Would it be possible to detect this ‘fall’ (of about 10 -13 m across 30 m)?

# Would it be possible to detect this ‘fall’ (of about 10 -13 m across 30 m)?

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## Would it be possible to detect this ‘fall’ (of about 10 -13 m across 30 m)?

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1. Does light actually accelerate downwards at 9.8 m/s2 as it goes through Earth’s gravity despite its zero mass? • Would it be possible to detect this ‘fall’ (of about 10-13 m across 30 m)? • Yes! But the fall is twice what is expected from Newton due to curvature of space due to gravity • As a photon has momentum, does it have mass? • No. A photon has no rest mass

2. A clock slows down when travelling at high speed • It also slows down in a strong gravitational field. • Is there some sort of equivalence between the two situations? • Yes! Consider a rotating disk…

3. Apply Equivalence Principle • Gravitational red shift for clocks at different heights Resting clock Fast moving clock = slow by time dilation

4. Centripetal acceleration Apply Equivalence Principle

5. Apply Equivalence Principle • Gravitational red shift for clocks at different heights High fast clock Centripetal acceleration Low slow clock

6. Does the light which "lenses" around a distant galaxy follow a "geodesic" - a natural pathway in curved space-time? • A laser beam fired horizontally on the moon will curve gently as it emerges into space. • A bullet fired from the same spot might actually go into orbit, metres above the moon's surface • Are both the laser beam and the bullet following the same curve in space-time? • No. The bullet follows a parabolic projectile trajectory • The light is following a geodesic • Why does Mercury's orbit precess, which is supposed to be a proof of general relativity? • It precesses because of the extra volume of space near the Sun created by the Sun’s gravity!

7. Constructing geodesics Parallel lines converge on a curved surface

8. Earth Sun Curved space: Gravity of Sun • Radio signals from distant space craft are delayed when Sun is near the path • There is more space in between!

9. Earth clear path near Sun path Venus Curved Space: Radar echo from Venus • Radar echo from Venus takes longer when Sun is nearby Time delay Date

10. Curved Space: Advance in Perihelion of Mercury • Perihelion (closest approach to Sun) advances owing to gravitational influence from rest of solar system by 531” every 100 years • However this is insufficient to account for the observed advance of 574” every 100 years • Residual 574 – 531 = 43” is due to General Relativity Mercury