1. Introduction to Relativity
Special Theory of Relativity – 1905
Applies to objects moving at a constant velocity
March 14, 1879

2. Discussion
Which way is up? How would you define the concept of “up?”

4. Discussion
Suppose a supersonic airplane is flying at a speed of 1,650 km/hr from Nairobi, Kenya, to Quito, Ecuador. How fast is the plane going?

6. Velocity is relative
In order to talk about the speed of an object, you need to have a reference frame in mind. The speed something is moving must always be measured relative to something else.

7. Discussion
Suppose you are running on a treadmill at 8 miles/hr. How fast are you moving relative to the ground? What does it mean to say you are running at 8 miles/hr?

8. Discussion
I can throw a ball at 30 m/s. If I’m riding on a train traveling at 10 m/s toward you and I throw a ball to you standing by the side of the track as the train comes toward you, how fast is the ball going when you try and catch it?

10. Principle of relativity
Newton’s laws are exactly the same whether one is moving at a constant velocity in an airplane or at rest of the ground.

14. Electric and Magnetic Waves
The speed of light is 3.00 × 108 m/sec in a vacuum

15. Water Waves

17. Michelson-Morley experiment

18. Einstein’s postulates
The laws of nature are the same for everyone.
2. The speed of light in a vacuum is constant for all observers.

19. Discussion
If Jackie is in a space ship traveling at 1×108 m/s and she turns on her headlights, the light leaves the ship at 3×108 m/s. If you are in front of the ship, how fast would you measure the light to be traveling past you?

21. The speed of light
All the strange results of Relativity come from the observation that the speed of light is constant for all observers.

22. Discussion
Consider a space ship traveling at a very high speed (maybe even faster than the speed of light). It has a light on the front of it. How fast does the light leave the ship as measured by those traveling with the ship?

23. Discussion
Consider an observer watching the ship pass at a very high speed. How fast will they measure the light to be traveling that the ship has emitted?

24. Discussion
From the perspective of those on the ship, the light must always proceed the ship. Is this true for observers watching the ship pass? What must they conclude about the speed of the ship relative to the speed of light?

25. Bottom line
No matter can ever travel at or faster than the speed of light.

26. Discussion
If I’m traveling at high speed, relative to you, with a laser, I will measure the speed of the light emitted by it to be c. If you measured the speed of that same light at the same time, you would also get c for the speed. How can this be possible?
Hint: How do we define speed?

27. Length and time are relative
Speed is a distance traveled in a period of time. In order to agree on the speed of light, we must disagree on the distance traveled, or the time it took or both.
Speed of light is not relative, space and time are relative

28. Throwing a ball up
If you throw a ball straight up it will come straight back down.
If you are standing in an airplane in smooth and level flight and you throw a ball straight up what happens?

29. Throwing a ball up
If I walk at a steady velocity and throw the ball straight it how will you see the motion of the ball?

31. Discussion
Repeat the experiment in the boxcar with light. Remembering that the speed of light must be the same for all observers, for which observer will the light travel time be the greatest? Explain.

32. Light clocks
We could make a clock consisting of two mirrors a fixed distance apart facing each other. One of the mirrors is only partially silvered and allows 1% of the light to pass through. A laser can then be bounced back and forth between the two mirrors. Each time the light pulse is detected behind the partially silvered mirror, the clock records another tick.

33. Time dilation
From your point of view, time runs slower in the reference frame moving relative to you.
The faster it is moving the slower you observe the time to pass in the other frame.

35. Discussion
Consider Jackie’s view of your light experiment as she speeds by you. How will she measure the time interval for the light to complete one round trip as compared to your measurement?

36. Discussion
You and Jackie are each on separate trains that will pass each other at high speed. Both of you decide to measure how fast the trains pass each other. How can you do this without leaving your seat?

37. Discussion
Now that you and Jackie have the relative speed of the trains, both of you decide to measure the length of the other’s train. How would you do this again without leaving your seat?

38. Discussion
How can you measure the length of your train without leaving your seat?

39. Discussion
Will the length of your train that you measure be the same as the length of your train that Jackie measures? Explain.

40. Discussion
How will your measurement of Jackie’s train compare with her own measurement of her train? Explain.

41. Length contraction
From your point of view, length of an object moving by you (or distance between objects moving by you) is shorter in the direction of motion than it would be if it were at rest.
The faster the objects are moving, the shorter the lengths.

43. What about height and width?
Can’t happen without a paradox

44. Theory of Invariantness?
Length and time measurements depend on the relative velocity of the observers in such a way as to make the speed of light constant for all observers in any reference frame.

