Jacques Distler has something interesting about the prospects for producing black holes at the LHC. This has often been promoted as one of the most exciting possibilities for new physics from the LHC. Evidently it turns out that cosmic-ray experiments currently in progress also are sensitive to this kind of hypothetical black hole prediction. Depending on one’s assumptions about the minimal mass of a black hole that can be cleanly distinguished, either all or almost all of the range of new fundamental gravity scales accessible to the LHC will have been covered by the cosmic-ray experiments. So, if there is a new unexpected gravity scale in the range of a few Tev, this is very likely to first be seen in cosmic-rays, not at the LHC.

These Tev-scale gravity models have gotten a lot of attention in recent years, much of it in the form of claims of string-theory “predictions” that could be tested at the LHC. A few days ago I was talking to one of my colleagues, who believed, based on hearing a talk by Nima Arkani-Hamed, that string theory made predictions about what would happen at the LHC. Of course this is nonsense. There are lots of models you can construct involving string theory and any gravity scale you want. Past experiments rule out the possibility of a gravity scale up to the range of 100’s of Gev-1 Tev, but there is no reason other than wishful thinking and a desire to have something to say to people who point out that string theory makes no predictions, to believe that there is a gravity scale just a bit too high to have been seen at the Tevatron, but observable at the LHC. Such an assumption actually ruins what string theorists consider the major success of the whole string theory/supersymmetry picture, the fact that the 3 coupling constants in the standard model nearly come together at an energy somewhat below the Planck mass.

Personally I’ve always found the current “Large Extra Dimensions” Tev-scale gravity models to be just hideous and completely unmotivated. On the other hand, the one thing we know is that the electroweak-breaking scale is in this region, and since we don’t yet know what is causing this breaking, it is not completely inconceivable that it has something to do with gravity. The argument that the scale of quantum gravity is the Planck scale is not water-tight. It is based on the assumption that whatever generates the Einstein-Hilbert action as the effective low-energy action for gravity produces it with a magnitude of order one. If instead it comes with an exponential factor, the underlying gravity scale could be quite different than the Planck scale.

Besides some enthusiasts whose talks give the impression that Tev-scale gravity is a prediction of string theory, most string theorists believe that this is something unlikely to occur (Distler is one of these). One of the weirder things I’ve encountered in arguing with prominent string theorists is that they like to say that the Tev-scale gravity models are one of the major achievements in string theory in recent years, while at the same time saying they don’t believe in these models. What’s up with claiming as a point in favor of your theory that it “predicts” something you don’t believe?

For extra dimensions in general, I like the reinterpretation of Giorgi, Cohen and Arkani, going from 4D to higher dimensions by using a dinamical process and getting symmetry breaking from it.

Also, to see mathematically the Higgs field as an extra dimension is already a well known theme.

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