On the magnitude of the energy flow inherent in zero-point radiation

Abstract

The spectrum of zero-point radiation is relativistically invariant and its spectral density function is therefore inversely proportional to the cubes of its wavelengths. For its energy to be finite, there must exist a minimum wavelength, $q_\lambda$. The measurements of the apparent attraction between two uncharged conductor plates, placed in a vacuum at a temperature close to absolute zero, made by Sparnaay in 1958 allow us to deduce that the energy flow of the zero-point radiation which comes of or into an area $(q_\lambda)^2$, corresponds with the emission of one photon of wavelength $q_\lambda$ per $q_\tau$ $(q_\tau=q_\lambda/c)$, plus one photon of wavelength $2q_\lambda$ per $2^3q_\tau$, etc., up to one photon of wavelength $nq_\lambda$ per $n^3q_\tau$. This energy flow is enormous, but Sparnaay's experiments implied only photons whose wavelengths were greater than $5\times10^{-5}$ cm, and zero-point radiation may include only photons with wavelengths greater than $xq_\lambda$, being $x$ an integer, perhaps very great.