We are performing measurements of gravity on small length scales in order to test theories that propose the existence of extra spatial dimensions. According to recent theoretical attempts to address the hierarchy problem*, evidence for the existence of spatial dimensions beyond the usual three could be observed in relatively inexpensive "table-top" measurements of gravity on small length scales. In this scenario, the strong and electroweak forces are confined to the three known spatial dimensions, while gravity is free to "explore" the hypothesized extra dimensions. If these dimensions exist, the scaling or strength of the gravitational force should be altered from standard Newtonian theory, when measured on length scales on order of the size of the compactification radius of these extra dimensions. Until recently, gravity has not been tested on length scales below about 1 mm. We are in the process of measuring gravity between masses on the order of 100 microns apart, employing an experiment reminiscent of the Cavendish original, though miniaturized. The integral torsion balance is replaced by a micromachined silicon cantilever. Additionally, special steps must be taken to minimize the spurious forces that become problematic at such small distances.
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Here is our recent preprint.*The essence of the hierarchy problem is the unexplained, large discrepancy between the weak scale and the Planck scale (sixteen orders of magnitude). It can be restated as "Why is gravity so weak compared to the other forces?".