## Part 1 - Wormhole Formation Theories (DRAFT COPY)

**Wormhole transportation **

Just when you thought it was confusing enough, those physicists had to come up with wormholes. Here's the premise behind a "wormhole." Although Special Relativity forbids objects to move faster than light within spacetime, it is known that spacetime itself can be warped and distorted. It takes an enormous amount of matter or energy to create such distortions, but distortions are possible, theoretically. To use an analogy: even if there were a speed limit to how fast a pencil could move across a piece of paper, the motion or changes to the paper is a separate issue. In the case of the wormhole, a shortcut is made by warping space (folding the paper) to connect two points that used to be separated. These theories are too new to have either been discounted or proven viable. And, yes, wormholes do invite the old time travel paradox problems again.

**Here's one way to build one: **

First, collect a whole bunch of super-dense matter, such as matter from a neutron star. [or a large explosion of Isogen-5] *How much? *- well enough to construct a ring the size of an average solar system. Then build another ring where you want the other end of your wormhole. Next, just charge them up to some incredible voltage, and spin them up to near the speed of light -- both of them.

**Traversable Wormholes **

The possibility of traversable wormholes in general relativity was first demonstrated by Kip Thorne and his graduate student Mike Morris . For this reason, the type of traversable wormhole they proposed, held open by a spherical shell of exotic matter , is referred to as a *Morris-Thorne wormhole *. Later, other types of traversable wormholes were discovered as allowable solutions to the equations of general relativity, including a variety analyzed in a paper by Matt Visser , in which a path through the wormhole can be made where the traversing path does not pass through a region of exotic matter. However, in the pure Gauss-Bonnet theory (a modification to general relativity involving extra spatial dimensions which is sometimes studied in the context of brane cosmology ) exotic matter is not needed in order for wormholes to exist—they can exist even with no matter. [14] A type held open by negative mass cosmic strings was put forth by Visser in collaboration with Cramer *et al. *, [10] in which it was proposed that such wormholes could have been naturally created in the early universe.

Wormholes connect two points in spacetime, which means that they would in principle allow travel in time , as well as in space. Morris, Thorne and Yurtsever worked out explicitly how to convert a wormhole traversing space into one traversing time. [2] However, according to general relativity it would not be possible to use a wormhole to travel back to a time earlier than when the wormhole was first converted into a time machine by accelerating one of its two mouths. [15]

### Raychaudhuri's theorem and exotic matter

To see why exotic matter is required, consider an incoming light front traveling along geodesics, which then crosses the wormhole and re-expands on the other side. The expansion goes from negative to positive. As the wormhole neck is of finite size, we would not expect caustics to develop, at least within the vicinity of the neck. According to the optical Raychaudhuri's theorem , this requires a violation of the averaged null energy condition . Quantum effects such as the Casimir effect cannot violate the averaged null energy condition in any neighborhood of space with zero curvature, [16] but calculations in semiclassical gravity suggest that quantum effects may be able to violate this condition in curved spacetime. [17] Although it was hoped that quantum effects could not violate an achronal version of the averaged null energy condition, [18] violations have nevertheless been found, [19] thus eliminating a basis on which traversable wormholes could be rendered unphysical.

### Time travel

The theory of general relativity predicts that if traversable wormholes exist, they could allow time travel . [2] This would be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back; relativistic time dilation would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer, similar to what is seen in the twin paradox . However, time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone traveling through the wormhole itself, no matter how the mouths move around. [20] This means that anything which entered the accelerated wormhole mouth would exit the stationary one at a point in time prior to its entry.

For example, consider two clocks at both mouths both showing the date as 100. After being taken on a trip at relativistic velocities, the accelerated mouth is brought back to the same region as the stationary mouth with the accelerated mouth's clock reading 105 while the stationary mouth's clock read 110. A traveler who entered the accelerated mouth at this moment would exit the stationary mouth when its clock also read 105, in the same region but now five years in the past. Such a configuration of wormholes would allow for a particle's world line to form a closed loop in spacetime, known as a closed timelike curve .

It is thought that it may not be possible to convert a wormhole into a time machine in this manner; the predictions are made in the context of general relativity, but general relativity does not include quantum effects. Some analyses using the semiclassical approach to incorporating quantum effects into general relativity indicate that a feedback loop of virtual particles would circulate through the wormhole with ever-increasing intensity, destroying it before any information could be passed through it, in keeping with the chronology protection conjecture . This has been called into question by the suggestion that radiation would disperse after traveling through the wormhole, therefore preventing infinite accumulation. The debate on this matter is described by Kip S. Thorne in the book *Black Holes and Time Warps *, and a more technical discussion can be found in *The quantum physics of chronology protection * by Matt Visser . [21] There is also the Roman ring , which is a configuration of more than one wormhole. This ring seems to allow a closed time loop with stable wormholes when analyzed using semiclassical gravity, although without a full theory of quantum gravity it is uncertain whether the semiclassical approach is reliable in this case.

## References

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