1. Time Dilation, Length Contraction and Doppler
Class 2: (ThT Q)

2. Did you complete at least 70% of Chapter 1:1-4?
Yes No
Relativity; Galilean Reference frame Events Simultaneous

3. Fig 39-CO Standing on the shoulders of a giant
Fig 39-CO Standing on the shoulders of a giant. David Serway, son of one of the authors, watches over his children, Nathan and Kaitlyn, as they frolic in the arms of Albert Einstein at the Einstein memorial in Washington, D.C. It is well known that Einstein, the principal architect of relativity, was very fond of children. (Emily Serway)
Fig 39-CO, p.1244

4. Reading was 1.3-1.4 + App 1 Doppler, length contraction, Lorentz transforms and velocity addition
Review: Length contraction Muon decay 43: start at 16 minutes (43: ')
HW 2 helps; start with PPT: Simultaneous Events, Relative Velocity, and Momentum (Class 32: from 123 )
Additional material to be used.
Velocities and space-time diagrams 43:14 starts at min 11.22' .
Last material; twin paradox from MU 43:20-21 starts at min 20.32' to 21:46
Assign 43: min. 1’ 43”- 5’40” and 44: 9’15” to 14’ 30”
Supporting ppt. :Simultaneous Events, Relative Velocity, and Momentum Class 32: from 123 MU

5. any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments
Galileo Galilei first described this principle in 1632 in his Dialogue Concerning the Two Chief World Systems using the example of a ship traveling at constant speed, without rocking, on a smooth sea; any observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary. (Wikipedia)

6. Imagine a person inside a ship which is sailing on a perfectly smooth lake at constant speed. This passenger is in the ship's windowless hull and, despite it being a fine day, is engaged in doing mechanical experiments (such as studying the behavior of pendula and the trajectories of falling bodies). A simple question one can ask of this researcher is whether she can determine that the ship is moving (with respect to the lake shore) without going on deck or looking out a porthole.
Since the ship is moving at constant speed and direction she will not feel the motion of the ship. This is the same situation as when flying on a plane: one cannot tell, without looking out one of the windows, that the plane is moving once it reaches cruising altitude (at which point the plane is flying at constant speed and direction). Still one might wonder whether the experiments being done in the ship's hull will give some indication of the its motion. Based on his experiments Galileo concluded that this is in fact impossible: all mechanical experiments done inside a ship moving at constant speed in a constant direction would give precisely the same results as similar experiments done on shore.

7. Galileo and Relativity
Figure 39.1 (a) The observer in the truck sees the ball move in a vertical path when thrown upward. (b) The Earth observer sees the path of the ball as a parabola.
Fig 39-1, p.1246

8. The conclusion is that one observer in a house by the shore and another in the ship will not be able to determine that the ship is moving by comparing the results of experiments done inside the house and ship. In order to determine motion these observers must look at each other. It is important to note that this is true only if the ship is sailing at constant speed and direction, should it speed up, slow down or turn the researcher inside can tell that the ship is moving. For example, if the ship turns you can see all things hanging from the roof (such as a lamp) tilting with respect to the floor
Generalizing these observations Galileo postulated his relativity hypothesis:
any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments

9. Figure 39.1 (a) The observer in the truck sees the ball move in a vertical path when thrown upward.
Fig 39-1a, p.1246

10. Figure 39.1 (b) The Earth observer sees the path of the ball as a parabola.
Fig 39-1b, p.1246

11. Figure 39. 2 An event occurs at a point P
Figure 39.2 An event occurs at a point P. The event is seen by two observers in inertial frames S and S¢, where S¢ moves with a velocity v relative to S.
Fig 39-2, p.1247

12. now do it with light.
ether and wind because you are going through the ether.
M& M in 1887

13. Figure 39.3 If the velocity of the ether wind relative to the Earth is v and the velocity of light relative to the ether is c, then the speed of light relative to the Earth is (a) c + v in the downwind direction, (b) c - v in the upwind direction, and (c) (c 2 - v2)1/2 in the direction perpendicular to the wind.
Fig 39-3, p.1248

14. Active Figure 39.4 According to the ether wind theory, the speed of light should be c - v as the beam approaches mirror M2 and c + v after reflection.
Fig 39-4, p.1249

