What is the assumption that c is the universal speed limit based on (other than relativity math)?
In the last paragraph of the first section, of his 1905 paper,
ON THE ELECTRODYNAMICS OF MOVING BODIES, Einstein is be quoted,
"In agreement with experience we further assume the quantity $$\frac{2AB}{t'_A - t_A} = c$$ to be a universal constant--the velocity of light in empty space."
From what I have read of the historical perspective, the experience that Einstein was referring to was the work of Fizeau, measuring the velocity of light in a variety of ways and in a variety of mediums.., air, liquid and vacuum, and Maxwell's work on electromagnetism, which also predicted $$c$$ as a constant velocity for electromagnetic waves.
Extending those experimental results and experience — to the status of a universal constant, became one of the foundations of the theory of special relative, first published in that paper, where the laws of physics are shown to be the same for all inertial observers... All observers who are moving with a constant velocity relative to one another, measure the velocity of light to be the same, reguardless of thier own velocity relative to the source of the light.
This holds for the flat spacetime of special relativity, but becomes somewhat more complicated within the context of general relativity where the curvature of space involves both length and time dilations due to an observer's location within a gravitational field.
Where the luminiferous aether and the Michelson and Morley experiments are concerned, it is commonly assumed today that Micheson and Morley proved the aether did not exist. This is not entirely accurate. Their experiments and those that have followed have continually returned what are called "null" results, meaning that they were unable to detect an ether medium. This is not quite the same as proving that the ether does not exist.
The luminiferous aether itself, has been dismissed as a valid approximation of experience, primarily because it is inconsistent with the theories of special and general relativity, both of which have been very successful descriptions of the world. The aether of the 1800s was a fixed and static medium, closely associated with the ridgedly defined space of Newtonian dynamics. With the introduction of the theories of special and general relativity Einstein showed that space was not fixed and static. Instead it became a dynamic counter part to matter. The ridgedly fix ether was and is inconsistent with a dynamic space/spacetime. Einstein's SR and GR are more accurate and successful descriptions of what we know now of physics and the universe, than the ideas of Newton that they replaced.
The curved spacetime of general relativity replaced the ether of the 1800s.
