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### Time Travel

By B. Justin Scholfield

What is the nature of Time?

- Time is used to relate events
- We define two actions as simultaneous when we see the two actions at the same time

Special Relativity

This is the boost matrix, or Lorentz tensor.

It describes the translation of position and time to another frame moving at speed v along one axis

Its called special relativity because it can’t handle acceleration that well.

It can be used for doing relativistic mechanics as long as gravity is not involved

Fun Fact: It took Einstein only 8 weeks to come up with special relativity.

General Relativity

This is the Einstein Field Equations

It is described as:

“16 coupled hyperbolic-elliptic nonlinear partial differential equations “

Meaning its very, very hard to solve.

In expanded form it is three pages long, just to define the problem

The Field Equations are used to predict how a distribution of mass will effect space

All the time machines I will mention will be based on solutions to this equation

Fun Fact: it took Einstein 8 years to create this

The Diagrams of Time Travel

Minkowski diagrams and Light cones

Minkowski diagrams

Minkowski diagrams are used to

show a particle traveling thru space

time, they have one time axis and

one space axis.

The particles in a diagram form a world line which is the line that a particle takes thru space time

Light Cones

Light Cones are used to show how a particle can move. The edge of the cone can’t be broken because that would mean that the particle has some how gone faster than light

Accepted forms of Time Travel

The following forms of time travel are all future ward and all of them have been experimentally verified

High speed based Time Travel

The equation shown is the formula for time dilation at high speeds

For example at .999999c the dilation factor is about 707

The difficulty with a practical application is that to reach such high speeds requires a good deal of acceleration

Time Travel Because of Acceleration

General Relativity shows that time dilation is created by acceleration. The acceleration can be anything from gravity to linear acceleration to angular acceleration

- Fun Facts:
- There is a 7% difference in the time measured on earth and on a neutron star
- On a rotating disk with a 66,000 g centripetal acceleration an atomic clock was used to measure the time dilation for an experiment

That rotation leads to time dilation implies that a possible time machine could be a high powdered dryer

The Twin Paradox

One twin leaves the earth and travels into space on a space ship (a fast one) and the other stays behind. The space twin is younger than the earth twin when he returns. Why can’t it be the other way around?

Answer: one has a curved world line, the other doesn't.

The Gödel Universe

Gödel's Idea was to make a Universe that would enable time travel. He dose this by using frame dragging and a rotating Universe

Frame Dragging happens when a rotating mass drags space with it, it there by causes light cones to tip.

Fun Fact: Yesterday (10/21/2004) the first experimental verification of frame dragging was published

The Tippler Cylinder

The Tippler cylinder is related to the Gödel universe. It uses an infinitely long rotating cylinder to achieve the same effect.

Worm Hole Time Travel

Worm Holes are solutions to the field equations that allow space to be non simply connected

How to make a Worm Hole into a Time Machine

Once a Worm Hole is made one end of it can be placed in a high gravity field or accelerated to a high speed then slowed down again. This provides a time machine for as long as the Worm Hole exists.

The a difficulty arises in doing this because worm holes tend to be unstable and my be destroyed if moved or placed into a high gravity field.

Problems With Worm Hole Creation

A worm hole requires an lot of tension to be kept open, for a 3 foot diameter worm hole it is on the order of 10^36 tones. Something that could hold at this level of tension would be classified as can rightly be called exotic matter.

No one is sure how to make a worm hole. There are many suggested methods of worm hole creation but most require a black hole or an ability to inflate one form the quantum foam.

A Worm Hole that passes thru time could also make a unbounded energy resonance that would destroy the worm hole.

Paradoxes with Backwards Time Travel

The diagram is a picture of a billiard ball going thru a worm hole time machine. This is a machine version of the grandfather paradox.

The billiard ball has an infinite number of possible paths, all self consistent. The solution to what the path of the ball will be is as a group of probabilities and can’t be solved until we have a better grasp of quantum gravity.

In Closing

All The time machines That I have mentioned are allowed by general relativity. There are no known physics that don’t allow this.

Sources

1.Time Machines: Time Travel and Physics, Metaphysics, and Science-fiction. Nahin, Paul J. 1999, Springer-Verlag New York, Inc

2. How to Build aTime Machine. Davies, Paul. 2001, Viking Penguin.

3. Black Holes & Time Warps, Throne, Kip S. 1994, H.W. Norton & Company.

4. Factors, Tensors, and the Basic Equations of Fluid Mechanics. Aris, Rutherford. 1962 Dover Books

5. The Einstein Equations. Author unknown. http://archive.ncsa.uiuc.edu/Cyberia/NumRel/EinsteinEquations.html#intro. Accessed 10/21/2004

6. Spinning Earth Twists Space. News report. http://www.nature.com/news/2004/041018/full/041018-11.html. Accessed 10/21/2004

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