Wednesday, August 23, 2006

New Dimensions at LHC

Picture courtesy of cyberchaos @ flickr

CERN's new LHC collider
aims to find the long-awaited "Higgs particle", which endows other particles with mass. In an entirely new energy range and with its special experimental conditions, the LHC could also discover other new physics effects.

Why is gravity so weak?
The traditional answer is because the fundamental scale of the gravitational interaction (i.e. the energy at which gravitational effects become comparable to the other forces) is up at the Planck scale of around 1019 GeV - far higher than the other forces.

However, that only raises another question: what is the origin of this huge disparity between the fundamental scale of gravity and the scale of the other interactions?

A possible explanation currently gaining ground in theoretical circles is that the fundamental scale of gravity is not really up at the Planck scale, it just seems that way. According to this school of thought, what is actually happening is that gravity, uniquely among the forces, acts in extra dimensions.

This means that much of the gravitational flux is invisible to us locked into our three dimensions of space and one of time.

Consider, by analogy, what two-dimensional flatlanders would make of three-dimensional electromagnetism. To them, the flux lines of the force between two charges would appear to travel in their planar world, whereas in reality we know that most of the flux lines would spread out through a third dimension, thus weakening the force between the two charges. The initial spreading of the flux lines into the third dimension does have a significant effect: the force appears weaker to a flatlander than is fundamentally the case, just as gravity appears weak to us.

Turning back to gravity, the extra-dimensions model stems from theoretical research into (mem)brane theories, the multidimensional successors to string theories (April 1999 p13).

One remarkable property of these models is that they show that it is quite natural and consistent for electromagnetism, the weak force and the inter-quark force to be confined to a brane while gravity acts in a larger number of spatial dimensions.
The requirement of correctly reproducing Newton's constant, G, at long distances leads to the size of the extra dimensions in which gravity is free to act being related to the number of extra dimensions. If there is just one extra dimension, then the model says that it should be of the order 1013 m, in which case solar system dynamics would be radically different and we would be taught a Newton's 1/r3 law in school rather than the 1/r2 law that we know and love.

So one extra dimension doesn't work. With two extra dimensions, the scale drops to slightly less than 1 mm and, small though that is, it at first seems surprising that extra dimensions of that size have not already been seen. However, because the extra dimensions only affect gravity, the most direct constraints come from experiments to measure G at short distances, and delving into the historical literature on the subject reveals that no measurements of G at the submillimetre scale have ever been made.

A team led by Aharon Kapitulnik at Stanford is currently in the process of accurately measuring G at submillimetre scales for the first time using a tabletop experiment. For more than two extra dimensions their size begins to get quite small: 1 fm, for example, for six extra dimensions, outside the range of even the improved submillimetre gravity experiments. Nevertheless, the model still makes a number of dramatic predictions.

If gravity does have extra dimensions at its disposal, they should manifest themselves at CERN's LHC proton collider, no matter what the number of extra dimensions might be. This is because the fundamental scale of the gravitational interaction should be around a few tera-electron volts, so, at TeV energies, gravitational effects will become comparable to electroweak effects.

Consequently, gravitons will be produced as copiously as photons, with the difference that the photons will remain in our familiar dimensions while many of the gravitons will escape into extra dimensions, carrying energy with them.

More dramatically still, the LHC could produce fundamental string relations of our familiar particles, such as higher-spin relatives of electrons or photons. There is also a possibility that, owing to the now much stronger gravitational interactions, microscopically tiny black holes could be produced with striking signals.

Fortunately, such small black holes are not at all dangerous, being much more similar to exotic particles than large astrophysical black holes, and they decay quite quickly as a result of Hawking radiation. With the recent outburst of ideas in these directions, it is clear that extraordinary discoveries at the LHC may be just around the (extra-dimensional) corner.

Original text from CERN Courier
locating a point on a plane (ie. a city on a map of the Earth) requires two parameters โ€” latitude and longitude. The corresponding space has therefore two dimensions, its dimension is two, and this space is said to be 2-dimensional (2D). Locating the exact position of an aircraft in flight (relative to the Earth) requires another dimension (altitude), hence the position of the aircraft can be rendered in a three-dimensional space (3D).
If time is added as a 3rd or 4th dimension (to a 2D or 3D space, respectively), then the aircraft's estimated "speed" may be calculated from a comparison between the times associated with any two positions. For common uses, simply using "speed" (as a dimension) is a useful way of condensing (or translating) the more abstract time dimension, even if "speed" is not a dimension, but rather a calculation based on two dimensions. Adding the three Euler angles, for a total 6 dimensions, allows the current degrees of freedom โ€”orientation and trajectory โ€”of the aircraft to be known.

Five dimensions
Kaluza-Klein theory
Fifth dimension
Ten, eleven or twenty-six dimensions
String theory
Why 10 dimensions?
Calabi-Yau spaces
Infinitely many dimensions
Hilbert space
Special relativity
General relativity
Laval nozzle and blackholes by Plato
Universe lifecycles from NASA gov
More about Extra Dimensions by Sabine Hossenfelder
Minimal length model by Sabine Hossenfelder

A special thank you to Cynthia for her supra-dimensional
thinking, dancing and boundless inspiration & energy.
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