 sec. 3 shows that a rigorous calculation in general relativity gives the same result. The Global Positioning System (GPS) of satellites must adjust its clocks for time dilation and gravitational redshifts to function properly. In fact, the effects are 10,000 times too large to be ignored. 3 The Local Inertial Frame Postulate Suppose that curved surface dwellers attempt to construct a square coordinate grid using rigid rods constrained (of course) to their surface.
By Eq. 15), A = 0. Thus Eq. 17) the sign chosen according as the motion is outward or inward. Differentiate Eq. 17) and substitute Eq. 17) into the result: m d2 r = − 2. 18) For a distant slowly moving particle, ds ≈ dt. Since the Newtonian theory applies to this situation, Eqs. 18) must coincide. Thus m = κM , in agreement with Eq. 6). 3 The Solar System Tests This section compares the predictions of general relativity with observations of the motion of planets and light in our solar system. Three general relativistic effects have been measured: perihelion advance, light deflection, and light delay.
17) and substitute Eq. 17) into the result: m d2 r = − 2. 18) For a distant slowly moving particle, ds ≈ dt. Since the Newtonian theory applies to this situation, Eqs. 18) must coincide. Thus m = κM , in agreement with Eq. 6). 3 The Solar System Tests This section compares the predictions of general relativity with observations of the motion of planets and light in our solar system. Three general relativistic effects have been measured: perihelion advance, light deflection, and light delay. Perihelion Advance.