15. p.1251 Albert Einstein German-American Physicist (1879–1955)
Einstein, one of the greatest physicists of all times, was born in Ulm, Germany. In 1905, at the age of 26, he published four scientific papers that revolutionized physics. Two of these papers were concerned with what is now considered his most important contribution: the special theory of relativity. In 1916, Einstein published his work on the general theory of relativity. The most dramatic prediction of this theory is the degree to which light is deflected by a gravitational field. Measurements made by astronomers on bright stars in the vicinity of the eclipsed Sun in 1919 confirmed Einstein’s prediction, and as a result Einstein became a world celebrity. Einstein was deeply disturbed by the development of quantum mechanics in the 1920s despite his own role as a scientific revolutionary. In particular, he could never accept the probabilistic view of events in nature that is a central feature of quantum theory. The last few decades of his life were devoted to an unsuccessful search for a unified theory that would combine gravitation and electromagnetism. (AIP Niels Bohr Library)
p.1251

16. Special theory of relativity
Postulates
The laws of physics are the same in any inertial frame of reference.
The velocity of light is the same in all inertial frames of reference.

17. How can this be & what does it have to do with time?

18. According to a stationary observer, a moving clock runs ______ than an identical stationary clock.
faster or
slower

19. Figure 39.5 (a) Two lightning bolts strike the ends of a moving boxcar. (b) The events appear to be simultaneous to the stationary observer O, standing midway between A and B. The events do not appear to be simultaneous to observer O¢, who claims that the front of the car is struck before the rear. Note that in (b) the leftward-traveling light signal has already passed O¢ but the rightward-traveling signal has not yet reached O¢.
Fig 39-5, p.1252

20. Figure 39.5 (a) Two lightning bolts strike the ends of a moving boxcar.
Fig 39-5a, p.1252

21. Figure 39.5 (b) The events appear to be simultaneous to the stationary observer O, standing midway between A and B. The events do not appear to be simultaneous to observer O¢, who claims that the front of the car is struck before the rear. Note that in (b) the leftward-traveling light signal has already passed O¢ but the rightward-traveling signal has not yet reached O¢.
Fig 39-5b, p.1252

22. What is a light clock?

23. Active Figure 39.6 (a) A mirror is fixed to a moving vehicle, and a light pulse is sent out by observer O¢ at rest in the vehicle. (b) Relative to a stationary observer O standing alongside the vehicle, the mirror and O¢ move with a speed v. Note that what observer O measures for the distance the pulse travels is greater than 2d. (c) The right triangle for calculating the relationship between Dt and Dtp .
Fig 39-6, p.1253

24. Active Figure 39.6 (a) A mirror is fixed to a moving vehicle, and a light pulse is sent out by observer O¢ at rest in the vehicle.
Fig 39-6a, p.1253

25. Active Figure 39.6 (b) Relative to a stationary observer O standing alongside the vehicle, the mirror and O¢ move with a speed v. Note that what observer O measures for the distance the pulse travels is greater than 2d.
Fig 39-6b, p.1253

26. Active Figure 39.6 (c) The right triangle for calculating the relationship between Dt and Dtp .
Fig 39-6c, p.1253

27. Table 39-1, p.1254

28. Figure 39. 7 Graph of g versus v
Figure 39.7 Graph of g versus v. As the speed approaches that of light, g increases rapidly.
Fig 39-7, p.1254

29. Figure 39.8 (a) Without relativistic considerations, muons created in the atmosphere and traveling downward with a speed of 0.99c travel only about 6.6 X 102 m before decaying with an average lifetime of 2.2 ms. Thus, very few muons reach the surface of the Earth. (b) With relativistic considerations, the muon’s lifetime is dilated according to an observer on Earth. As a result, according to this observer, the muon can travel about 4.8 X 103 m before decaying. This results in many of them arriving at the surface.
Fig 39-8, p.1255

30. Figure 39.8 (a) Without relativistic considerations, muons created in the atmosphere and traveling downward with a speed of 0.99c travel only about 6.6 X 102 m before decaying with an average lifetime of 2.2 ms. Thus, very few muons reach the surface of the Earth.
Fig 39-8a, p.1255

31. Figure 39.8 (b) With relativistic considerations, the muon’s lifetime is dilated according to an observer on Earth. As a result, according to this observer, the muon can travel about 4.8 X 103 m before decaying. This results in many of them arriving at the surface
Fig 39-8b, p.1255

32. Figure 39.9 Decay curves for muons at rest and for muons traveling at a speed of 0.999 4c.
Fig 39-9, p.1256

33. According to a stationary observer, a moving object is _______ than an identical stationary object.
shorter or
longer

34. Active Figure (a) A meter stick measured by an observer in a frame attached to the stick (that is, both have the same velocity) has its proper length Lp-. (b) The stick measured by an observer in a frame in which the stick has a velocity v relative to the frame is measured to be shorter than its proper length Lp by a factor
(1- v2/c2)1/2.
Fig 39-11, p.1259

