Repulsion/Levitation?


red ball There have been several proposals for repulsive Casimir forces.

yellow ball DARPA program on Casimir Effect Enhancement (Scientific American)

1. Exotic materials

red ball Similar materials (boundary conditions) attracts, but sufficiently dissimilar boundaries may repel.

    

yellow ball "van der Waals forces and zero-point energy for dielectric and permeable materials,"

T.H. Boyer, Phys. Rev. A 9, 2078 (1974) (large permittivity and large permeability repel)

yellow ball A material with large permeability is required for repulsion, but in ordinary materials permeability is close to one.

yellow ball Metamaterials, incorporating arrays of microengineered circuitry mimic, at certain frequencies, a strong magnetic response and have been proposed as candidates for Casimir repulsion across vacuum.

          

yellow ballMetamaterials have also been proposed as invisibility cloaks.

yellow ballThis connection between invisibility and levitation was apparently anticipated:

The Pilgrim

The Pilgrim: Rene Magritte 1966

yellow ball But invisibility cloaks are limited to a band of wavelengths, while Casimir force depends on all frequencies ...


2. Repulsion via Geometry & Shape

red ballAbraham-Lorentz (+Casimir) model of electron: A spherical conducting shell of radius R , with charge e

"Introductory remarks on quantum electrodynamics," H.B.G. Casimir, Physics 19, 846 (1956) ]

yellow ball Balancing the repulsive Coulomb energy, with the (presumed attractive) Casimir energy:

yellow ball "Quantum Electromagnetic Zero-Point Energy of a Conducting Spherical Shell and the Casimir Model for a Charged Particle," T.H. Boyer, Phys. Rev. 174, 1764 (1968)

2A = - 0.09235  is negative!  [also obtained by R. Balian and B. Duplantier (1977)]

yellow ballNot only for spheres, but also rectangular boxes:

["Vacuum means of energy-momentum ...,"  S.G. Mamaev and N.N. Trunov, Sov. Phys. J. (USA) 22, 51 (1979)]

The "Casimir energy" of a parallelopiped changes sign with aspect ratio:

red ball This putative repulisve force has been proposed as yet another means of levitation:

       ,     but

yellow ball "Attractive Casimir forces in a closed geometry,"

M. P. Hertzberg, R. L. Jaffe, M. Kardar, and A. Scardicchio, Phys. Rev. Lett. 95, 250402 (2005):

In the physically accessible geometry of a piston, the partition is always attracted to the closer side.

 ,

yellow ball "Opposites Attract: A Theorem about the Casimir Force,"

O. Kenneth and I. Klich, Phys. Rev. Lett. 97, 160401 (2006) (two halfs of a cut sphere attract)

red ball Contrained repulsion?

yellow ball "Casimir repulsion between metallic objects in vacuum,"

M. Levin, A.P. McCauley, A.W. Rodriguez, M.T.H. Reid, S.G. Johnson,  Phys. Rev. Lett. 105, 090403 (2010)