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Einstein’s Happiest Thought

Einstein’s Happiest Thought. Micro-world Macro-World Lecture 7. Equivalence between gravity & acceleration. a. Man in a closed box on Earth. m I a. m G g. g. Since m G =m I , if a=-g , the conditions are equivalent. Man in a closed box on an accelerating rocket in deep outer space.

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Einstein’s Happiest Thought

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  1. Einstein’s Happiest Thought Micro-world Macro-World Lecture 7

  2. Equivalence between gravity & acceleration a Man in a closed box on Earth mIa mGg g Since mG=mI, if a=-g, the conditions are equivalent Man in a closed box on an accelerating rocket in deep outer space.

  3. The happiest thought I cannot tell the difference between being on earth or in a deep-space rocket accelerating with a=-g

  4. Imagination This cannot be due to coincidence. There must be some basic truth involved.

  5. Einstein didn’t accept mG=mI as a coincidence These two environments must be exactly equivalent.

  6. Einstein Equivalence Principlein his words we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration o the reference system [Einstein, 1907]

  7. So what? What would happen if I were to shine a light beam through a window on the rocket? sraight line sraight line

  8. If the rocket is accelerating, the light beam bends ½at2

  9. L Since the accelerating rocket and gravity are equivalent, gravity must cause light to bend on Earth’s surface ½gt2 for our room L≈6m: very, very tiny effect

  10. Does gravity cause light to bend? Very tiny effect: need very strong gravity and a long lever arm. Look at the bending of light from a star by the Sun. (Only possible at an eclipse.) Sir Arthur Eddington 1882-1944 gsun ≈ 27xgearth

  11. Eddington’s 1919 Expeditions

  12. 1919 Eclipse Africa Measurement: q =0.000550±0.000030 in agreement with Einstein’s prediction 1919 eclipse

  13. New York Times:

  14. Gravitational lensing

  15. “Dark Matter” astronomy

  16. Mass induces curvature in space-time

  17. The curvature is what we feel as gravity

  18. 120 Seoul  Rio

  19. Cartesian vs non-Cartesian coords 170 Seoul  Rio

  20. The Earth is round 170 ?? This is how KAL goes

  21. Geodesics The shortest distance between 2 points is Along a “geodesic.” It is a straight line In Cartesian systems

  22. Great Circlesspherical geometry The shortest distance between two points on the Earth’s surface correspond to “Great Circles”: the intersections of planes passing through the center of the Earth with the Earth’s surface.

  23. In this figure, the shortest distances are indicated by the blue lines.

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