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Relativity and Wormholes. By Joaquin P Noyola PHYS 4117 – Learning by Seminar; Spring 2006. Outline. Brief Introduction to Relativity What are wormholes? Several wormhole systems Space Travel, Really? Current Reasearch. Inertial Frames.

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Relativity and wormholes

Relativity and Wormholes

By Joaquin P Noyola

PHYS 4117 – Learning by Seminar; Spring 2006


Outline
Outline

  • Brief Introduction to Relativity

  • What are wormholes?

  • Several wormhole systems

  • Space Travel, Really?

  • Current Reasearch


Inertial frames
Inertial Frames

…are coordinate systems which obeyNewton’s laws and are not accelerating.

static (x, y, z) coordinate system

moving (x’, y’, z’) coordinate system


Special relativity
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.


General relativity
General Relativity

  • The interval is no longer valid due to acceleration, and Δs2 ds2

  • We call the resulting equation the metric.

Comparing it to the interval in special relativity


Embedded diagram of a potential well

Gravitational fields cause spacetime to bend, creating a potential well

Because of this bending, the object’s “straight-line” trajectory becomes curved to account for the curvature of space.

Even light follows this curved trajectory

http://www.science-art.com/


Tidal forces
Tidal Forces

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

Fhead = 10g

Tidal force = 90g

Ffeet = 100g


Wormholes
Wormholes

www.lwg3d.org


What are wormholes
What are Wormholes?

  • They are tunnels through spacetime

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


What are wormholes1
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.


Wormholes are not black holes
Wormholes are not Black holes!

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


What do they look like?

http://www.astrosurf.org/lombry/Physique/trounoir-voielactee-mellinger.jpg


What causes the black spot
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.


What types of wormholes are there
What types of wormholes are there?

  • The Schwartzchild wormhole

  • The Morris-Thorne wormhole

  • The Visser wormhole


The schwartzchild wormhole
The Schwartzchild Wormhole

It is actually a Black Hole-Wormhole-White Hole system.

ds2 = - ( 1 - rs / r ) dt2 + ( 1 - rs / r )-1dr2 + r2dΩ2

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.


The morris thorne wormhole
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 = - e2Φ(r)dt2 + dr2 + R(r)dΩ2


The visser wormhole
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.



Basic idea
Basic Idea

We want to create a traversable and stable wormhole for use in space travel.

http://www.abc.net.au/science/slab/wormholes/default.htm


Problems engineering
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.


Current research
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.


Conclusion
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.


And that is all
And that is all!

http://www.zamandayolculuk.com/cetinbal/lighttravel.htm


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