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 (S) over finite times T, and also (S) over finite areas of typical linear dimensions a. With only one mirror, the mean-square deviations are ( Delta S 2 )=constant*h(cross) 2 /c 6 T 8 , the value of such constants depending on how the apparatus averages over time; if a< >cT, then (S 2 )=constant*h(cross) 2 /c 4 a 2 T 6 . On one of a pair of parallel mirrors a distance L apart, if cT>>a, cT>>L, then ( Delta S 2 )=( Delta S 2 )=constant*h(cross) 2 /c 4 L 2 T 6 . 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.