1. Einstein’s Second Revolution

2. Movement on the surface of the Earth is limited to two dimensions: forward-backward and left-right (or N-S and E-W) However, that two-dimensional surface is curved.

3. Satellites in space are NOT restricted to two-dimensions They can also go up and down Then why does a satellite end up right back where it started? Gravity It is mysterious: How can the Earth “pull on” a satellite? Could “curvature” have something to do with it?

4. Einstein’s Special Theory of Relativity made us realize that space and time are not separate things. Instead we talk about one thing – four-dimensional “spacetime” And we refer to the “fabric of spacetime” because it can be “warped”. A good analogy is a rubber sheet that is warped by weights placed on it. The heavier the weight, the more warping. (This represents two dimensions: one of space and one of time) spacetime

5. YouTube video: Spacetime demonstrationSpacetime demonstration Start at 0:35 End at 2:00

6. Thought experiment: Albert says you’re accelerating away from him at 1g. You say no, it’s him who’s accelerating away from you. BUT – there is a test you can do to see who is really accelerating: release a ball

7. = This leads to: The Equivalence Principle The fundamental postulate of General Relativity The effects of a gravitational field are the same as the effects of acceleration

8. Now compare these two situations: In both, you are firing your engines and Al is not. In both, you feel weight and Al does not. In the first you’re accelerating. In the second, you’re hovering in a gravitational field. Far from any planet or star (no gravitational field) At the surface of a planet (strong gravity) 1 2

9. Let’s try to understand “spacetime” a little better Space is 3-dimensional. Here’s how you demonstrate those three dimensions: In that 3- dimensional space, objects can appear different to different observers:

10. But what about “spacetime”? It’s not just where something is located, but when: A spacetime diagram for the car It shows the car’s “worldline”

11. Spacetime diagrams show only 1 spatial dimension, but they also show the time dimension.

12. Spacetime diagrams are drawn from a particular perspective, or reference frame.

13. What is the shape of the worldline of an object at rest, when time is plotted on the vertical axis? a)a horizontal line b)a diagonal line going up to the right c)a diagonal line going down to the right d)a vertical line e)a point

14. What does it mean for spacetime to be “warped” or “curved”?

15. In grade school you learned the rules of “Euclidean” geometry

16. Consider what geometry would be like on a sphere Those “rules” have now changed!

17. Real-life example: Planes fly the shortest route to save time. From Chicago to Tokyo, the route should look like this, right?

18. Real-life example: Planes fly the shortest route to save time. From Chicago to Tokyo, the route should look like this, right? NO! It looks like this: Because the surface of the Earth is a sphere, not a flat plane!

19. Consider what geometry would be like on a saddle Those “rules” have changed again! This is known as “hyperbolic” geometry

20. Straight worldliness represent objects that are NOT accelerating (they are free-floating or free-falling) This assumes no masses are present

21. Straight worldliness represent objects that are NOT accelerating (they are free-floating or free-falling) This assumes no masses are present The presence of mass warps spacetime, so free- falling objects now follow curved paths The geometry of spacetime is altered by mass

22. Straight worldliness represent objects that are NOT accelerating (they are free-floating or free-falling) This assumes no masses are present The presence of mass warps spacetime, so free- falling objects now follow curved paths The geometry of spacetime is altered by mass Gravity is no longer a force that one object exerts on another. We now say that mass warps spacetime, and spacetime dictates how objects move.

23. In general relativity, the orbital path of a planet a)is determined by the curved shape of spacetime that it is moving through. b)never returns to the same point in four-dimensional spacetime. c)is the straightest possible path through four-dimensional spacetime. d)all of the above

24. True statement: Light has no mass. True or False: That means that light cannot be affected by gravity. A) True B) False

25. So far we’ve seen images of the warping of space (rubber sheet analogy). What does it mean for time to be warped?

26. On an accelerating spaceship, the clocks at the front of the ship run faster than the clocks at the rear of the ship The clocks are synchronized when at rest, and designed to send flashes to each other every 0.01 s. The observer at the front is accelerating away from the rear clock, and so the flashes have further to travel. The result is that the flashes from the rear arrive less frequently. The observer at the rear is accelerating towards the front clock, and so the flashes have a shorter distance to travel. The result is that the flashes from the front arrive more frequently. Use the Equivalence principle…

27. According to the Equivalence Principle, the same thing must happen when at rest in a gravitational field. The clock that is “downhill” must run more slowly than the “uphill” clock. Note that the observers agree on this result. They both say the uphill clock runs faster than the downhill clock!

28. This has been observed in many forms, and agrees with the predictions of General Relativity! Gravitational Redshift We’ve even checked it directly with atomic clocks separated by several floors: the lower clock runs slower by an amount predicted by general relativity

29. If you want to age more slowly, would it be better to live on the top floor of a tall high-rise, or the ground floor? A) Top floor B) Ground floor

30. Astro-Cash Cab! Jessica Faleen Alejandro Conner V.

31. 1) The general theory of relativity describes gravity as a)a distortion of the shape of four-dimensional spacetime. b)a distortion of the shape of three-dimensional space. c)a force that acts through the action of photons at the speed of light. d)a force that acts through the action of gravitons that travel instantaneously.

32. 2) The equivalence principle states that a)all frames of reference are equivalent. b)the speed of light will have the same value regardless of who measures it. c)the effects of gravity are equivalent to the effects of acceleration. d)mass and energy are equivalent.

33. 3) Astronaut Bill is hovering 15,000,000 miles above a neutron star while astronaut Susan is down close the surface making measurements. When Bill compares his clock to Susan’s, he says her clock is running slower than his. What does Susan say when she compares her clock to Bill’s? Bill’s clock is running faster than hers. Bill’s clock is running slower than hers. The two clocks are running at the same rate.

34. 4) True / False Planes always fly straight line routes to their destinations.