Physical interpretation of flux momentum

The Poynting vector $ \vec{S}$ is a physical magnitude that represents the local flux of electromagnetic energy. Assuming that an electromagnetic field can be described as a flux of photons, one can write

$\displaystyle \vec{S}=E \rho \vec{c}$ (B.13)

where $ E=\hbar\omega$ is the energy of one photon and $ \rho$ and $ \vec{c}$ are the density and the speed of photons respectively. The flux of momentum can be calculated similarly. The momentum of a photon ($ p$) can be obtained from the relativistic expression for the kinetic energy of one particle $ E=\sqrt{m^2c^4+p^2c^2}$, where $ m$ is the mass of the particle. A photon has zero mass ($ m=0$) and the resulting expression is

$\displaystyle E=pc$ (B.14)

and the density of flux momentum can be expressed in terms of the previous relations according to
$\displaystyle \vec{\phi}_\mathrm{field}$ $\displaystyle =$ $\displaystyle p\rho\vec{c}$  
  $\displaystyle =$ $\displaystyle \frac{E}{c}\rho\vec{c}=\frac{E\rho\vec{c}}{c}$  
  $\displaystyle =$ $\displaystyle \frac{\vec{S}}{c}~.$ (B.15)

Thus we have informally justified Eq. 2.16

JM Huguet 2014-02-12