Pay close attention... because

Transcription

1 Pay close attention... because

2 Galilean Relativity

3 Galilean Relativity

4 I drive past a baseball field traveling north at 25 MPH. A player throws the ball south at a speed (relative to the ground) of 70 MPH. What is the speed of the ball in my inertial reference frame (assuming classical Galilean Relativity)? A: 25 MPH B: 45 MPH C: 70 MPH D: 74 MPH E: 95 MPH

5 Galilean Relativity Laws of physics should be the same in any inertial reference frame

6 Galilean Relativity z S y x

7 Conventions The velocity v is the velocity of the S frame origin as viewed by someone in S frame. Use u to represent the velocity of an object. We define our coordinates such that the x, y, and z directions are the same for both coordinate systems, v is always in the x direction, and the origins of the two coordinate systems overlap at time t = 0.

8 Galilean Transformations

9 Problems with Galilean Relativity Maxwell s equations describe light... But Different from other waves Speed the same in any reference frame Ether wind

10 Michelson & Morley: 1881, 1887

11 Michelson & Morley: 1881, 1887

12 Michelson & Morley: 1881, 1887

13 Michelson & Morley: 1881, 1887

14 Michelson & Morley: 1881, 1887

15 Michelson & Morley: 1881, 1887

16 Michelson & Morley: 1881, 1887

17 Michelson & Morley: 1881, 1887

18

19 Postulates Einstein s Relativity 1. The mathematical form of the laws of physics must be the same in every inertial reference frame. 2. The speed of light in vacuum is a constant, and is the same constant in every inertial reference frame.

20 Simple postulates, but with bizarre consequences

21 A Single Observer

22 A Single Observer

23 An Array of Observers

24 In Earth Reference Frame

25 In Earth Reference Frame

26 In Earth Reference Frame Both lightning bolts strike at the same time The observers on the ground conclude that the observer on the train sees the light from the right bolt before they see light from the left bolt.

27 In Train Reference Frame Either the observer on the train sees light from both beams at the same time or the lightning bolts didn t strike at the same time!

28 Simultaneity Things which happen simultaneously in one inertial reference frame do not have to occur simultaneously in a different inertial reference frame.

29 2 NEPHI 26:23 For behold, my beloved brethren, I say unto you that the Lord God worketh not in darkness.

30 Time Dilation

31 Time Dilation

32 Time Dilation

33

34 Time Dilation The inertial frame in which two events occur at the same place is known as the proper frame for the two events. Not all pairs of events have a proper frame! If two events occur in the same place, separated by a time Δt p light can travel a distance L = c Δt p / 2 and back. But in the frame of someone moving at a speed v relative to the proper frame, the light must travel further than L. So the time between the two events in the moving frame is larger than the time in the proper frame!

35

36 Thought Question Two people in different inertial frames measure the time between two events. In which frame will the time interval between two events be the shortest? A : The one moving fastest with respect to the lab B : The one moving slowest with respect to the lab C : The one in which the events occur furthest apart D : The one in which the events occur closest together E : It depends on other information.

37

38 Time Dilation t = γ t p γ = 1 1 v2 c 2

39 This has been verified... many times A muon created on earth at rest lives an average of 2.2 x 10-6 s (2.2 μs) A muon traveling at.990c lives an average of 1.56 x 10-5 s (15.6 μs)

40 Discussion question: The value of γ is 1 v 2 A. Less than 1 1 c 2 B. Greater than 1 C. Can be either depending on the velocity

41 The Twin Paradox

42 After the trip, which twin will be the oldest? A : The little twin who went into space B : The little twin who stayed home C : The little twin who had roast beef D : The little twin who had none E : They will be the same age

43 Length Contraction: Goslo s Frame

44 Length Contraction: Speedo s Frame

45 Who measures the proper time for the oneway trip to Planet X? A : Goslo B : Speedo C : Neither of them D : Both of them E : Miss Manners

46 Length Contraction

47 Length Contraction L = L p γ Proper frame is the one in which the object isn t moving

48 The Barn Door Paradox

49 Discussion question: A rocket, when measured at rest, is 47 meters long. How long will you measure it to be if flies past you at 0.70 c? A meters B meters C. 47 meters D. 1.4 meters E. None of the above

50 Discussion question: The crew of a spaceship watches a movie that is two hours long in a spacecraft that is moving at high speed through space. An Earthbound observer, who is watching the movie through a powerful telescope, measures the duration of the movie to be... Notice I wrote A. Less than 2 hours measure the duration rather than B. 2 hours see the movie. C. More than 2 hours Make sure you understand why!

51 According to the special theory of relativity, if a 30- year old astronaut is sent on a space mission is accelerated to speeds close to that of light, and then returns to earth after 20 years as measured on earth, what would be his biological age upon returning? A. Less than 50 years B. 50 years C. More than 50 years