In solid state physics there is a concept called Phonons, which are vibrations in a solid (such as a solid crystal).

These are described as "quantized sound waves". They have particle-like qualities (similar to Bosons), and show the same particle/wave duality as real particles do - except of course in this case, these are 100% waves. They are even described using QM formulas. I also find it interesting that the quantization of these sound particles even shows when the crystal lattice is not discrete.

Phonon - Wikipedia, the free encyclopedia
Why do I bring this up?
Because I recently read a book called "Classical Wave Theory of Matter" at Verum Versa, and the concept there is that all of QM and relativity can be derived by this simple premise: that space is an "elastic solid" and that light/matter are vibrations in it (pure waves). Robert Close derives a special relativity and the Dirac equation (and more) based on that (relativity applies to any kind of wave actually - so it applies to Phonons as well).
Illustrative example of how SR can be derived from waves can be found here: Underwater Relativity

I could find no contradiction with any experiment (it is consistent with the null result of MM, for instance), or with any mathematical formula (it uses the exact same mathematics - so it is also consisten with the tensor of GR, for instance ).

I would very much like to discuss the book with someone who is interested!

Chantal