Consider two rooms (Einstein’s “closed elevator thought experiment”).

1. A theory of Gravitation, explaining the gravitational attraction between masses resulting from their warping ofspace and time

2. Consider two rooms (Einstein’s “closed elevator thought experiment”). The first one is sitting quietly on the ground (in a uniform gravitational field). The other is in deep space…and is being towed by a starship that is accelerating at 9.8 m/s2. Let’s try some experiments to see if we can determine which room we are in…

3. What would be the apparent weight in each room? F=ma = mg A=9.8m/s2 SAME!

4. What would each observe if the donut is dropped? (start with scene on right) A=9.8m/s2 SAME!

5. What path would a bullet take in each room? A=9.8m/s2

6. The Equivalence Principle No experiment performed in one place can distinguish a gravitational field from an accelerated reference frame. Albert Einstein Or… there is no way in which gravitational effects can be distinguished from acceleration (inertial) effects Albert Einstein

7. Thus… • Gravitational mass is unified with inertial mass • Inertial mass, m=ΣF / a (the measure of the “sluggishness” of an object to acceleration) • Gravitational mass, m = Weight/g (that which attracts one object to another) The same!

8. Consequences of General Relativity (write these down!) • Gravitational mass and inertial mass are the same

9. Consequences of General Relativity (write these down!) • Gravitational mass and inertial mass are the same • Speed of light in a grav. Field is the same as in any accelerating F.O.R.

10. …now back to Homer in the elevator…

11. What path would a bullet take in each room? A=9.8m/s2

12. So what about for light? • …Put on your thinking caps!!!

13. The Accelerating Room

14. For the accelerating FOR, light BENDs! A=9.8m/s2

15. The Equivalence Principle And since Accelerating FOR’s = gravitational FOR’s… THEN……

16. Light also BENDS due to gravitational fields! A=9.8m/s2

17. This is a strong statement about the nature of our universe! Light bending in a gravitational field is a direct consequence.

18. Consequences of General Relativity • Gravitational mass and inertial mass are the same • Speed of light in a grav. Field is the same as in any accelerating F.O.R. • Near a massive body: • Light bends toward it

19. The Room in a Gravitational Field

20. How Much Does Light Bend? Not much (at least in our ordinary experience)!

21. How Much Does Light Bend? Not much (at least in our ordinary experience)! Consider a distance of 30 meters --- light takes time t = 30m/3x108 m/s = 10-7 sec to cross the room

22. How Much Does Light Bend? Not much (at least in our ordinary experience)! Consider a distance of 30 meters --- light takes time t = 30m/3x108 m/s = 10-7 sec to cross the room How far does it “fall” in this time? -- The same amount anything falls in that time d = ½ gt2 = 5x10-14m a very small distance.

23. This is such a small distance, how could you ever measure the bending of light due to gravity?

24. How Much Does Light Bend? How can we make this bigger?

25. How Much Does Light Bend? • How can we make this bigger? • Increase the flight path length

26. How Much Does Light Bend? • How can we make this bigger? • Increase the flight path length • Increase the gravitational field strength.

28. Observed position of the star Cant see the little star from Earth, right? Unless my graviational field BENDS the light! Actual position of the star

29. First Experimental Test of General Relativity… “GRAVITATIONAL LENSING”

30. Of course this could only be done during a solar eclipse.

31. As luck would have it, an ideal eclipse for this test was due to occur fairly soon, in 1919. Expeditions were organized, and went to Brazil and Africa to make measurements during the solar eclipse. There was great fanfare and anticipation. This was the first joint scientific expedition of the countries who had just concluded World War I the year before.

32. Results: the change of position was 1.74” arc seconds, in agreement with Einstein’s prediction of 1.74” arc seconds (3600 arc seconds = 1 degree). More recently, more precise measurements have been made, with these being closer to the predicted amount.

33. Eddington’s telegram to Einstein

34. “Well of course, I would have been surprised if it had not been true”.

35. Albert Einstein and Arthur Eddington: the father of relativity and the man who proved him right.

36. More Experimental Evidence… Called “Gravitational Lensing” (bending of light)

37. O.K. So how does gravity bend light?

38. Easy, mass warps space, and the light appears to bend as it travels through warped space.

39. Normally, away from all masses, space is flat….

41. ... like a heavy man sitting in the middle of a bed... Mass curves space…(and time!)

43. Can you see… This can explain the orbit of planets around the sun!

45. Matter tells space how to curve, Space tells matter how to move. Theory of General Relativity: gravity = bending of space by mass, light follows curved space

46. Other Cool Stuff….BLACK HOLES

48. Black Hole… forms when a star (large mass) collapses into a very small space, such that even its own light cannot escape)

49. A Black Hole looks like: Schwarzchild Radius Any object (including light!) passing closer to the center of the black hole than Rs will fall into the “hole” • RS= 2 G M / c2

50. 2. Time slows down in the presence of gravity • Clocks near a massive object run slower than ones at higher elevation (the general relativity analogue of time dilation) • (… for further details, see reading packet pg 676 bottom)