45. Discussion
Suppose you have two identical space ships, one is at rest with respect to you, the other is moving at high velocity. As the ship passes you, you give each ship an identical push for the same duration of time. How do passengers on the moving ship perceive the duration of push you give them as compared to the duration of the push you gave the stationary ship?

46. Discussion
If the moving ship observers you giving the stationary ship a push for a longer duration, how does this change the acceleration they feel as compared to the acceleration they observe you giving the stationary ship? Explain.

47. Discussion
According to Newton’s second law F = ma. If the force F applied is the same in both cases and the acceleration is less in the case of the moving ship, what does this mean for the mass of the moving ship? Explain.

48. Mass increase
From your point of view, objects moving by you have a greater mass than they have while at rest with respect to you.
The bigger the velocity, the greater the effective mass

49. E = mc2
As the speed of an object approaches the speed of light, its mass tends toward infinity, resisting any further increase in speed.
Kinetic energy added to a high speed object gets converted into mass.

50. Special Theory of Relativity
No matter can travel at or faster than the speed of light in a vacuum
Length contraction
Time dilation
Mass increase

51. Space fleet maneuvers
Consider three space ships moving in formation. The flag ship is midway between the lead ship and the rear ship.

52. The “go” order
The flag ship now signals to the other two ships to fire their engines for exactly one minute. The signal travels at the speed of light to each ship which obeys the command. The flag ship simply adjusts its own speed to remain at the midpoint between the two ships.

53. Because both ships are the same distance from the flag ship, both ships fire their engines at the same time. Because they are all moving together at the same speed, they all stop firing their engines at the same time and the formation is preserved.

54. Eat lunch
The flag ship then signals to the other two ships that it is time to eat lunch. From the moving ships perspective they are all at rest with the flagship at the midpoint. Thus both ships received the “lunch” command at the same time and lunch takes place on both ships simultaneously.

55. The relativity of time
For someone at rest with respect to the moving ships, the signals also travel at the speed of light, but during the time it takes to reach the back ship it moves forward, toward the signal and thus receives the command a little early. Also during the travel time for the light the lead ship has moved forward, away from the light and receives the signal a little late.

56. Not simultaneous
Thus, from someone at rest with respect to the moving ships, the last ship eats lunch first and the lead ship eats lunch last.

57. Discussion
After lunch, the flagship again gives an order for another engine burn. From the perspective on someone at rest which ship receives the order first? What happens to the formation of the ships?

58. Desynchronized motion
Again the rear ship receives the order first and fires its engine before the other two. Thus, the rear ship for a time is going faster than the other two ships and gets closer to the flag ship. The lead ship gets the message last and starts its engine burn later, allowing the other two ships to catch up.

59. The formation length has shrunk
After the lead rocket shuts down its engine, all ships will again be going the same velocity, but the distance between them is now smaller than it was before.
Desynchronized time causes length contraction

60. Discussion
How will this appear to the captains of the ships flying in formation? Will they see their ships as being closer? Why or why not?

61. Are the captains blind?
The ships can consider themselves at rest before the second engine burn. Therefore, from their perspective all the ships fired their engines at the same time and the distance between them did not decrease.

62. Discussion
How could the ships get closer to each other without the captains knowing it? Consider doing another engine burn. The ships will get closer still. Eventually, even if the fool captains cannot see the difference won’t they feel it as the run into each other?

63. Length contraction
No. The ships will never run into each other. From the perspective of someone at rest the distance between the ships will decrease to 0 as the speed approaches the speed of light. But the lengths of the ships also decrease in size so that they never hit.

64. Space is contracting
It is not just objects that contract, but space itself is contracting. The spaceships contract because the space between their atoms is contracted.

65. A fist fight
The force of a punch depends on how fast you can throw a punch (the speed) and the mass of your fist.

66. A high speed fight
Suppose two twin brothers get into a fight. Each is traveling on a train going in opposite directions with a constant velocity and each tries to punch the other as the trains pass.

67. Time dilation again
But it takes time to throw a punch. Each twin will consider himself at rest and he will see the other twin as moving in slow motion.
Each will also conclude that the other’s slow motion punch will have little effect on them, and that their fast punch is going to knock the other’s fist back in his mouth.

68. Who is right?
Which twin wins the fight?

69. Discussion
Neither. The punches will hit with equal force and neither is able to shove the other’s fist back into his brother’s mouth. How can the other twin’s slow motion punch have as much force as their own fast punch?

70. No magnetic fields
The Special theory of Relativity shows that the magnetic field is just an electric field which arises due to the relative motions of charged particles.