1. Announcements HW 9 due today HW10 posted, due Apr. 14 Gregory, Chapter 21, pp. 447 to end, Chapter 25, pp. 522-24 Alistair McGrath, “In the Beginning” in the coursepack Reminder: go to lunch questions

2. Last time Guest lecture: Steve Detweiler, UF physics - History of black holes: objects so dense that light cannot escape from them - Noneuclidean geometry: Einstein said spacetime was curved by mass. Objects follow straightest path in curved spacetime Film: Bronowski: Knowledge or certainty - Using light of different wavelengths as a probe of nature - Early history of quantum mechanics

3. In the film Bronowski said that Heisenberg's Uncertainty Principle was badly named. He said we should instead call it the Principle of 1. Certainty 2. Tolerance 3. Unknowability 4. Taste 5. Deviance

4. Recap: Einstein theory of general relativity Einstein felt there should be a way to formulate laws of nature in every kind of frame, including accelerated ones He began with the “Principle of Equivalence”: “There’s no way to tell the difference between acceleration and gravity”

5. Equivalence principle Rocket far from any gravitating body (star, planet…), at rest. Acceleration=0, no gravity Rocket far from any gravitating body, accelerating a = g, no gravity a Rocket at rest on Earth a=0, gravity Can’t tell the difference

6. a a a Equivalence principle cont’d Rock falls according to you as though It were under the influence of gravity t

7. Equivalence principle cont’d Rock thrown horizontally in frame of outside observer t How rock looks to you in rocket

8. A strange consequence of equivalence Light shone horizontally in frame of outside observer t How light looks to you in rocket Light bends in accelerating frame  light bends in gravitational field

9. Eddington 1919 expt. confirms bending of light Einstein theory of general relativity says any mass curves spacetime around it: Light travels on a geodesic – the shortest path between 2 pts. on the curved surface