Upper limits to submillimetre-range forces from extra space-time dimensions

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String theory is the most promising approach to the long-sought unified description of the four forces of nature and the elementary particles1, but direct evidence supporting it is lacking. The theory requires six extra spatial dimensions beyond the three that we observe; it is usually supposed that these extra dimensions are curled up into small spaces. This ‘compactification’ induces ‘moduli’ fields, which describe the size and shape of the compact dimensions at each point in space-time. These moduli fields generate forces with strengths comparable to gravity, which according to some recent predictions2,3,4,5,6,7 might be detected on length scales of about 100 µm. Here we report a search for gravitational-strength forces using planar oscillators separated by a gap of 108 µm. No new forces are observed, ruling out a substantial portion of the previously allowed parameter space4 for the strange and gluon moduli forces, and setting a new upper limit on the range of the string dilaton2,3 and radion5,6,7 forces.

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Figure 1: Major components of the apparatus.
Figure 2: Distributions of data samples.
Figure 3: Means of the off- and on-resonance data samples.
Figure 4: Current limits on new gravitational strength forces between 1 µm and 1 cm.


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We thank E. Lagae for work in the laboratory, and C. Briggs, T. Buxkemper, L. Czaia, H. Green, S. Gustafson and H. Rohner of the University of Colorado and JILA instrument shops for technical assistance. We also gratefully acknowledge discussions with S. de Alwis, B. Dobrescu and S. Dimopoulos. This work is supported by grants from the US National Science Foundation.

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Correspondence to John C. Price.

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