Physics. Special Relativity

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1 Physics Special Relativity 1

2 Albert Einstein, the high school dropout and patent office clerk published his ideas on Special Relativity in

3 Special vs. General Relativity Special Relativity deals with non-accelerated motion or uniform motion. General Relativity deals with motion in an accelerated frame of reference. 3

4 Motion is Relative A frame of reference is a place from which motion is observed and measured. An object may have different velocities relative to different frames of reference. 4

5 Old Ideas Originally, it was though that space was filled with a mysterious substance called ether. 5

6 First Postulate All laws of nature are the same in all uniformly moving frames of reference. 6

7 Second Postulate The speed of light in free space has the same measured value for all observers regardless of the motion of the source or the motion of the observer; that is, the speed of light is a constant. 7

8 Second Postulate 8

9 Simultaneity 9

10 Simultaneity 10

11 How many dimensions are there? It takes 3 dimensions to locate a point. There is a 4th Dimension: TIME 11

12 Space and Time are Integrally Linked SPACETIME! 12

13 Time Dilation 13

14 Time Dilation 14

15 Time Dilation 15

16 Time Dilation 16

17 Time Dilation 17

18 Time Dilation 18

19 Lorentz Factor as a Function of Speed 19

20 Twin Paradox 20

21 Length Contraction As objects move through spacetime, space as well as time changes. In a nutshell, space is contracted, making the objects look shorter when they move by us at relativistic speeds. 21

22 Length Contraction Lorentz Contraction George F. FitzGerald Hendrik A. Lorentz 22

23 Length Contraction 23

24 Length Contraction 24

25 Length Contraction 25

26 Length Contraction 26

27 Length Contraction 27

28 Length Contraction 28

29 Twin Paradox 29

30 Let s Do a Thought Experiment We have two ships, identical except for their color. (Same Size, Length) Ships are traveling in opposite directions, at constant and equal speeds. First, let s define 4 different events that we can observe from different frames of reference. 30

31 A C B D 31

32 From the Yellow Ship s Perspective A The blue ship appears contracted. What are the implications? B Events B and C no longer occur simultaneously! Event B happens first. 32

33 From the Yellow Ship s Perspective C Then comes Event C after Event B D 33

34 From the Blue Ship s Perspective The yellow ship appears contracted. What are the implications? A Event C occurs before Event B! C 34

35 From the Blue Ship s Perspective Event B occurs after Event C B D 35

36 Relativity Breaks Simultaneity Event order for the yellow ship - A B C D Event order for the blue ship - A C B D The amount of time elapsed from A to D is the same for each ship. BUT The amount of time from A to B is very different! 36

37 So how does this apply to the twin paradox? From the perspective of the rocket, passing Earth at 0.9c on its way to a distant planet. A 37

38 So how does this apply to the twin paradox? Rocket went from A to B. Event C has not yet occurred. B DONE! 38

39 So how does this apply to the twin paradox? A But now let s examine the situation from Earth s perspective. 39

40 So how does this apply to the twin paradox? C From Earth s perspective, Event C will occur a long time before Event B ever does! 40

41 So how does this apply to the twin paradox? Waiting 41

42 So how does this apply to the twin paradox? Event B! Finally! B 42

43 So how does this apply to the twin paradox? In Earth s reference frame, more time has elapsed from A to B. We can see that because event C happened in the interim. But in the Rocket s reference frame, event C has not occurred at all! The time from A to B was shorter. So the twin on Earth has aged much more than the twin in the Rocket. When they meet up again in the same reference frame, more time has elapsed for one than the other! 43

44 Relativistic Velocities

45 Relativistic Velocities 45

46 Relativistic Velocities 46

47 Relativistic Velocities 47

48 Relativistic Velocities 48

49 Relativistic Momentum The Stanford Linear Accelerator 49

50 Relativistic Momentum 50

51 Mass Effects Mass, like time and length, is also affected by the motion of objects. As the speed of an object approaches c, the mass of the object, m, increases. 51

52 Relativistic Momentum 52

53 Mass and Energy E = mc 2 53

54 The Correspondence Principle 54

55 Check Questions 1. What is the perceived length of a meterstick if it is moving with a velocity of 0.5c (50% of the speed of light) relative to Earth? 2. A spaceship traveling at 0.8c passes parallel to Earth. A rod of length L is inside the spaceship. According to an astronaut inside the spaceship, what is the length of the rod? 55

56 Check Questions 3. A spacecraft with a speed of 0.99c in the +x direction passes by a stationary observer. The dimensions of the spacecraft will appear altered along which axis or axes (x, y, or z)? 4. Two spaceships approach each other. Spaceship A has a speed of 80% the speed of light. Spaceship B has a speed of 60% the speed of light. A passenger on spaceship A aims a laser at spaceship B. How fast does the laser light appear to be moving as observed by a passenger on spaceship B? 56

