# Giant string in space

I saw an interview with Ed Witten, where he said one way to confirm string-theory is to observe a giant string floating in space, left over from the Big-Bang.

How does one observe such a string, does it have thickness? Is this string any different then the strings that (hypothetically) make up elementary particles?

What is required to produce such a large string, why is this string so much bigger then others?

What happends if one tries to interact with this string, can one stretch/cut it etc?

Can we have a stable mega-string on earth, and can it be used for anything?

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The things in question are called "cosmic strings." They are predicted as a byproduct of some but by no means all theories of the early Universe. There's no experimental evidence that they actually exist, although I suppose the possibility hasn't been ruled out.

• How would we observe this?

A long cosmic string would have a couple of observable signatures. The main effect is a sort of gravitational lensing. If a cosmic string lies directly between you and a background object, you will see two copies of the object, one from light that passed around the string to the left, and one from light that went to the right.

To go into a bit more detail, a cosmic string produces a "conical singularity" in the space around it. This means that the circumference of a circle surrounding the string will be slightly less than $2\pi$ times the radius. The fractional deficit is independent of radius. It's as if someone had removed a triangular wedge of space, and then "glued together" the faces adjoining the removed bit. To see why this is called a conical singularity, imagine taking a piece of paper, cutting out a triangular wedge (i.e., removing all points with $0<\phi<\alpha$ for some constant $\alpha$), and then gluing together the edges $\phi=0$ and $\phi=\alpha$. The paper will now have the shape of a cone; an ant walking around the singularity will cover a circumference $C=(2\pi-\alpha) r$.

Light travels in straight lines (geodesics) in this conical space, but two such straight lines can pass around opposite sides and meet again. (Draw it on your conical paper if you don't see this.)

So one way to look for cosmic strings is to look for pairs of identical images of something.

If the cosmic string happens to be moving transverse to your line of sight, then there's another observational signature. Background light that reaches you from the "downstream" side will be blueshifted compared to background light reaching you from the upstream side. In effect, the conical geometry gives a kick to photons coming from one side relative to the other. (That's actually a kind of imprecise way to put it: this is a purely geometrical effect, not an actual force.)

• Does it have a thickness?

Cosmic strings are predicted to have some nonzero thickness, but very small. I don't remember the details.

• Are they the same as the strings that (are theorized to) make up elementary particles?

Cosmic strings are not the same as the strings in string theory. There are connections between the two theories, which I don't understand at all. I understand cosmic strings pretty well and string theory not at all. I hope someone else will talk about the connections.

• What is required to produce such a large string?

Cosmic strings are predicted to result in some theories of the early Universe. They are "topological defects" resulting from a phase transition. During the phase transition, some field tries to "relax" into a lower-energy configuration. There are multiple different versions of the lower-energy state, and the field chooses different versions in different parts of space. A cosmic string results from different regions making incompatible choices, so that the whole system can't relax to the same state.

If you simulate such a phase transition, in which different points "choose" randomly which state to relax into and then the whole system tries to settle down into a low-energy final configuration, you find that many such strings result. There are large numbers of small loops and smaller numbers of big strings. The very long ones that Witten is talking about are predicted to be rare, but there should be a small number in our observable Universe (if a string-producing phase transition actually occurred).

• What happens when you interact with such a string?

The strings are under high tension and have a high energy density confined to a very small cross-sectional area. It'd be hard to cut one, without supplying enough energy to "undo" the phase transition. When two strings (or two sections of the same string) meet, they can "reconnect," essentially swapping with each other at the intersection point. A loop of string can "pinch off" smaller loops via this process: imagine the string twisting around into a figure-8 shape, and then splitting into two smaller loops.

There's a lot more to the dynamics of these strings. They can lose energy by emitting gravitational waves, for example.

• Can we have one on Earth?

In principle we could probably produce some small ones, if we could get the energy density in some region up high enough to undo the phase transition, but nobody's done anything remotely like this. If we did have a big one, I don't know how easy it would be to control it.

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This is the conversion of a superstring into a cosmic string. A cosmic string is a one dimensional region where the vacuum state is that of the unbroken Lagrangian. It is similar to the physics of supercooled water that can be colder than the freezing point. In the phase transition of a gas or liquid to solid there can be boundary zones or grains where the gas or liquid state persists.

The connection to string theory is with F-theory, which takes one into 12-dimensions, or with D-strings that are related to F-strings by S-duality between strong and weak interactions. One of the corner stones of string theory is the Nambu-Goto action, which is a starting point for the string action determined by the area of the string world sheet. The one spatial quantum dimension theory also describes the cosmic string. If a superstring is drawn into a very large filament so that its states remain invariant under the symmetries of the Lagrangian the string can be converted into this "defect" that is a cosmic string. The string has a huge tension, related to the string parameter $\alpha'$, and if this string is stretched to enormous lengths this can have a large gravitation. The curvature of space can be thought of as an orbit around the string, but where the area enclosed by the loop is the disk with a wedge cut out of it. This deficit angle $\theta$ then defines a curvature bounded within that loop as $R~\sim~\theta/2\pi r^2$, where $r$ is the radius of the loop.

The universe might have these floating around out there, sort of menacing cosmic bullwhips of sorts, that could have an imprint on the CMB. It would be bad new if one of these cut through the Earth, for it would gravitationally pancake the Earth some. As I recall the Earth would be squashed inwards at 4km/sec as it passed through. We would get a global quake many orders of magnitude worse than the recent Sendai quake.

It is hard to know how stable these are, and it could be that interactions with them might break the string up into small strings near the string length. The deficit angle above would have a gravitational lensing effect, and if one passed between the Earth and a distant object it might be detected that way.

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This paper: http://arxiv.org/PS_cache/astro-ph/pdf/0302/0302547v1.pdf was a speculative look at a possible double galaxy image. They considered that it had been mirrored down the centre by a cosmic string to repeat the galaxy. It turned out to be untrue however when looked at in more detail by hubble.

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