Diverging light pulses in vacuum: Lorentz-invariant mass and mean propagation speed

Abstract

We show that the concept of the Lorentz-invariant mass of groups of particles can be applied to light pulses consisting of very large but finite numbers of noncollinear photons. Explicit expressions are found for the invariant mass of this manifold of photons for the case of diverging Gaussian light pulses propagating in vacuum. As the found invariant mass is finite, the light pulses propagate in vacuum with a speed somewhat smaller than the light speed. A small difference between the light speed and the beam-propagation velocity is found to be directly related to the invariant mass of a pulse. Focusing and/or defocusing light pulses is shown to strengthen the effect in which the pulse slows down while the pulse invariant mass increases. A scheme for measuring these quantities experimentally is proposed and discussed.