Presentation is loading. Please wait.

Presentation is loading. Please wait.

Faster-Than-Light Paradoxes in Special Relativity Brice N. Cassenti.

Similar presentations


Presentation on theme: "Faster-Than-Light Paradoxes in Special Relativity Brice N. Cassenti."— Presentation transcript:

1 Faster-Than-Light Paradoxes in Special Relativity Brice N. Cassenti

2 Faster-Than-Light Paradoxes in Special Relativity Principle of Special Relativity Paradoxes in Special Relativity Relativistic Rockets Conclusions

3 Principle of Special Relativity Postulates Lorentz Transformation Lorentz Contraction Time Dilation

4 Postulates of the Special Theory of Relativity The laws of physics are the same in all inertial coordinate systems The speed of light is the same in all inertial coordinate systems

5 Inertial Reference Systems

6 Lorentz Transformation Derivation Assume transformation is linear Assume speed of light is the same in each frame

7 Relative Motion v (x,ct)

8 Lorentz Transformation Inverse transformationUse of hyperbolic functions

9 ct x Coordinate Systems ct x

10 Lorentz Contraction Length is measured in a frame by noting end point locations at a given time. When observing a rod in a moving frame, with its length in the direction of motion the frame, the length is shorter by: The result holds in either frame.

11 Time Dilation Time is measured in a frame by watching a clock fixed in the moving frame. When observing a clock in a moving frame the clock runs slower by: The result holds in either frame.

12 Paradoxes in Special Relativity Pole Vaulter Twin Paradox Faster-than-Light Travel Instant Messaging

13 Pole Vaulter & Barn 10 ft 15 ft

14 Pole Vaulter & Barn 10 ft 7.5 ft v

15 Pole Vaulter & Barn 5 ft 15 ft v

16 Pole Vaulter Paradox Barn View Front door opens

17 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn

18 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn

19 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes

20 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes Pole entirely inside barn

21 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes Pole entirely inside barn Back door opens

22 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes Pole entirely inside barn Back door opens Front end of pole leaves barn

23 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes Pole entirely inside barn Back door opens Front end of pole leaves barn Back end of pole leaves barn

24 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes Pole entirely inside barn Back door opens Front end of pole leaves barn Back end of pole leaves barn

25 Pole Vaulter Paradox Pole Vaulter View Front doors opens

26 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn

27 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens

28 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn

29 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn Both ends of pole never in barn simultaneously

30 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn Both ends of pole never in barn simultaneously Back end of pole enters barn

31 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn Both ends of pole never in barn simultaneously Back end of pole enters barn Front door closes

32 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn Both ends of pole never in barn simultaneously Back end of pole enters barn Front door closes Back end of pole leaves barn

33 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn Both ends of pole never in barn simultaneously Back end of pole enters barn Front door closes Back end of pole leaves barn

34 Pole Vaulter Paradox Resolution Use Lorentz transformation In barn view, time interval from back door closing to front door opening is less than time light needs to cover distance In pole vaulter view, time from front of pole to leave and back to enter is less than time light needs to cover distance along pole Lorentz transformation correctly predicts both views correctly from both the barn and pole vaulter frames

35 Pole Vaulter Paradox - Conclusion Faster-than-light signals would allow contradictions in observations

36 Twin Paradox One of two identical twins leaves at a speed such that each twin sees the other clock running at half the rate of theirs The traveling twin reverses speed and returns Does each think the other has aged half as much?

37 Twin Paradox Resolution In order to set out turn around and stop at the return the traveling twin accelerates. The traveling twin feels the acceleration. Hence, the traveling twin is not in an inertial frame. The stationary twin ages twice as much as the traveling twin.

38 Twin Paradox - Resolution Constant Acceleration

39 Twin Paradox - Resolution Infinite Acceleration

40 Twin Paradox - Conclusion Accelerating reference frames need to be treated with a more General Theory of Relativity

41 Faster-Than-Light Travel

42

43

44

45

46

47

48 Faster-than-Light Travel – Conclusion Faster-than-Light motion reverses travel through time – a time machine

49 The Mathematics of Faster-than-Light Travel Recall Then Setting If Then Or Let And

50 Instant Messaging

51

52

53

54

55

56

57

58 Instant Messaging – Conclusion Instant communications is a nonlinear process (exponential) and does not satisfy the postulates of Quantum Mechanics. The number of messages must collapse to a single message. Faster-than-light travel may result in the collapse of the wave function

59 Relativistic Rockets Relativistic Energy Constant Acceleration Rocket Photon Rocket

60 Relativistic Energy

61

62

63

64

65

66 There is a relativistic rest mass energy For is imaginary –Particles are tachyons –Tachyons have never been observed – & constant in all reference frames,

67 Relativistic Accelerating Rocket

68

69

70 In rocket frame

71 Relativistic Accelerating Rocket In rocket frame

72 Relativistic Accelerating Rocket In rocket frame

73 Relativistic Accelerating Rocket In rocket frame

74 Constant Acceleration Rocket

75 Constant Acceleration Results In the reference frame of the rocket when sinh >1, dx/d >c. Accelerating at one gravity a crew could circumnavigate the universe within their working lifetime.

76 Photon Rocket

77

78

79

80

81

82 Photon Rocket Results Velocity parameter replaces velocity in the rocket equation

83 Photon Rocket Results Velocity parameter replaces velocity in the rocket equation Circumnavigating the universe at one gravity requires an enormous mass ratio

84 Photon Rocket Results Velocity parameter replaces velocity in the rocket equation Circumnavigating the universe at one gravity requires an enormous mass ratio But the mass required is not larger than the mass of the universe

85 Conclusions Faster-than-light paradoxes in the Special Theory of Relativity are: More than curiosities They can provide a better understanding of space and time They can add insight into other paradoxes Collapse of the wave function They can lead to new physical theories And may allow unlimited access to the universe.


Download ppt "Faster-Than-Light Paradoxes in Special Relativity Brice N. Cassenti."

Similar presentations


Ads by Google