Casimir force, antennas, and salt water

As famously predicted by Hendrik Casimir in 1948, parallel conductors in a vacuum will attract each other because the conductors impose boundary conditions that affect the vacuum energy of the electromagnetic field (see the article by Steve Lamoreaux in Physics Today, February 2007, page 40 ). In general, the Casimir force depends on the shape of the conductors and its value is notoriously difficult to calculate, but research groups worldwide have been developing increasingly applicable computational techniques. Now a team at MIT has shown how tabletop measurements might provide the key information needed for the general calculation. The Casimir force may be expressed as an integral over frequency (ω) of correlation functions that involve electric and magnetic fields. In principle, those frequency-dependent correlations can be obtained in a suitably scaled tabletop experiment from measurements of how an antenna at one point responds to a current generated at a distant point. In practice, such measurements won’t work because the integrand oscillates wildly with ω. The integrand becomes well behaved—it decays and doesn’t oscillate—if the integration is performed in the complex plane, but real antennas respond to real frequencies. The key observation made by the MIT team is that their mathematical expressions always involve ω in the combination ɛω², where ɛ is the permittivity. Thus, the researchers predict, a force integral with real vacuum permittivity and complex contour can be calculated from a tractable number of antenna measurements made at real ω in a medium of complex permittivity—for example, salt water. (A. W. Rodriguez et al., Proc. Natl. Acad. Sci. USA 107 , 9531, 2010 http://dx.doi.org/doi:10.1073/pnas.1003894107 .)