My question is about the relations and equations that makes us to impose constraints on the velocity at which electromagnetic waves propagate.
Do Maxwell's equations independently impose constraints on the speed of EM waves?
Are these equations compatible with the two special relativity principles with no need to consider some constraints?
Does exceeding the limitation for speed of light violate the implications of Maxwell's equations?
Does considering unequal constant values of velocity of light for different inertial references violate what Maxwell's equations imply?
Who imposed such a limitation theoretically at first? What motivated him/her to suppose there is a limitation for the group velocity of electromagnetic waves?
We know Lorentz transformations are constructed on the assumption of constant speed of light in moving frames. What made him consider such an assumption, if Einstein was not the first one to consider the second postulate of special relativity (i.e. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light)?
Added:
Einstein assumed "constancy of the speed of light for all observers of all moving frames" to derive and use his "Lorentz transformation" like transformation! Then he constructed his special theory of relativity based on two principles which we all heard about. Did I get this right?
Considering the transformation for a moving frame along the $x$ axis for a frame moving at the speed of $v$ you get $${x_2} = {{{x_1} - {v_1}{t_1}} \over {\sqrt {1 - {{({v \over c})}^2}} }}.$$ This transformation mathematically implies that no frame is allowed to move at a speed higher than $c$. So this assumption puts some constraints on the speed of any moving frame too!
Summing all these up, say:
A) "the maximum speed of light has an upper bound which is called $c$"
B) "nothing travels faster than light"
C) "the speed of light is measured to be the same by all observers"
From those, some questions arise:
Considering the definition of a frame and the observer which could be at a quite arbitrary conditions of velocity and so on, what motivated him to accept such a limitation for the speed of frames? I mean such a precise assumption can't come from nowhere! Particularly when its consequences seems unbelievable!
Why light? How was he so sure that nothing else could be faster than light? Was there any evidence of light being the fastest thing ever exists?
Where does the role of Maxwell's equations rise up in the creation story of this assumption?
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