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 $g_{55}$ 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.

• Received 16 September 1982

DOI:https://doi.org/10.1103/PhysRevLett.50.141