Exploring Einstein's Theory of Relativity: A Journey through Physics

1. Physics 2C Relativity

2. Chapter 36 The Theory of Relativity

3. The idea of relativity When doing experiments on a boat sailing at constant speed on a straight line on a smooth lake, the results are the same as on shore! Without looking outside one cannot tell whether the ship is moving at all Velocity is RELATIVE to the reference frame

4. Frames of reference A set of rods and rulers and clocks that allow us to determine the time of any event and the position of any object with respect to a reference point Reference point object

5. An inertial reference frame is a reference frame where isolated bodies are seen to move in straight lines at constant velocity.

6. Space according to Newton The arena where Nature occurs Absolute space in its own nature, without relation to anything external, remains always similar and immovable.

7. Time according to Newton Time Is Just One Thing After Another Absolute and mathematical time, of itself, and from its own nature, flows equally without relation to anything external

8. Not all frames are inertial: Roberta is in a non-inertial reference frame Ingrid is in an inertial reference frame

9. Relative and absolute velocities Not moving target v=Speed of this bullet with respect to the target u= itsspeed with respect to the tank w= the speed of the tank v=u+w And I claim everything , including light, will behave like that: absolute space and time imply all velocities (including c) are relative Just shoot me

10. The motion of the source and the speed of light target And I claim the speed of light is the same for all observers: c is absolute! Just shoot me …again

11. Meet Einstein Hi

12. The next results require an engaged and OPEN mind A lecture is the process by which the notes of the teacher become the notes of the students WITHOUT going through the minds of either

13. The principle of relativity The Laws of Pysics are the same for all inertial observers

14. Remember these? Gauss's law: electric flux~charge Magnetic Gauss's law: magnetic flux=0 Faraday's law: changing B generates an emf (Generalized) Ampere's law: Moving charges generate B

15. Remember this? – the wave eqn

16. Electromagnetic waves If we look at Maxwell’s eqns where there are no charges or currents - after a bit of math we will get… the speed of light A constant!

17. The speed of light By stating this Einstein also implied that Newtonian mechanics is flawed, but Maxwell’s equations are OK Maxwell’s equations: light moves with speed c Maxwell’s equations are some of the laws of physics If we accept the principle of relativity, light always moves with speed c The speed of light is absolute

18. Isaac Albert Nothing can speed-up light: c is the largest possible speed! And this happens to be right This happens to be wrong The velocity of the source affects the velocity of the projectile… But the effect is smaller and smaller as the projectile speed approaches c The speed of light is unaffected by the motion of the source The velocity of the source just adds to the velocity of the projectile… …even for light

19. The faster a bullet is shot the smaller the effect of the motion of the gun The speed of light is independent of the speed of the source: The speed of light is absolute The speed of bullets depends on the motion of the source The speed of bullets is relative

20. In dog-years I’d be dead Two mirrors …and a light Time and Special Relativity Time is relative…. Look first at a “light clock”. We need:

21. reflection t=1/2 At rest with the mirrors t=0 t=1

22. reflection Moving with respect to the mirrors Motion of mirrors

23. v Mirrors at rest h vT/2 Light always travels at speed c time dilation

24. If you ride with the clock the up-down trip takes 1 second If you watch the clock move the up down trip takes more than 1 second Moving clocks slow down

25. v Mirrors at rest He’s at rest with this mirror I’m moving with this clock. In my reference frame the trip takes T0 seconds time is relative

26. boom In the reference frame where we are at rest: 6 minutes clock Distance that separated us from John Us John

27. boom In the reference frame where John is at rest: 5 minutes clock Distance that separated us from John Us John

28. If the principle of relativity is correct length is relative In the reference frame where we are at rest: 6 minutes 5 minutes clock clock Separation in our rest frame Separation in John’s rest frame Different distances In the reference frame where John is at rest:

29. The numerical calculations: Time dilation Length contraction In our reference frame: t = fuse-time l = distance traveled by John v = John’s speed of approach In John’s reference frame: t’ = fuse-time l’ = distance traveled by us v’ = our speed of approach

30. Distances along the direction of motion are contracted Distances perpendicular the direction of motion are NOT contracted

31. Exercise 9.3 In a laboratory frame of reference an observer notes that Newton’s 2nd law is valid (to the accuracy of the instruments). Show that the same is true for an observer moving at constant speed with respect to the first.

32. An astronomer on Earth observes a meteoroid approaching Earth at a speed of 0.8c. At the time of discovery it is 20 light years away. Find the Earth-time and meteoroid time for impact and the distance to Earth measured in the meteoroid frame of reference at time of discovery. 1 light year ~ 1016m=1year*c

33. Exercise 9.11 A spacecraft with proper length of 300 m takes 0.75 ms to pass an Earthly observer. What is the spacecraft speed with respect to Earth?

34. A meter stick is moving along its long axis near the speed of light. A stationary observer will observe that the meter stick is • a. longer than one meter. • b. shorter than one meter. • c. one meter in length. • d. moving faster than the speed of light. • e. moving into the future.

35. The addition of velocities v=velocity of reference frame u’=velocity of object in reference frame u=velocity on earth If u=c, then u'=c

36. Exercise A spacecraft moves at 0.8 c relative to Earth and fires a rocket in the forward direction moving at 0.9 c. What must be the rocket’s speed relative to the Earth?

37. If the principle of relativity is correct, Energy and mass are equivalent E=m c2 E=mc2

38. Exercise 9.39 The power output of the sun is 3.77 x 1026 W. How much mass is converted into energy every second?

39. In a nuclear power plant fuel rods last 3 years. During that time the plant produces 1 GW of power, what is the loss of mass in the rods?

40. If the radiance of a thousand sunsWere to burst at once into the sky,That would be like the splendor of the Mighty One...I am become Death,The shatterer of Worlds.

41. Hiroshima: • 66,000 people died and 69,000 injured from the blast, • In a few weeks the number of dead had risen to 130,000 • Then to 200,000 in 5 years • Nagasaki • Between 60,000 and 70,000 people died form the blast, • 50,000 more died within 5 years. • The fate of more than 300,000 people was sealed in the fraction of a second it took these bombs to explode. • For comparison, there were about 620,000 casualties in the American civil war that lasted 5 years. • Current atomic weapons are roughly 100 times more potent than those dropped on Japan in 1945.

42. 1. What happens to the way a clock measures time as observed by a stationary observer as the clock increases its speed? • a. It speeds up. • b. It slows down. • c. It stays the same. • d. It stops. • e. The hands move with simple harmonic motion.

43. Which of the following is a postulate of relativity theory? • a. Space and time are invariant. • b. Mass and energy are equivalent. • c. The speed of light in a vacuum is the same for all observers no matter what the source velocity is. • d. Energy is conserved in elastic collisions. • e. Gravity can bend light.