Relativity and Wormholes

8/4/2019 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 obeyNewtons 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

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

which is invariant from one inertial frameto another.


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General Relativity The interval is no longer valid due to

acceleration, ands2 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


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Gravitational fields causespacetime to bend, creating apotential well

Because of this bending, theobjects straight-line trajectorybecomes curved to account forthe curvature of space.Even light follows this

curved trajectory

Embedded diagram of a potential well


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

Fhead = 10g

Ffeet

= 100g

Tidal force = 90g


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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, dynamicthroat, spinning, not spinning, with littleor great tidal forces, etc.


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Wormholes are not Black holes!

Wormholes are two-mouth tunnels, butblack holes are a one way trip.


12/24http://www.astrosurf.org/lombry/Physique/trounoir-voielactee-mellinger.jpg

What do they look like?


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What causes the black spot?

It is caused by the

bending of lighttowards the wall ofthe throat as itpasses through thewormhole.


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What types ofwormholes are there?

The Schwartzchild wormhole

The Morris-Thorne wormhole

The Visser wormhole


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The Schwartzchild Wormhole

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

-1dr2 + r2d2

Where rs = 2 G M / c2

It is actually a Black Hole-Wormhole-

White Hole system.

It has tremendous tidal forces in itsthroat and outside its mouth due tothe black hole. The throat is dynamic.


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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 theSchwartzschild wormhole

ds2 = - e2(r)dt2 + dr2 + R(r)d2


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The Visser Wormhole

Require cutting two similar holes

in space-time and sewing theedges together.

It uses a lot of negative mass,

therefore it has smaller tidalforces.


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Space Travel, Really?


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Basic IdeaWe want to create a traversableand stable wormhole for use in

space travel.

http://www.abc.net.au/science/slab/wormholes/default.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 openthem, 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 whetherfuture generations will do it.


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Current Research

Mostly theoretical, no significantexperimental approach has beentaken directly on the subject.

Exotic matter experiments haveshown that this material isobtainable.


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Conclusion

We have not seen wormholes directly,

but our known laws of physics do notban their existence. It is notoutrageous to believe they exist.

Regarding space travel, maybe only

future generations will be capable oftelling whether it is possible or not.


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And that is all!

Relativity and Wormholes

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