Relativity and Wormholes

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Relativity and Wormholes

• By Joaquin P Noyola
• PHYS 4117 Learning by Seminar Spring 2006

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Outline

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

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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
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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.
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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• The interval is no longer valid due to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
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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/
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Tidal Forces

• Forces caused by the difference in a
  gravitational field from one point to another.

Fhead 10g
Tidal force 90g
Ffeet 100g
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Wormholes
www.lwg3d.org
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What are Wormholes?

• They are tunnels through spacetime

http//www.astrosurf.org/lombry/Physique/wormhole-
alpha-centauri.jpg
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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.

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Wormholes are not Black holes!

• Wormholes are two-mouth tunnels, but black holes
  are a one way trip.

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What do they look like?
http//www.astrosurf.org/lombry/Physique/trounoir-
voielactee-mellinger.jpg
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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.

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What types of wormholes are there?

• The Schwartzchild wormhole
• The Morris-Thorne wormhole
• The Visser wormhole

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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.
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(No Transcript)
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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
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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.

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Space Travel, Really?
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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
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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.

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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.

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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.

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