Physics
Scientific paper
Dec 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet.1409y&link_type=abstract
"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R
Physics
Scientific paper
Since the pionering work of Kaluza and Klein, theories with small extra dimensions have captured the imagination of theoretical physicists. Here we will argue that quantum fluctuations of the gravitational field can produce effects which grow as the compactifcation length decreases, and hence have the possibility of placing lower bounds on the sizes of compact dimensions. The basic idea is very simple. The uncertainty principle requires that there be an inverse relation between the spatial dimensions of a quantum syatem and the quantum fluctuations of the variable conjugate to the position. A quantum particle confined in a small potential well must have large momentum fluctuations and have a large ground state energy. A quantum field confined in a small region must undergo large fluctuations, which manifest themselves in a large mean squared value for the field. The Casimir effect affords a simple example of this phenomenon; when a pair of plates are close together, both the Casimir energy and the mean squared electric and magnetic fields increase. In particular, the mean squared fields are proportional to 1/z4, where z is the distance to the nearest boundary...
Ford L. H.
Yu Hongwei
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