1. Lecture Six

2. Kinematical Relations in Special Relativity

3. adapted from …

6. Four Gedanken Experimente “thought experiments” thought 是由過去分詞轉變 而成的分詞形容詞 不是名詞 正譯：想像實驗 誤譯：思想實驗

7. Experiment I Comparison of parallel measuring sticks oriented perpendicular to their direction of motion

8. Experiment II Comparison of clock rates

9. Experiment III Comparison of lengths parallel to the direction of motion

10. Experiment IV The synchronization of clocks

11. Experiment I Comparison of parallel measuring sticks oriented perpendicular to their direction of motion (invariance of perpendicular length)

13. Experiment II Comparison of clock rates (time dilation)

16.  t' being measured by a single clock is a proper time

17. Frequently used symbols in special relativity except

18. Experiment III Comparison of lengths parallel to the direction of motion (length contraction)

19. Two Derivations of Length Contraction 1.Simple derivation 2.Detailed derivation

20. Simple Derivation For observer on the station (S): The time of passage t 0 is a proper time, the length L of the train is not a proper length.

21. Simple Derivation For observer on the train (S ): The time of passage t is not a proper time, the length L 0 of the train is a proper length.

22. Simple Derivation

23. Detailed Derivation

24. train station

26. Experiment III For train observer:  t' is a proper time interval, being observable with a single clock  t' = 2L' /c

27. Experiment III For station observer:  t is not a proper time interval, being measured between two points with two clocks  t =  t 1 ＋  t 2

28. Experiment III  t 1 ： light signal from B 0 to M 1  t 2 ： light signal from M 1 to B 2

29. Experiment III c  t 1 = B 0 M 1 = B 0 B 1 ＋ B 1 M 1 = v  t 1 ＋ L c  t 2 = M 1 B 2 = M 1 B 1 － B 1 B 2 = L － v  t 2

32.  t' is a proper time interval, being observable with a single clock  t' = 2L' /c

33. Summary Proper time: time interval measured by a single clock Proper length: length measured by an observer stationary relative to the observed.

34. Summary Length Contraction The length of a moving stick is shortened by a factor of

35. Summary L 0 : proper length of a stick L : length of this stick in motion

36. Summary Time Dilation A moving clock runs slow by a factor of

37. Summary  t 0 : time interval measured in a clock  t : time interval measured in a frame in which this clock is moving

38. Experiment IV The Synchronization of Clocks The phase difference in the Synchronization of Clocks

40. Two stationary clocks A and B synchronized and separated by proper distance L' in S'-frame

41. Single clock S in a stationary in S-frame

42. By comparing S with A and B, observer in S claims that A and B are not synchronized.

44. Event E A : clock in  meets clock A. Event E B : clock in  meets clock B. Times in  : t A = t 0, t B = t 1 (proper time) Times in  ' : t ' A = t ' 0, t ' B = t ' 1

45.  t' = t' B － t' A  t = t B － t A

46.  t = t B – t A is the time interval measured by a single clock in  proper time

47. For an observer in , the time interval on both of the  ' clocks individually would appear too large by the same time dilation factor, but they will not be in time with each other to a single observer in .

48. The leading clock at A lags the trailing clock at B by 

51. 領頭鐘落後 尾隨鐘超前

53. Synchronization in S' Clocks at A and B set to read t' = 0 at the arrival of the light signal from the midpoint.

54. Off-Synchronization as seen by an observer in S Leading clock at B lags behind the trailing clock at A

55. Off-Synchronization The off-synchronization in S is The off-synchronization in S' is (moving clock runs slow) The leading clock lags by  t'

56. Calculation of t A and t B In S the distance between clock A and clock B is

57. Calculation of t A and t B

58. Calculation of  t

59. Calculation of  t'

60. Summary 領頭鐘落後 尾隨鐘超前