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A recap of the main points so far… Observers moving uniformly with respect to each other

A recap of the main points so far… Observers moving uniformly with respect to each other do not agree on time intervals or distance intervals do not agree about the simultaneity or otherwise of events A moving clock appears to run slow – time dilation

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A recap of the main points so far… Observers moving uniformly with respect to each other

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  1. A recap of the main points so far… • Observers moving uniformly with respect to each other • do not agree on time intervals or distance intervals • do not agree about the simultaneity or otherwise of events • A moving clock appears to run slow – time dilation • A moving ruler appears short – length contraction • A moving object has an increased relativistic mass • Mass can be converted into energy (and vice-versa) • E = m c2

  2. The Twins Paradox

  3. Symmetry As far as the observer on Earth is concerned, a clock on the spaceship is running slow and lengths are contracted in the direction of motion. As far as the observer on the spaceship is concerned, a clock left on Earth is running slow and lengths are contracted in the direction of motion. The frames of reference are equivalent?

  4. Hammer and feather on the moon

  5. Underlying principles of General Relativity The Equivalence Principle No difference between a steady acceleration and a gravitational field

  6. Gravity and Acceleration cannot be distinguished

  7. V = a h/c h

  8. Equivalence principle – this situation should be the same Gravitational field h

  9. Consequences I. Gravitational Redshift Size of effect (doppler shift equivalent speed) Earth 0.2 m/s Sun 0.6 km/s White Dwarf 70 km/s Neutron Star 100,000 km/s Black-hole infinite

  10. Gravitational redshift of Sirius B Equivalent velocity 80 km/s

  11. Corrections to GPS Orbital radius 26,000 km gh/c2 = 0.0000000026 Clocks “on the ground” would lose about 0.2 ms per day (actually a bit less). Clocks on the GPS satellites run intentionally slowly!

  12. Lensing of distant galaxies by a foreground cluster

  13. QSO 2237+0305 The Einstein cross

  14. Abell 1689 Plus derived Mass Map

  15. Einstein Rings Galaxies at 3, 6 and 11 billion light years away

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