Physicists in the US have devised a new way to test Coulomb’s inverse-square law that is 10,000 times more sensitive than previous measurements. The experiment, which the team is currently building, involves looking for small violations of the law by carefully monitoring charged particles as they pass through a metal tube. If discovered, any deviation from Coulomb’s law could have profound implications on theoretical physics.

Coulomb’s inverse-square law states that the force between two electric charges is inversely proportional to the square of the distance between the charges. The law is a cornerstone of electromagnetic theory and if it were found not to hold, Maxwell’s equations and the Standard Model of particle physics would have to be modified. Another important consequence of a violation is that the photon would have a non-zero mass -- something for which there is no experimental evidence.

The last significant test of Coulomb’s law was made in 1983, when Richard Crandall at Reed College in the US measured the electric fields between conducting shells. He concluded that the inverse square relationship (as defined by the deviation from the exponent “-2”) is correct to about one part in 1017.

Now Dallin Durfee and colleagues at Brigham Young University in Utah have proposed a much more sensitive experiment based on a new technique called “charged-particle matter-wave interferometry” (Phys. Rev. Lett. 99 200401). It will involve sending a beam of atoms down a three-metre long metal tube (see figure). A laser ionizes the atoms, leaving them with a positive charge. This ion beam is then split into two parallel beams by mirrors and an optical grating. The two beams are then recombined at the other end of the tube.

If Coulomb’s law is violated, each beam will experience different electric fields when an oscillating voltage is applied to the tube. These differences in electric field will affect the relative phase of the two ion beams, which can be measured by observing how the two beams interfere when recombined.

The test challenges an important consequence of Coulomb’s law: that the electric fields inside a conducting shell must be independent of any voltages applied to the shell. As a result, any change in phase will show that a violation has occurred.

According to calculations done by the team, their experiment should be sensitive to deviations from the inverse-square law as small as about one part in 1022. Durfee’s experiment should also be able to tell if the photon has a mass at the level of about 10-49g, which is about 100 times better than current limits on the mass.