In ancient times whether or not the aether exists depended on whether light was considered a wave or to consist of particles. With the Renaisance the question raised itself again. DesCartes and Newton thought of it in terms of particles. Interference phenomena led Huygens develop a wave theory of light. But Maxwell showed that electromagnetism was consistent with the aether being an imcompressible fluid. If the aether was a fliud its density was a constant. This suggested that the aether had a connection with space itself. The Michelson-Morley experiment supported this view.
Wolfgang Pauli stated this in his Theory of Relativity (1958). (Translated from Encyclopdädie der mathematischen Wissenschaften, Vol. V19, 1921.):
"Once the postulate of relativity is stated, the concept of the aether as a substance is thereby removed from the physical theories. For there is no point in discussing a state of rest or of motion relative to the aether when these quantities cannot, in principle, be observed experimentally. Nowadays this is all the less surprising as attempts to derive the elastic properties of matter from electrical forces are beginning to show success. It would therefore be quite inconsistent to try, in turn, to explain electromagnetic phenomena in terms of the elastic properties of some hypothetical medium. Actually, the mechanistic concept of an aether had already come to be superfluous and something of a hindrance when the elastic-solid theory of light was superseded by the electromagnetic theory of light. In this latter the aether subatance had always remained a foreign element. Einstein has recently suggested an extension of the notion of an aether. It should no longer be regarded as a substance but simply as the totality of those physical quanties which are to be associated with matter-free space. In this wider sense there does, of course, exist an aether; only one has to bear in mind that it does not possess any mechanical properties. In other words, the physical quantities of matter-free space have no space coordinates or velocities associated with them."
Quantum Mechanics fudges the question of whether or not light is particle or wave. It is somewhat at odds with Maxwell's electromagnetism. Photons behave like waves with discrete energy and as a result display aspects of both. They are created and annihilated as electrons change state. They can also scatter off electrons. And electrons do not continuously emit radiation as they are accelerated about a nucleus.
One thing that still bothers me about the above is that if one subtracts all the matter from a given region of space is there a remainder? Have we missed something?