35. Active Figure (a) A meter stick measured by an observer in a frame attached to the stick (that is, both have the same velocity) has its proper length Lp-.
Fig 39-11a, p.1259

36. Active Figure (b) The stick measured by an observer in a frame in which the stick has a velocity v relative to the frame is measured to be shorter than its proper length Lp by a factor (1- v2/c2)1/2.
Fig 39-11b, p.1259

37. Figure (Example 39.4) Space–time graphs for the pole-in-the-barn paradox. (a) From the ground observer’s point of view, the world-lines for the front and back doors of the barn are vertical lines. The world-lines for the ends of the pole are tilted and are 9.9 m apart horizontally. The front door of the barn is at x = 0, and the leading end of the pole enters the front door at t = 0. The entire pole is inside the barn at the time indicated by the dashed line. (b) From the runner’s point of view, the world-lines for the ends of the pole are vertical. The barn is moving in the negative direction, so the world-lines for the front and back doors are tilted to the left. The leading end of the pole exits the back door before the trailing end arrives at the front door.
Fig 39-13, p.1261

38. Figure (Example 39.4) Space–time graphs for the pole-in-the-barn paradox. (a) From the ground observer’s point of view, the world-lines for the front and back doors of the barn are vertical lines. The world-lines for the ends of the pole are tilted and are 9.9 m apart horizontally. The front door of the barn is at x = 0, and the leading end of the pole enters the front door at t = 0. The entire pole is inside the barn at the time indicated by the dashed line.
Fig 39-13a, p.1261

39. Figure (Example 39.4) Space–time graphs for the pole-in-the-barn paradox. (b) From the runner’s point of view, the world-lines for the ends of the pole are vertical. The barn is moving in the negative direction, so the world-lines for the front and back doors are tilted to the left. The leading end of the pole exits the back door before the trailing end arrives at the front door.
Fig 39-13b, p.1261

40. 1. (2 pts) A meter stick moves parallel to its axis with a speed of 0
1. (2 pts) A meter stick moves parallel to its axis with a speed of 0.96 c relative to you.
(a) What would you measure for the length of the stick?
(b) How long does it take for the stick to pass you?

41. 2. (2 pts) An observer on Earth sends light with frequency 1
2. (2 pts) An observer on Earth sends light with frequency 1.2× 1015 Hz to spaceship A traveling with a speed of 0.8c away from Earth.
(a) What will be the frequency of the light observed on the spaceship A?
(b) Spaceship A then transmits the light received from earth, at the frequency that it is observed, to spaceship B, which is traveling ahead of it, away from Earth, with a speed of 0.6c relative to spaceship A. What is the frequency of light observed by spaceship B?

42. 3. (4 pts) Two relativistic rockets move toward each other
3. (4 pts) Two relativistic rockets move toward each other. As seen by an observer on Earth, rocket A, of proper length 500 m, travels with a speed of 0.8c, while rocket B, of proper length 1000 m, travels with a speed of 0.6c.
(a) What is the speed of the rockets relative to each other?
(b) If the captain of rocket B, sitting near the nose of his rocket, sets his clock to t = 0 when the two noses pass each other, what will his clock read when he passes the tail of rocket A?
(c) The earthbound observer sets her clock to t = 0 when the two noses of the rockets justs pass each other. What will the observer's clock read when the tails of the rocket's just pass each other?

43. 4. (4 pts) The nucleus of a particular atom, initially at rest in the laboratory system, is unstable and disintegrates into two particles. Particle one moves to the left at a speed of 0.80c, and particle two moves to the right at a speed of 0.98c.
(a) What is the velocity of particle one with respect to an observer at rest with particle two?
(b) An observer at rest with respect to the laboratory system finds that both particles are unstable. Particle one decays after 6.6 μs. Particle two decays after 6.0 μs. What are the lifetimes of the two particles from a reference frame in which particle two is at rest?

44. Figure (a) As one twin leaves his brother on the Earth, both are the same age. (b) When Speedo returns from his journey to Planet X, he is younger than his twin Goslo.
Fig 39-10, p.1257

45. Figure 39.10 (a) As one twin leaves his brother on the Earth, both are the same age.
Fig 39-10a, p.1257

46. Figure (b) When Speedo returns from his journey to Planet X, he is younger than his twin Goslo.
Fig 39-10b, p.1257

47. Figure 39. 12 The twin paradox on a space–time graph
Figure The twin paradox on a space–time graph. The twin who stays on the Earth has a world-line along the ct axis. The path of the traveling twin through space–time is represented by a world-line that changes direction.
Fig 39-12, p.1259