These deeper mysteries are simply taken for granted as a base level upon which to build extended theory, and so the same approach should ideally be taken as regards the finer level of matter which pervades all of space and serves as the medium for the propagation of light. We should be able to make some headway in identifying the structure in question in terms of knowns, without needing to know everything. Unfortunately, in practice, it doesn't work like this. For example, should it be proposed that electrons are involved in the structure of the luminiferous medium, this is likely to be imediately challenged on the grounds that we don't know what an electron actually is. But we don't necessarily need to know. Unfortunately,  when it comes to the medium for the propagation of light, the deeply ingrained attitude seems to be that unless the theory provides the answer to everything, then it tells us nothing at all, and so must be rejected out of hand. Modern physicists are prepared to accept the absurd idea that wireless electromagnetic radiation constitutes waves of electric and magnetic fields propagating through space, yet without any source charges or source electric currents to justify the existence of these fields in the first place. The concept described by Tesla will typically be dismissed out of hand, simply because no explanation can be given for the structure of the fluid-like aether in terms of knowns. The article in the link here deals with this topic and shows how Tesla's concept of space fits exactly with Maxwell's equations, and is therefore almost certainly correct.