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

2. Equivalence between gravity & acceleration a Man in a closed box on Earth Man in a closed box on an accelerating rocket in deep outer space. Since m G =m I, if a=-g, the conditions are equivalent g mGgmGg mIamIa

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 m G =m I as a coincidence These two environments must be exactly equivalent.

6. Einstein Equivalence Principle in 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

8. If the rocket is accelerating, the light beam bends ½at 2

9. Since the accelerating rocket and gravity are equivalent, gravity must cause light to bend ½gt 2 for our room L≈6m: very, very tiny effect L on Earth’s surface

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 g sun ≈ 27xg earth

11. Eddington’s 1919 Expeditions

12. Africa 1919 eclipse Measurement:  =0.00055 0 ± 0.00003 0 in agreement with Einstein’s prediction 1919 Eclipse

13. New York Times:

15. Gravitational lensing

16. “Dark Matter” astronomy

17. Mass induces curvature in space-time

18. The curvature is what we feel as gravity

19. Seoul  Rio 12 0

20. 17 0 Seoul  Rio Cartesian vs non-Cartesian coords

21. The Earth is round 17 0 ?? This is how KAL goes

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

23. Great Circles spherical 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.

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