Mentioned in Jackson's Electrodynamics in a section title "Elementary treatment of electrostatics with ponderable media".

I googled for this word and get a paragraph of Einstein:

Recapitulating: we may say that according to the general
theory of relativity space is endowed with physical
qualities; in this sense, therefore, there exists ether.
According to the general theory of relativity space
without ether is unthinkable; for in such space there not
only would be no propagation of light, but also no
possibility of existence for standards of measuring rods
and clocks, nor therefore any space-time intervals in the
physical sense. But this ether may not be thought of as
endowed with the quality characteristic of ponderable
media, as consisting of parts which may be tracked
through time. The idea of motion may not be applied to it.

Have this anyting to do with the one in Jackson's book?
What's exactly the meaning of "ponderable media"?

Thanks!

The word "ponderable" is very old-fashioned. It means "weighable" literally. To "ponder" something is to weigh it in your mind. The English word "pound" as a unit of weight comes from this root word. "Ponderous" means "heavy."

The specifically physical meaning is that the medium carrying the waves has mass. An "imponderable" medium would have no mass. In the case of sound waves, the waves are carried by motions of molecules of air, which have mass, and so sound is carried by a ponderable medium. Electromagnetic waves can travel through the vacuum, which of course has no mass, so they have an imponderable medium. Actually, it is rather strange to call it a medium at all; this is a leftover from the old aether theory, from the days when it was commonly believed that there must be something that carried light the way air carries sound. The physical properties of this "aether" were very strange (planets must pass through it without resistance, yet it must be many times stiffer than steel in order to carry waves so rapidly). The aether also provided a reference frame for light, which is incompatible with the Michelson-Morely experiment and Special Relativity, which is the primary reason that it was dropped from mainstream physics.

Why is it important whether the medium is ponderable or imponderable? Because the presence of mass means that mechanical modes of vibration will be present, in addition to the electromagnetic ones. Electromagnetic waves are already a vibration just by themselves, and if there is some material with mass moving too, the picture is much more complicated. (In the case of sound, these mechanical vibrations ARE the wave, so there is no confusion.) Recall that vibration always requires TWO energy reservoirs (usually kinetic and potential) because energy needs to shift back and forth between them during the vibration. If electromagnetic waves are traveling through a medium without mass (imponderable) then there is no kinetic energy reservoir and no mechanical vibration can take place.

If there IS mass, and if the electromagnetic fields exert force on it, then the field vibrations will induce mechanical vibrations. The only way that the fields can exert force is if the masses are charged, but that means that when the masses vibrate, their charges will also vibrate, which will cause them to emit a secondary EM wave. Therefore, the EM vibration and mechanical vibration can pass energy between them, and affect each other's amplitude and frequency. The vibrations are said to be "coupled." Mechanical vibrations are usually much slower than electrical ones, so the coupling slows down the EM vibrations, affects the speed of light, and so on.

The basic ponderable medium is the plasma. In a plasma, there are free electrons and ions, which have both charge and mass, so EM waves passing through a plasma will cause the plasma to oscillate, and these oscillations will in turn affect the EM wave. These are called plasma oscillations or plasma modes.

Hope this helps!

--Stuart Anderson