According to wikipedia and other sources, there are no longitudinal electromagnetic waves in free space. I'm wondering why not.
Consider an oscillating charged particle as a source of EM waves. Say its position is given by $x(t) = \sin(t)$. It is clear that at any point on the $x$ axis, the magnetic field is zero. But there is still a time-varying electric field (more or less sinusoidal in intensity, with a "DC offset" from zero), whose variations propagate at the speed of light. This sounds pretty wave-like to me. Why isn't it? Is there perhaps a reason that it can't transmit energy?
A very similar question has already been asked, but it used a "rope" analogy, and I feel that the answers overlooked the point that I'm making.
Best Answer
I think this is partly a question of vocabulary, and partly a reflection of the fact that the longitudinal Coulomb oscillations you describe fall off so rapidly with distance. (Basically $1/r^2$ instead of $1/r$.) Therefore they are usually called "near field effects" and are totally dominated by the transverse "waves" after a distance of only a very few wavelengths. Nevertheless, they do exist, even in a vacuum, and they do extend to infinity, just very, very weakly.