Fifth Force - Theory and Experiment

Theory and Experiment

There are at least three kinds of searches that can be undertaken, which depend on the kind of force being considered, and its range.

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 on board a submarine (USS Dolphin (AGSS-555)) while deeply submerged. A further experiment measuring the gravitational constant in a deep borehole in the Greenland ice sheet found discrepancies of a few percent, but it was not possible to eliminate a geological source for the observed signal.

In 2012 Bhuvnesh Jain and others examined existing data on the rate of pulsation of cepheid variable stars in 25 galaxies comprising over a thousand stars in all . Theory suggests that the rate of pulsation would follow a different pattern in galaxies screened from a hypothetical 5th force by neighbourhood clusters from those that are un-screened. They were unable to find any variation from Einstein’s theory of gravity.

Some experiments used a lake and a 320m high tower. A comprehensive review suggested there is no compelling evidence for the fifth force, though scientists still search for it. Fishbach's article was written in 1992 and since then other evidence has come to light that may indicate a 5th force.

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.