Relativity II

1. Relativity II Postulates Simultaneity Time Dilation Length Contraction

2. Reading Question Which of these topics was not discussed in this chapter? 1. Teleportation 2. Simultaneity 3. Time dilation 4. Length contraction

3. Reading Question Which of these topics was not discussed in this chapter? 1. Teleportation 2. Simultaneity 3. Time dilation 4. Length contraction

4. Reading Question Proper time is • 1. the time calculated with the correct relativistic expression. • 2. the longest possible time interval between two events. • 3. a time interval that can be measured by a single clock. • 4. the time measured by a light clock • 5. not discussed in Chapter 36.

5. Reading Question Proper time is • 1. the time calculated with the correct relativistic expression. • 2. the longest possible time interval between two events. • 3. a time interval that can be measured by a single clock. • 4. the time measured by a light clock • 5. not discussed in Chapter 36.

6. Relativity Special Theory of Relativity 1905 Introduction to Relativity inertial frame • length contraction • time dilation • mass and energy General Theory of Relativity 1916 • twin paradox • mass-spacetime • red shift • black holes

7. Relativity • What is the difference between mechanical waves and electromagnetic waves? Mechanical waves require a medium, where as, electromagnetic waves do not. Electromagnetic waves travel at constant speed c in all inertial reference frames.

8. Relativity Constancy of the Speed of Light (all EM waves) Light travels at speed c in all inertial reference frames.

9. Relativity Special Theory of Relativity • What are the two postulates for the Special Theory of Relativity. The speed of light is constant. The laws of physics are the same in all inertial reference frames. Everything that you have heard about relativity comes from these two postulates: time dilation, length contraction, the twin paradox, E = mc2.

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11. Relativity In relativity we are always making a comparison between what one person measures in one frame to what another person measures in another moving at a constant velocity relative to the other.

12. Relativity “Seeing” vs. measuring What you see involves the time it takes light to travel from the object to your eye. Measuring does not. We will always set things up so that this effect cancels out.

13. Relativity • Events Events and Measurements • Measurements • Clock synchronization

14. Relativity Events and Measurements How do we synchronize two clocks in the same frame

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18. Relativity Simultaneity of Events • Two events separated in space that are simultaneous in one frame are not simultaneous in another. • Discuss this in your group in terms of the example used in class where lighting strikes the front and back of the train.

19. Relativity Consider two rods A and B moving relative to each other. Simultaneity of Events

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25. Class Question A tree and a pole are 3000 m apart. Each is suddenly hit by a bolt of lightning. Mark, who is standing at rest midway between the two, sees the two lightning bolts at the same instant of time. Nancy is at rest under the tree. Define event 1 to be “lightning strikes tree” and event 2 to be “lightning strikes pole.” For Nancy, does event 1 occur before, after or at the same time as event 2? 1. at the same time as event 2 2. before event 2 3. after event 2

26. Class Question A tree and a pole are 3000 m apart. Each is suddenly hit by a bolt of lightning. Mark, who is standing at rest midway between the two, sees the two lightning bolts at the same instant of time. Nancy is at rest under the tree. Define event 1 to be “lightning strikes tree” and event 2 to be “lightning strikes pole.” For Nancy, does event 1 occur before, after or at the same time as event 2? 1. at the same time as event 2 2. before event 2 3. after event 2

27. Class Question A tree and a pole are 3000 m apart. Each is suddenly hit by a bolt of lightning. Mark, who is standing at rest midway between the two, sees the two lightning bolts at the same instant of time. Nancy is flying her rocket at v = 0.5c in the direction from the tree toward the pole. The lightning hits the tree just as she passes by it. Define event 1 to be “lightning strikes tree” and event 2 to be “lightning strikes pole.” For Nancy, does event 1 occur before, after or at the same time as event 2? 1. at the same time as event 2 2. before event 2 3. after event 2

