Lecture 17 Special relativity IV: Paradoxes or how twins can or cannot find out who is the older one - PowerPoint PPT Presentation

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Lecture 17 Special relativity IV: Paradoxes or how twins can or cannot find out who is the older one

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... Klingon space ship) and by a Klingon in the back (i.e. closer to the space station) ... from the Space Station, the Klingon by the captain of the Klingon's ship ... – PowerPoint PPT presentation

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Title: Lecture 17 Special relativity IV: Paradoxes or how twins can or cannot find out who is the older one


1
Lecture 17Special relativity IV Paradoxes or
how twins can or cannot find out who is the older
one ?
2
World lines slowly moving
3
World lines fast moving
4
Spacetime interval
?s2 (c??t)2 ?x2
  • sign difference between space and time
  • ?s2 is invariant under Lorentz transformation
  • for particle moving at speed of light?x c??t
    ? ?s2 0 ? light like (null) distance

5
Character of spacetime intervals
  • ?s2gt0 ? c??t gt ?x
  • spatial distance can be traveled by speed of
    light
  • there exist an inertial frame, in which the two
    events happen at the same position
  • but they never happen simultaneously ? time like
    distance
  • ?s2lt0 ? c??t lt ?x
  • spatial distance cannot be traveled by speed of
    light
  • there exist an inertial frame, in which the two
    events happen simultaneously
  • but they never happen at the same place? space
    like distance

6
Future, past, and elsewhere
Future
?s2gt0
?s2lt0
?s2lt0
Past
?s2gt0
7
Principle of causality
  • A
  • Cause must always precede the effect? A must
    not influence D and vice versa? nothing can
    movefaster than speed of light

8
Faster than speed of light ?
9
A comment on superluminal speed
  • The key issue is that no information can be
    transmitted faster than the speed of light.
  • This does not exclude or forbid the existence of
    apparent superluminal velocities.

10
World lines accelerated
11
World lines decelerated
12
The Twin Paradox
  • Ann and Betty are fraternal twins. Betty takes
    the chance to participate the first interstellar
    space mission traveling to Alpha Centauri and
    back nearly at the speed of light.

Ann
Betty
13
Anns view (she stays back on Earth)
  • Betty is traveling with the Enterprise at
    velocities near the speed of light. Her clock
    ticks slower. Therefore, upon her return ?
    Betty is younger.

14
Bettys view (she is traveling to Alpha Centauri)
  • Ann is traveling with the Earth at velocities
    near the speed of light. Her clock ticks slower.
    Therefore, upon her return ? Ann is younger.

15
So who is right ?
  • Obviously either Ann or Betty must be wrong.
  • Lets recall the principle of relativity All
    inertial frames of reference are equivalent
  • Do both stay in an inertial frame of reference?
  • Ann (on Earth) yes
  • Betty (in the Enterprise) no.
  • While she is in an inertial frame during her
    travel to and during her travel from Alpha
    Centauri, she changes the frame of reference at
    least 3 times.

16
Anns and Bettys travel in the Minkowski diagram
3
Ann
Betty
2
1
? Betty is younger
17
A relativistic murder trial Setup I
  • A murdered man is found in the cargo bay of the
    star ship Enterprise.
  • He has two head wounds caused by laser beams.
  • The incident is observed from three locations a
    space station (at rest), the Enterprise (moving
    at 0.5c) and a Klingon ship moving at 0.75c ahead
    of the Enterprise

18
0.5c
0.75c
19
A relativistic murder trial Setup II
  • All parties agree that the dead man was hit by
    the two laser beams simultaneously
  • The laser was fired by a human at the front of
    the Enterprise (i.e. closer to the Klingon space
    ship) and by a Klingon in the back (i.e. closer
    to the space station).
  • The human is defended by James T. Kirk who
    witnessed the incident from the Space Station,
    the Klingon by the captain of the Klingons ship

20
Captain Kirks plea
K
H
? The Klingon fired first, his guilt is
the greater one !
21
Klingons plea
K
H
? The human fired first, his guilt is the
greater one !
22
Witness McCoy
K
H
? Both fired at the same time !
23
So what is the verdict ?
  • The two suspects (the Klingon and the human) are
    separated by a space-like distance (?s2lt0 ).
  • For space-like distances, the order of events is
    relative
  • But events separated by a space-like distance do
    not influence each other.
  • When the Klingon and the human were firing, they
    were not aware that the other is firing, too.
    Actually, they only see the other firing when the
    victim is already hit by their own laser beam.
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