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Test of the inverse square law of gravitation.

Contact C. C. Speake



There is great interest in the possibility that Newton’s inverse square law of gravitation may break down at particle separations of much less than 1mm. The main reason for this is that String theorists have proposed that the Universe in which we exist may have more than three spatial dimensions! This proposal, if true, would pave the way towards a theory that would encompass the forces that are described by the Standard Model of particle physics (the electroweak and Strong nuclear force) and gravitation. The basic idea is that gravitation exists in all the spatial dimensions but that the other forces are constrained to exist only in the 3 known dimensions. In order for these ideas to be consistent with our knowledge of gravity, the new dimensions must be small. This simple idea of Arkani-Hamed et al (1997) implies that the true strength of gravity is only apparent at these small scales and that we see a diluted form of it in our usual experiences. If ‘real’ gravity is significantly stronger than it normally appears then it can be unified with the other forces at a lower energy than previously thought. With sub-millimeter new dimensions we might expect evidence for unification at energies as low as a few TeV, which is within reach of new particle accelerators such as the LHC at CERN.Naturally these ideas lead to violations of Newton’s inverse square law of gravitation at the scale of the new dimensions and this can be searched for with laboratory experiments. We are planning a test of the inverse square law using our Spherical Superconducting Torsion balance for which we have received a PPARC grant. We are currently seeking a Post-doctoral researcher for this work (see Jobs link). We have also proposed a space experiment which could take advantage of the quiet environment of a drag-free spacecraft to achieve high sensitivity (see Speake, Hammond and Trenkel, Gen Rel and Grav 36 503-521 2004).

There are many other plausible and exciting theoretical ideas that motivate these experimental searches and drive experimental gravitation to the frontier of modern physics. However the problems associated with convincing tests of the inverse square law at short ranges are many-fold. We discuss, at some length, these issues in the GRG paper. Systematic uncertainties come from the Casimir force, electrostatic forces due to contact potentials. Random noise comes from suspension thermal noise, detector noise, patch-field potentials (see Speake and Trenkel PRL 90 160403 2003) and environmental noise.

We show below the current state of knowledge of the inverse square law at short ranges, together with a projected sensitivity of a space experiment. The vertical scale represents the strength of gravity allowed by experiment (measured in terms of Newton’s constant). The horizontal scale is the range of the new component of gravitation.

Birmingham Gravitation Group, University of Birmingham © 2004, all rights reserved.