Kinematical Relations in Special Relativity: Gedanken Experiments

1. Lecture Six

2. Kinematical RelationsinSpecial 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 relativityexcept

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

19. Two Derivations of Length Contraction • Simple derivation • Detailed derivation

20. Simple Derivation For observer on the station (S): The time of passage t0 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 L0 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 =  t1＋  t 2

28. Experiment III  t1：light signal from B0 to M1  t2 ：light signal from M1 to B2

29. Experiment III c t1= B0 M1 = B0 B1＋ B1 M1 = v t1＋ L c  t2 = M1 B2 = M1 B1－B1 B2 = L－ v t2

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 L0 : 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  t0 : 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 EA: clock in  meets clock A. Event EB: clock in  meets clock B. Times in : tA = t0, tB = t1 (proper time) Times in ' : t'A = t'0, t'B = t'1

45. t' = t'B －t'A • t = tB －tA

46.  t = tB – tA 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 

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