How did light speed become the governor of relativity?

[D H]

How do Maxwell's equations shout out that the one-way speed of light is the same to all observers?

Yes, if you know how to listen. All you have to do is cast them in the form of the wave equation.

It is my understanding that Maxwell used his equations to derive a solution with a wave speed equal to the speed of light which led him to suggest that the propagation of light relative to the absolute rest state of the ether could be determined by a suitable experiment with enough precision, so he obviously missed the shouting coming from his own equations that the speed of light is the same to all observers.

Maxwell was listening to too much shouting coming from elsewhere, "All wave phenomena require a medium. Everyone knows that!" and "The universe obeys Galilean invariance. Everyone knows that!", to hear the shouting from his own equations. One last bit of shouting is that physicists at Maxwell's time much preferred dynamics over kinematics. Special relativity is very much a kinematics theory.

For Maxwell to have derived special relativity he would have had to ignore all that shouting from elsewhere. Physicists in the latter part of the 19th century thought they were on the verge of a complete dynamical description of the universe. Ignoring the "Everyone knows that" type of shouting and back-stepping to a mere kinematics description was too much for the physicists of Maxwell's time, including Maxwell himself.

But in hindsight, it is still conceivable that Maxwell could have done this. He could have, for example, looked at just how ludicrous his concept of a luminiferous aether truly was (a non-solid that somehow supports transverse waves and somehow doesn't interact with ordinary matter) and saw how it was contradicted by the known phenomena of the aberration of light.

 

[ghwellsjr]

But in hindsight, it is still conceivable that Maxwell could have done this. He could have, for example, looked at just how ludicrous his concept of a luminiferous aether truly was (a non-solid that somehow supports transverse waves and somehow doesn't interact with ordinary matter) and saw how it was contradicted by the known phenomena of the aberration of light.

Yes, it is conceivable that Maxwell could have derived special relativity, if he hadn't died at such a young age, but he needed more than his equations. He needed Einstein's second postulate, which is not derivable from his equations, they were already covered in Einstein's first postulate and fully compatible with Lorentz's Ether Theory. That's my only point.