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

static (x, y, z) coordinate system moving (x’, y’, z’) coordinate system

Special Relativity• Time is the fourth dimension and is

measure in meters of light travel, not seconds.

• Distance is now measured by the interval

2 2 2 2 2 2s c t x y z

which is invariant from one inertial frame to another.

General Relativity• The interval is no longer valid due to

acceleration, and Δs2 ds2

• We call the resulting equation the metric.

2 2 2 2 2 2s c t x y z

2 2 2 2 2 2( ) ( ) ( ) ( )ds f c dt g dx h dy j dz

Comparing it to the interval in special relativity

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

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

Embedded diagram of a potential well

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

Fhead = 10g

Ffeet = 100g

Tidal force = 90g

Wormholes

www.lwg3d.org

What are Wormholes?• They are tunnels through spacetime

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

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

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

What do they look like?

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?

The Schwartzchild wormholeThe Morris-Thorne wormholeThe Visser wormhole

The Schwartzchild Wormhole

ds2 = - ( 1 - rs / r ) dt2 + ( 1 - rs / r )-1 dr2 + r2 dΩ2

Where rs = 2 G M / c2

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

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

• 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

• 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.

Space Travel, Really?

Basic IdeaWe 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

• 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

• Mostly theoretical, no significant experimental approach has been taken directly on the subject.

• Exotic matter experiments have shown that this material is obtainable.

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!

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