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Wikipedia says:
If extra dimensions exist, they must be hidden from us by some physical mechanism. One well-studied possibility is that the extra dimensions may be "curled up" at such tiny scales as to be effectively invisible to current experiments.
I'm just curious, could there be any plausible "hiding" mechanism except the above?
Is there any theory dealing with such other possibilities?
There are models where the extra dimensions don't need to be curled up.
The main issue with extra dimensions is, 'why don't the particles/fields we interact with travel in those directions?' We have extremely good limits on standard model particles (electrons, photons) travelling in extra dimensions.
However, it is possible to imagine a string inspired scenario where standard model fields are confined to a 'brane'--that is, some 3 dimensional spatial surface living in a higher dimensional space. Then the particles we interact with simply are not free to travel in the extra dimension.
Then the issue becomes confining gravity to the brane. Already the experimental constraints on gravity are much weaker than the standard model fields--this is the essence behind the proposal of Arkhani-Hamed, Dimopolous, and Dvali (ADD) (http://arxiv.org/abs/hep-ph/9803315). In that proposal the extra dimensions are still curled, but are allowed to be much larger than the limits coming from observations of standard model particles.
There are other models though where gravity looks four dimensional to us but the extra dimensions are not infinite. Probably the most famous example is the Randall Sundrum model (http://arxiv.org/abs/hep-ph/9905221). There, the extra dimensions are 'warped,' and the warping has the net effect of having gravity be localized near our brane. They are not compact, however. Another example is the model of Dvali, Gabadadze, and Porrati (DGP), with a brane living in an infinite dimensional flat space-time (http://arxiv.org/abs/hep-th/0005016). The way gravity is confined in that case is that there are two gravitational constants, a "4d" one living on the brane and a "5d" one living in the bulk, and the relative sizes of the constants is chosen so that on short distances on the brane the gravitational force is dominated by the 4d gravitational constant.
None of these models have any observational evidence in their favor. In the case of the DGP model there are also various theoretical problems--there is superluminal propagation around certain backgrounds, and there is a "ghost instability" around the background you would have wanted to use for cosmology.
