Some time evolution properties of an electromagnetic wave

We investigate several time evolution properties of a free, spatially bounded, electromagnetic wave in empty space. In particular, we obtain expressions for the second time derivative of the second (energy) moment of the position vector $r:∫[(r−R)(r−R)u]dτ/W$ [$u$ is the energy density, $W$ is the stored energy, R is the centroid of energy]. This is shown to evolve qualitatively differently than, say, for a Schrödinger wave packet. Another quantity considered is $∫(G⋅G/u)dτ$ [G is the momentum density]. This is shown to approach a constant for $t→±∞$ and to vanish for at most one instant of time. The implication of this for so-called E parallel to B waves $(E∥B)$ is discussed.