# Measuring extra-dimensions

I have read and heard in a number of places that extra dimension might be as big as $x$ mm. What I'm wondering is the following: How is length assigned to these extra dimensions?

I mean you can probably not get your ruler out and compare with the extent of an extra-dimension directly, can you? So if not how can you compare one dimension with the other? Does one have some sort of canonical metric? Could one also assign a length (in meters) to time in this way?

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In addition to what dmckee said, another hint at ("large") extra dimensions would be the detection of Kaluza-Klein particles at the LHC for example.

Kaluza-Klein particles are in principle nothing but the known standard model particles which can propagate into the extra dimensions if these are large enough. It can be shown that the angular momentum in these extra dimensions is quantized. This leads to the effect that particles propagating into the extra dimensions would be observed as heavier versions of the known standard model particles due to the additional momentum in the otherwise not directly visible dimensions. The energy (or mass squared) spectrum of the corresponding expected particle tower would have a step size proportional to 1/r (where r is the radius of the extra dimension).

As Prof. Strassler explains here, to determine the shape and extent of such large extra dimensions it would be necessary to measure the whole mass spectrum using more than one KK particle.

Up to now no KK particles have shown up at the LHC so far (which was run only at 7TeV and now continues at 8 TeV). But note that even if there could be such large extra dimensions leaving hints at themselves at the "LHC scale" (up to 14 TeV), this does not have to be the case for ST to work; the "large" extra dimensions are only a feature of certain (phenomenologica) models ...

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• Make some assumptions about the physics associated with the dimensions in questions (say electric field strength goes by $r^{-(n-1)}$ over distances in which $n$ dimensions are significant).

• Make predictions on that basis

• Compare to experiment

Many predictions can be made and tested in the realms of high energy particle physics, but so far all are null.

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