Credit: GETTY

Beautiful as they are, and useful as their concept is (see, for example, Keith Burnett's News & Views article on page 589 of this issue), vortices remain elusive in many respects. David Thouless and James Anglin have turned their attention to vortices in superfluids — in these, vortices are quantized, meaning that the circulation around a closed loop can take only discrete values — and revisit the question of vortex inertial mass (Phys. Rev. Lett. (in the press); preprint at http://arxiv.org/abs/cond-mat/0703523; 2007).

The inertial mass of a vortex is an important parameter in understanding its dynamics. But, so far, there seems to be no agreement in the literature on how this mass should be defined when dealing with a superfluid. Although Thouless and Anglin reconcile aspects of earlier approaches, they conclude that the mass of a vortex might not be well defined at all; rather, it depends on the way it is measured. Or, put another way, inertial effects in vortex dynamics might depend on the context in which they occur.

Earlier definitions of the mass of a vortex in a superfluid — such as basing it on the energy required to form a vortex at rest — were mostly indirect. Thouless and Anglin follow a more direct route, and propose measuring the inertial mass by driving the vortex around in circles. The required handle on the vortex could be provided by an external potential that 'pins' it. When the potential is then moved around in a circular orbit, dragging the vortex with it, the mass can be derived from the force on the accelerated vortex.

In the specific framework considered here, the Gross–Pitaevskii model for superfluids, a simple expression for the vortex mass is found. But the study also shows that the mass depends on the form of the pinning potential, suggesting that, after all, an unambiguous vortex mass might not be decipherable.