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String theory requires ten (or eleven for M-theory) extra dimensions. These dimensions are not observed at large scales and so it has been hypothesised that they are curled up and invisible at larger scales. Often times the example of an ant on a lamppost is given. To the ant, the space is two-dimensional (up/down and around) but to an outside observer it appears to have just one dimension (up/down).

Have any experiments been conducted to find these extra dimensions and down to what size have they excluded/failed to find the existence of these dimensions?

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Roughly $10^{-19}$ meters.

http://arxiv.org/abs/1012.3375 , Search for Microscopic Black Hole Signatures at the Large Hadron Collider

Mureika et al, http://arxiv.org/abs/1111.5830 , Any black holes at the LHC?

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    – Community Bot
    Aug 28 at 15:01

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