Unusual properties of conductive rectangular cavities in the zero point electromagnetic field: Resolving forward’s Casimir energy extraction cycle paradox

Abstract

Two infinite parallel uncharged conducting planes experience an attractive force between them (called the Casimir force) due to the alteration of the zero point electromagnetic field between the plates. Similarly, there are forces on the surfaces of a rectangular cavity with conductive walls of dimension a1,a2,a3. Recently a paradox was published describing a method for the extraction of mechanical energy from the zero point fluctuations of the electromagnetic field in a rectangular conductive cavity by cyclical changes in the dimensions of the walls without doing any work (Forward, 1998). The validity of the analysis depends on the implicit assumption that the energy density within the cavity is approximately isotropic, so that positive average energy densities within the cavity result in outward forces, and negative average energy densities result in attractive forces. However, detailed computations of the forces on the cavity walls show this assumption is not valid, and that there are positive energy regions in which there are outward forces on some faces and inward forces on other faces (Hacyan, 1993). Specifically, for a cavity with a1=a2=1 the energy is positive for 0.4<a3<3.3, however, the average pressure P1 on the 1×1 faces and the average pressure P3 on the 1×a3 faces are both positive only if 0.7<a3<1.6. For all other values of a3, P1 and P3 have opposite signs. Specifically, for a3>1.6, P3>0, P1<0 and for a3<0.7, P3<0, P1>0. The implications of these and other unusual features of rectangular cavities in the vacuum are discussed.