On the corrections to the Casimir effect depending on the resolution of measurement

The Casimir force $\text{cF}=-\frac{{\pi }^2\mathrm{\hslash }c}{240a^4}$, which attracts to each other two perfectly conducting parallel plates separated by the distance $a$ in vacuum, is one of the blueprints of the reality of vacuum fluctuations. Following the recent conjecture, that quantum fields should be described in terms of the fields depending on the resolution of measurement, rather than the position alone (M.V.Altaisky, Phys. Rev. D 81(2010)125003), we derive the correction to the Casimir energy depending on the ratio of the plate displacement amplitude to the distance between plates.