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Relativity and Wormholes

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Title: Relativity and Wormholes


1
Relativity and Wormholes
  • By Joaquin P Noyola
  • PHYS 4117 Learning by Seminar Spring 2006

2
Outline
  • Brief Introduction to Relativity
  • What are wormholes?
  • Several wormhole systems
  • Space Travel, Really?
  • Current Reasearch

3
Inertial Frames
  • are coordinate systems which obey Newtons laws
    and are not accelerating.

static (x, y, z) coordinate system
moving (x, y, z) coordinate system
4
Special Relativity
  • Time is the fourth dimension and is measure in
    meters of light travel, not seconds.
  • Distance is now measured by the interval

which is invariant from one inertial frame to
another.
5
General Relativity
  • The interval is no longer valid due to
    acceleration, and ?s2 ? ds2
  • We call the resulting equation the metric.

Comparing it to the interval in special relativity
6
Embedded diagram of a potential well
Gravitational fields cause spacetime to bend,
creating a potential well
Because of this bending, the objects
straight-line trajectory becomes curved to
account for the curvature of space.
Even light follows this curved trajectory
http//www.science-art.com/
7
Tidal Forces
  • Forces caused by the difference in a
    gravitational field from one point to another.

Fhead 10g
Tidal force 90g
Ffeet 100g
8
Wormholes
www.lwg3d.org
9
What are Wormholes?
  • They are tunnels through spacetime

http//www.astrosurf.org/lombry/Physique/wormhole-
alpha-centauri.jpg
10
What are Wormholes?
  • Wormholes are spheres, although represented as 3D
    tunnels in embedded diagrams.
  • They are caused by gravitational forces described
    by a metric.
  • Great variety! static throat, dynamic throat,
    spinning, not spinning, with little or great
    tidal forces, etc.

11
Wormholes are not Black holes!
  • Wormholes are two-mouth tunnels, but black holes
    are a one way trip.

12
What do they look like?
http//www.astrosurf.org/lombry/Physique/trounoir-
voielactee-mellinger.jpg
13
What causes the black spot?
  • It is caused by the bending of light towards the
    wall of the throat as it passes through the
    wormhole.

14
What types of wormholes are there?
  • The Schwartzchild wormhole
  • The Morris-Thorne wormhole
  • The Visser wormhole

15
The Schwartzchild Wormhole
It is actually a Black Hole-Wormhole-White Hole
system.
  • ds2 - ( 1 - rs / r ) dt2  ( 1 - rs / r )-1 dr2
     r2 dO2
  • Where rs 2 G M / c2

It has tremendous tidal forces in its throat and
outside its mouth due to the black hole. The
throat is dynamic.
16
(No Transcript)
17
The Morris-Thorne Wormhole
  • Huge tidal forces at the mouth, but no horizons.
  • Less mass required, but still planet-size chunks.
  • Throat is fairly stable compared to the
    Schwartzschild wormhole

ds2 - e2F(r)dt2  dr2  R(r)dO2
18
The Visser Wormhole
  • Require cutting two similar holes in space-time
    and sewing the edges together.
  • It uses a lot of negative mass, therefore it has
    smaller tidal forces.

19
Space Travel, Really?
20
Basic Idea
  • We want to create a traversable and stable
    wormhole for use in space travel.

http//www.abc.net.au/science/slab/wormholes/defau
lt.htm
21
Problems - Engineering
  • All wormholes require exotic (negative) matter to
    keep their throat open.
  • It takes to much energy to just open them, leave
    alone maintain them.
  • Fine tuning problems too much precision needed.
  • At the moment it is beyond our reach, but there
    is no telling about whether future generations
    will do it.

22
Current Research
  • Mostly theoretical, no significant experimental
    approach has been taken directly on the subject.
  • Exotic matter experiments have shown that this
    material is obtainable.

23
Conclusion
  • We have not seen wormholes directly, but our
    known laws of physics do not ban their existence.
    It is not outrageous to believe they exist.
  • Regarding space travel, maybe only future
    generations will be capable of telling whether it
    is possible or not.

24
And that is all!
http//www.zamandayolculuk.com/cetinbal/lighttrave
l.htm
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