It would seem that the answer should be negative. However, if you think about it, the answer is not so obvious. Indeed, it is enough to take the vector field of accelerations (velocities) of particles as ether and we will get a mathematical definition of moving matter. Another question is where and how it moves this matter and why we do not see it, but this question may already have an answer1. Matter moves on the surface of the seven-dimensional sphere, and it is invisible because we move with it.

1)

Preprint Математические заметки о природе вещей