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Many physicists believe that there is little possibility of observing extra dimensions at LHC so that some extra dimension models originally designed to solve hierarchy problem (ADD/Randall-Sundrum) will probably be useless for the original purpose.

However some people claim that even if unobserved at LHC, these models will not be forgotten and people will continue to use them for other purposes. I am confused here -- if the proposed model fails to solve the very problem it was supposed to tackle, how can such models still be used? Will these not be inconsistent with nature?

Apart from the confusion, I am interested to know what insight such extra dimension models (RS/ADD) have provided which would be impossible unless such models were developed and studied?

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There is some confusion in this question on what new physics one expects to see at the LHC. The predominant models with extra dimensions are string theory models. String models are actively pursued because they allow quantization of gravity and have many group symmetries which can be used to embed the successful Standard Model results of particle physics. They also have at least extra six dimensions than the four we are used to up to now. The grand majority of models compactify these extra dimensions so that they would never be observable at the LHC.

What these models have also is supersymmetry, and it is the supersymmetric particles which, if found at the LHC, would signal that the string models with their extra dimensions are successful. If no supersymmetric particles are found at the next stage of the LHC this would just mean that the models must modify the models with a supersymmetric sector to energies larger than the LHC can reach. Nothing definitive will be decided , and we go on to the International Linear Collider to continue the search and test of models.

Maybe you are thinking of the models of large extra dimensions where some of the compactified dimensions could be large enough so that it could result in generating small black holes at the LHC . If these are not found it just means that these particular models are invalid.

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hi Anna, from wikipedia, it seems that the ILC will only probe up to 1 Tev. Why would ILC be able to probe regions that are unexplored by the LHC? my understanding is that the ILC will be leptonic rather than hadronic, so it will provide less statistical noise –  lurscher Dec 14 '12 at 15:53
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It is very important to remember that a proton is composed of 3 quarks, so on average the available energy for deep inelastic scattering is about 1/3. Feynman had said it graphically : "If I want to see what a watch is made out of I do not throw another watch on it, I take a screwdriver". Electrons which to first order interact with the electromagnetic and weak interaction only are the equivalent to a screw driver : simple vertices, not only better statistical background. –  anna v Dec 14 '12 at 15:57
    
@lurscher the comment above is for you –  anna v Dec 14 '12 at 16:01
    
great insight anna, i wasn't aware of leptons are able to resolve smaller details of interactions at lower energies, but it makes sense –  lurscher Dec 14 '12 at 16:01

By way of analogy, you can't observe what's going on inside a black hole. But you can still make some indirect observations that are consistent with the theories about how a black hole works, such as the observance of radiation (called Hawking Radiation) from just outside the event horizon.

In other words, just because extra dimension models may not be observable, doesn't mean that the theory won't have some orthogonal utility.

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