1. Einstein’s postulates
The laws of nature are the same for everyone.
2. The speed of light in a vacuum is constant for all observers.

2. Special Theory of Relativity
No matter can travel at or faster than the speed of light in a vacuum
Length contraction
Time dilation
Mass increase

3. Discussion
Given the results of the Special Theory of Relativity, why did Einstein conclude that Newton’s law of gravity needed to be revised?

4. Accelerated motion

5. Discussion
Jackie claims that she is at rest and you are moving. But you claim that you are at rest and she is accelerating away from you. Assuming Jackie cannot tell your engines are running, how can she prove that you are accelerating?

6. Inertial forces
Fictitious forces felt by an object trying to move in a straight line at a constant velocity but unable to do so because its reference frame is being accelerated.

7. Einstein’s happiest thought of his life
If you fall in a gravitational field, you will not feel gravity. You will feel weightless.

8. Discussion
If the space shuttle orbits at a distance of 20 miles from the Earth’s surface, according to Newton’s universal law of gravity, Earth’s gravitational force is a little less (because the distance from Earth’s center is 20 miles larger) than on the Earth’s surface. Yet, astronauts are weightless. How can this be?

9. Accelerated motion in a gravitational field (freefall) can cancel gravity.
Accelerated motion far from any gravitational field, feels just like gravity.

10. The equivalence principle
The effects of gravity are exactly equivalent to the effects of acceleration.

12. Discussion
You are driving in a car with a bunch of helium balloons in the back seat. When you accelerate at a stop light, which way to the balloons move? Use the equivalence principle to explain.

13. Discussion
If you planted some seeds in a pot that you rotated on a turntable with the light source directly above the rotating pot, in which direction would the plants grow?

14. Discussion
How does the equivalence of accelerated motion and gravity make even accerated motion relative?

17. Spacetime
The constancy of the speed of light, connects the three dimensions of space with time. The speed of light (measured in m/s) can be considered a conversion factor between space and time.

18. Spacetime is not relative
All observers will agree on distances measured in the 4-dimensions of spacetime.

19. 4-dimensions
We live in a 4-dimensional universe and all the objects we see have 4-dimensions.

21. Imagining the fourth dimension

22. Discussion
What would a 3-dimensional sphere look like to a 2-deminsional being as it passed through a 2-dimensional plane?

24. Discussion
What would a 4-dimensional sphere look like as it passed through our 3-dimensional space?

25. Discussion
What does a person look like in 4-dimensional spacetime?

26. But, time is different, or is it?
Consider what a universe with 4 equal space dimensions and no time dimension would be like if you and me and everything else were moving very close to the speed of light in some direction.

27. Moving the speed of light
Lengths in the direction of motion would shrink to 0.
We wouldn’t be able to move in this fourth dimension.
We would be forever stuck at a single point.

28. Spacetime diagrams
We can try to visualize spacetime by collapsing the 3 dimensions of space onto one or two axes and plotting time on the remaining axis.

29. Spacetime diagrams
time
future
present y
past x

30. Discussion
Draw a spacetime diagram of your path through spacetime during this class.

31. Spacetime diagrams
time
future
You sitting
in class
present y
past x

32. Me on the way to work time Traveling the speed limit
Getting speeding ticket
hours
Speeding y
miles x

33. Stopping at a red light

34. Discussion
What does the Earth’s orbit look like on a three dimensional spacetime diagram?

36. Discussion
What is the shortest distance between two points?

37. Discussion
What is Newton’s first law of motion?

38. Newton’s 1st law of motion
In the absence of net external forces, an object will travel the shortest possible path through spacetime.
The shortest path is the one for which time ticks the fastest.

39. Discussion
If you were to fly a plane from Philadelphia to Beijing, approximately at the same latitude, you would just follow a straight path due west? Why or why not?

42. General Relativity
Gravity is not a mysterious “force” of nature between two masses as viewed by Newton. Instead, mass warps or curves spacetime.
Objects falling in a gravitational field are following geodesics, the shortest path between two points in a curved spacetime.

43. Discussion
Imagine a time (before 500 BCE) when people thought the Earth was flat. Two explorers set out in exactly opposite directions, one east, one west. What do they discover?

45. Discussion
How can you do this in Earth orbit?

46. Discussion
Consider being in outer space. Because you did not study your astronomy, you firmly believe that spacetime is flat. You decide to explore the Universe by sending out two probes in exactly opposite directions. To your great surprise, the probes send back pictures of one another!
Where can we do this experiment and get this result in out lifetime?

49. Gravity slows time
Clocks tick more slowly in a gravitational field.

51. Not the Same as SR time dilation
Both clocks remain at rest relative to each other regardless of the acceleration.
Both observers agree that the clock in front is ticking faster than the clock in back.

52. Discussion
If you shine a laser into the window of a rocket that is accelerating past you, draw the path of the laser as it would appear to those inside the rocket.

53. Discussion
If you shine a laser into the window of a rocket moving past you at a constant velocity, draw the path of the laser as it would appear to those inside the rocket.

54. Discussion
Because this is the same as being in a gravitational field, what can you say about the path of light near the surface of the Earth?

55. Gravity bends light rays
Light always takes the shortest path between two points. In a gravitational field, where spacetime is curved, light follows a geodesic, a curved path.

57. Gravitational lens

58. Discussion
Explain physically why light bends in a gravitational field. What is happening to the light to make it curve?
Hint: How does a lens made of glass bend light?

60. Discussion
You’re on the top floor of the Empire State building. On the ground floor there is a clock that you can see that flashes very second. However, if you time the flashes, you find that they arrive a intervals greater than a second. Explain why.

61. Discussion
If time moves more slowly on a star that has a higher surface gravity, how will this effect this the light we see emitted from the surface of the more massive star compared to that of the less massive star?
Hint: Think about how the light we see is actually created.

62. Gravitational redshift

63. General Theory of Relativity
Gravity is the same as the effects of acceleration, caused by a warping of spacetime
Slows the passage of time
Bends the path of light
Causes light to be redshifted