28. Class Question A tree and a pole are 3000 m apart. Each is suddenly hit by a bolt of lightning. Mark, who is standing at rest midway between the two, sees the two lightning bolts at the same instant of time. Nancy is flying her rocket at v = 0.5c in the direction from the tree toward the pole. The lightning hits the tree just as she passes by it. Define event 1 to be “lightning strikes tree” and event 2 to be “lightning strikes pole.” For Nancy, does event 1 occur before, after or at the same time as event 2? 1. at the same time as event 2 2. before event 2 3. after event 2

29. Dt=Dt’ is the proper time. Relativity Time Dilation • Define proper time in words. • Write the equation that describes time dilation. The time measured with one clock or a clock at the same location. A moving clock runs slower. The time interval between events is shorter in a reference frame where the two events occur at the same place

30. Relativity Time Dilation • Now let’s derive this relationship. Solve for Dt

31. Relativity

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35. Class Question Molly flies her rocket past Nick at constant velocity v. Molly and Nick both measure the time it takes the rocket, from nose to tail, to pass Nick. Which of the following is true? 1. Both Molly and Nick measure the same amount of time. 2. Nick measures a shorter time interval than Molly. 3. Molly measures a shorter time interval than Nick.

36. Class Question Molly flies her rocket past Nick at constant velocity v. Molly and Nick both measure the time it takes the rocket, from nose to tail, to pass Nick. Which of the following is true? 1. Both Molly and Nick measure the same amount of time. 2. Nick measures a shorter time interval than Molly. 3. Molly measures a shorter time interval than Nick.

37. Relativity We agree to disagree. We can live with this disagreement because we each say the other did not make the measurements sim

38. The first thing to note is that this all takes place in one frame. Relativity comes into play when we make a comparison between two frames. O Relativity • Pluto is 5.8 X 109 km from earth as measured from earth. According to an earth clock how long would it take a spacecraft traveling at 65% of the speed of light to make the trip? earth Pluto v = Dx/Dt Dt = Dx/v = 5.8 X 109 km/0.65c = 5.8X109 km/0.65X3.0X108 m/s = 2.97X104 s = 8.25 hr

39. event 1 O’ O same location O’ event 2 O Relativity Another way to look at the problem is in terms of fixed clocks and moving clocks. • How long would the trip take according to a clock on the spacecraft?

40. Now we are on the earth and asking for the time on the spacecraft. We are comparing time in two different frames. O’ O Relativity • How long would the trip take according to a clock on the spacecraft? earth Pluto

41. O’ O Relativity but we need to decide which time is the proper time. • How long would the trip take according to a clock on the spacecraft? • Which is the proper time? Explain your answer. so the proper time is the time read by the clock on the spaceship since it is at the same location for both events.

42. Relativity • The famous muon problem. 560 muons/hr expect 25 muons/hr found 414 muons/hr

43. Dl or Dl0 is the proper length Relativity Length Contraction or Lorentz Contraction • Define proper length in words. • Write the equation for length contraction. an objects length in a frame in which the object is at rest Sara on the spacecraft can measure the length of the door or Bob on earth can

44. Relativity

45. 0.75c Relativity • A spaceship passes earth with a speed of 0.75c. Bill on earth measures the spaceship to be 45 m long. Sally is inside the spaceship and measures the length. How long does Sally find the spaceship? • Which length is the proper length. Explain why. Sally measures the proper length of the spaceship because the ship is stationary with respect to Sally.

46. Relativity • Is space contracted or just objects? Discuss this in your group. Explain. We can not measure space we can only measure objects in space, so we say that space is contracted. • Are objects contracted in a direction perpendicular to the motion? Objects are contracted in the direction of motion only.

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49. Class Question Beth and Charles are at rest relative to each other. Anjay runs past at velocity v while holding a long pole parallel to his motion. Anjay, Beth, and Charles each measure the length of the pole at the instant Anjay passes Beth. Rank in order, from largest to smallest, the three lengths LA, LB, and LC. 1. LA > LB = LC 2. LA = LB = LC 3. LA > LB > LC 4. LB = LC > LA 5. LB > LC > LA

50. Relativity Accelerator