The Added Mass Effect and the Higgs Mechanism

Abstract

A rigid body accelerated through an inviscid, incompressible fluid appears to gain mass, which is encoded in an added mass tensor. Swimmers, air bubbles, submarines and airships are slowed down by the associated `added mass' force proportional to their acceleration, which is distinct from viscous drag and buoyancy. In particle physics, otherwise massless electrons, quarks, $W$ and $Z$ bosons, moving through the Higgs scalar field acquire masses encoded in a mass matrix. In this expository article we give an introduction to the fluid mechanical added mass effect through examples of potential flows in various dimensions and exploit a correspondence with the Higgs mechanism [introduced in Proc. R. Soc. A471: 20140803 (2015)] to relate this to how the $W$ and $Z$ bosons can get their masses, while leaving the photon massless. The correspondence relates the Higgs scalar field to the fluid, the vacuum expectation value of the Higgs field to a constant fluid density and quantum fluctuations around the Higgs condensate to compressional waves in the fluid. The shape of the rigid body encodes the pattern of gauge symmetry breaking through the eigenvalues of the corresponding mass matrices. Possible directions of acceleration of the rigid body are related to directions in the gauge Lie algebra with a `flat' direction in the body corresponding to a massless photon. Moreover, symmetries of the body are related to those of the scalar vacuum manifold. The Higgs boson may be viewed as the analog of a long wavelength fluid mode around an accelerated body.