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The phenomenon of dimensional reduction in quantum theories of gravity is studied. In the five-dimensional Kaluza-Klein model, the one-loop effective potential as a function of g₅₅ is computed. When the distance around the fifth dimension is larger than the Planck length, the loop expansion is reliable. The result leads to a force tending to make the fifth dimension contract to a size on the order of the Planck length. This can be interpreted as a gravitational version of the Casimir effect in electrodynamics.
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Appelquist et al. (1983) studied this question.
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