The idea is difficult to test, because gravity is such a weak force: the gravitational interaction between two objects is only significant when one has a great mass. Therefore, it takes very precise equipment to measure gravitational interactions between objects that are small compared to the Earth. Nonetheless, in the late 1980s a fifth force, operating on municipal scales (i.e. with a range of about 100 meters), was reported by researchers (Fischbach et al.) who were reanalyzing results of Loránd Eötvös from earlier in the century. The force was believed to be linked with hypercharge. Over a number of years, other experiments have failed to duplicate this result, and physicists now believe that there is no evidence for a fifth force.
One way is to search for a fifth force with tests of the strong equivalence principle: this is one of the most powerful tests of Einstein's theory of gravity, general relativity. Alternative theories of gravity, such as Brans-Dicke theory, have a fifth force—possibly with infinite range. This is because gravitational interactions, in theories other than general relativity, have degrees of freedom other than the "metric," which dictates the curvature of space, and different kinds of degrees of freedom produce different effects. For example, a scalar field cannot produce the bending of light rays. The fifth force would manifest itself in an effect on solar system orbits, called the Nordtvedt effect. This is tested with Lunar Laser Ranging Experiment and very long baseline interferometry.
Another kind of fifth force, which arises in Kaluza-Klein theory, where the universe has extra dimensions, or in supergravity or string theory is the Yukawa force, which is transmitted by a light scalar field (i.e. a scalar field with a long Compton wavelength, which determines the range). This has prompted a lot of recent interest, as a theory of supersymmetric large extra dimensions—dimensions with size slightly less than a millimeter—has prompted an experimental effort to test gravity on these very small scales. This requires extremely sensitive experiments which search for a deviation from the inverse square law of gravity over a range of distances. Essentially, they are looking for signs that the Yukawa interaction is kicking in at a certain length.
Australian researchers, attempting to measure the gravitational constant deep in a mine shaft, found a discrepancy between the predicted and measured value, with the measured value being two percent too small. They concluded that the results may be explained by a repulsive fifth force with a range from a few centimetres to a kilometre. Similar experiments have been carried out onboard a submarine (USS Dolphin (AGSS-555)) while deeply submerged.
The above experiments search for a fifth force that is, like gravity, independent of the composition of an object, so all objects experience the force in proportion to their masses. Forces that depend on the composition of an object can be very sensitively tested by torsion balance experiments of a type invented by Loránd Eötvös. Such forces may depend, for example, on the ratio of protons to neutrons in an atomic nucleus, or the relative amount of different kinds of binding energy in a nucleus (see the semi-empirical mass formula). Searches have been done from very short ranges, to municipal scales, to the scale of the Earth, the sun, and dark matter at the center of the galaxy.