Statistical foundation of the Minkowski tensor for ponderable media.

Abstract

The Minkowski stress tensor is statistically derived from the Maxwell-Lorentz field equations and the Liouville equation for a system of composite particles subject to an electromagnetic field. The derivation is subject to the condition that the fluctuations of field vectors are not statistically correlated. It is also shown by deriving the electromagnetic-field-momentum balance equation and the mechanical-momentum balance equation that the electromagnetic field momentum may be taken with ${c}^{\mathrm{\ensuremath{-}}1}$D\ifmmode\times\else\texttimes\fi{}B instead of ${c}^{\mathrm{\ensuremath{-}}1}$E\ifmmode\times\else\texttimes\fi{}H. The pressure in ponderable media is shown to contain an electromagnetic contribution: p=${p}_{0}$+(D\ensuremath{\cdot}E+B\ensuremath{\cdot}H)/2, where ${p}_{0}$ is the pressure in the case of no field. The electromagnetic contribution does not contain an adjustable, or undetermined, parameter unlike that in the existing theories.