57 57 General Relativity

58 Special vs. General Relativity Special Relativity deals with non-accelerated motion or uniform motion. General Relativity deals with motion in an accelerated frame of reference. 58

59 Principle of Equivalence In a spaceship far from gravitational influences, at rest or in uniform motion, a person would float freely; there would be no up and no down. But when the rocket motors were turned on and the ship accelerated, things would be different; phenomena similar to gravity would be observed. 59

60 Principle of Equivalence Is she in an accelerated reference frame or under the influence of gravity? Both interpretations are equally valid! 60

61 61 Principle of Equivalence Observations made in an accelerated reference frame are indistinguishable from observations made in a Newtonian gravitational field. So what? Why do we care? Because Einstein went further. He said the principle holds for all natural phenomena; optical as well as electromagnetic!

62 Bending of Light by Gravity To an inside observer, the path of the ball bends as if in a gravitational field. 62

63 Bending of Light by Gravity The same holds true for a beam of light. To observers in the spaceship, the light has followed a downward curving path just as the thrown ball was deflected. 63

64 Bending of Light by Gravity Light bends when it travels in a spacetime geometry that is bent. The presence of mass results in the bending or warping of spacetime. 64

65 Bending of Light by Gravity Einstein predicted that starlight passing close to the sun would be deflected by an angle of 1.75 seconds of arc large enough to be measured. And we have measured it Einstein was right! 65

66 Bending of Light by Gravity Light bends in the Earth's gravitational field also but not as much. We don't notice it because the effect is so tiny. 66

67 Gravity and Time One (experimentally proven) prediction of Einstein s General Relativity is that gravitation causes time to slow down. Really!

68 Gravity and Time 68

69 Gravity and Time This slowing down will apply to all clocks, whether physical, chemical, or biological. An executive working on the ground floor of a tall city skyscraper will age more slowly than her twin sister working on the top floor. The difference is very small, only a few millionths of a second per decade, because by cosmic standards, the distance is small and the gravitation weak. 69

70 Gravitational Red Shift All atoms emit light at specific frequencies characteristic of the vibrational rate of electrons within the atom. Every atom is therefore a clock, and a slowing down of atomic vibration indicates the slowing down of such clocks. An atom on the sun should emit light of a lower frequency (slower vibration) than light emitted by the same element on the Earth. 70

71 Gravity and Time So time depends not only on relative motion, but also upon gravity! Often these are competing effects. 71

72 Gravity and Time Imagine an indestructible volunteer who stands on the surface of a giant star that begins collapsing. We, as outside observers, will note a progressive slowing of time on the clock of our volunteer as the star surface recedes to regions of stronger gravity. He himself, however, does not notice any differences in his own time, nothing unusual. 72

73 Gravity and Time As the collapsing star proceeds toward becoming a black hole and time proceeds normally from the viewpoint of the volunteer, we on the outside perceive time for the volunteer as approaching a complete stop; we see him frozen in time with an infinite duration between the ticks of his clock or the beats of his heart. 73

74 Motion of Mercury Einstein directed his attention to the varying gravitational fields experienced by the planets orbiting the sun and found that the elliptical orbits of the planets should precess independently of the Newtonian influence of other planets. 74

75 Gravity, Space, and a New Geometry Recall the Lorentz contraction from special relativity: The measuring stick will appear contracted to any observer not moving along with the stick, while an identical measuring stick moving much more slowly near the center will be nearly unaffected. 75

76 Gravity, Space, and a New Geometry The familiar rules of Euclidean geometry pertain to various figures you can draw on a flat surface are are valid only in flat space, but if you draw these figures on a curved surface like a sphere or a saddle-shaped object, the Euclidean rules no longer hold. 76

77 Geodesics Lines of shortest distance in a given space are called geodesic lines or simply geodesics. The path of a light beam follows a geodesic. 77

78 Geodesics One familiar example of a positively curved space is the surface of the Earth. Our planet forms a closed curvature, so that if you travel along a geodesic, you come back to your starting point. 78

79 Mass warps spacetime We cannot visualize the four-dimensional bumps and depressions in spacetime because we are three-dimensional beings, but we can get a glimpse by considering a simplified analogy in two dimensions: a heavy ball resting on the middle of a waterbed. 79

80 Gravitational Waves Every object has mass and therefore warps the surrounding spacetime. When an object undergoes a change in motion, the surrounding warp moves in order to readjust to the new position. These readjustments produce ripples in the overall geometry of spacetime, called gravitational waves. 80

81 Newtonian and Einsteinian Gravitation 81

82 82

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