Are Casimir Forces Conservative?

The belief among investigators of the Casimir effect is that it is conservative and that the two interpretations as to the source of energy behind the Casimir effect are equivalent. In the first, the energy source is considered to be the zeropoint fields in the vacuum of space between the plates. In the second, the source is considered to come from the potential energy of atoms in the bulk matter making up the plates. The bulk matter interpretation will be trivially conservative because the plates comprise a closed system. The vacuum energy interpretation is not as clear. If the zero-point fields between the plates are static, the system will be closed and the forces will be conservative. However the fields may be a dynamic steady state in which case the system could be open and the forces not conservative. This paper examines a plausible but speculative extension of the vacuum centric proximity force approximation that incorporates the local geometry of non-parallel plates. This inclusion eliminates problems of local scale nonsensical distances between plates as well as some absurd results but introduces non-conservative forces. While only an experiment or more fundamental analytic approach can determine whether Casimir forces are conservative, the purpose of this paper is to merely raise the question.