ON THE FLUCTUATIONS OF THE CASIMIR FORCE

Standard statistical and quantum physics are used to analyse the fluctuations of the Casimir stress S (normal force per unit area) exerted on a flat perfect mirror (conductor) by the zero-point electromagnetic fields in adjacent space, partly in order to help dispel the apologetics that often befog zero-point effects generally. S is measurable only when averaged (SBAR) over finite times T, and also (S congruent-to) over finite areas of typical linear dimensions a. With only one mirror, the mean-square deviations are [DELTA-SBAR2] = constant x h2/c6T8, the value of such constants depending on how the appartus averages over time; if a << cT, then [DELTA-S congruent-to 2] = [DELTA-SBAR2]. If, unrealistically, a >> cT, then [DELTA-S congruent-to 2] = constant x h2/c4a2T6. On one of a pair of parallel mirrors a distance L apart, if cT >> a, cT >> L, then [DELTA-S congruent-to2 ] = [DELTA-SBAR2] = constant x h2/c4L2T6. Mirror transparency at frequencies well above 1/T has negligible effect. An appendix outlines the mathematical problems, mostly unsolved, met in attempts to evaluate the full probability distributions underlying such mean-square deviations.