Analogy..wave equation for stretched string..
y''=c^2*L(y).. L=laplacian op=d2/dx^2 in one dimension..y=displacement..c=speed..propnl to tension/linear density ..ie props of medium
Maxwell's equations.. (all the stuff about Gauss' law, Faraday's Laws and Amperes circuital theorem put in maths terms!)
CurlE=-dB/dt (faraday)
CurlB=uo*e0*dE/dt (ampere law)
Curl(curlE)=-d/dt(curlB)= -uo*eo*d2E/dt^2
Now Curl(curlE)=div(div.E)-div^2(E)
div(divE)=0 from Gauss Equn
>-uo*eo*d2E/dt^2=-div^2(E)=-L(E) (where L=laplacian)
>d2E/dt^2=L(E)/(uo*eo)
If we compare this with our string equation..then 1/rt(uo*eo) corresponds to wave speed, where uo=mag permeability and eo= permittivity of free space..or the respective 'coupling consts' for the mag and electric fields resp.
A similar equation gives the variation of the B-field as it travels in free space.
So the speed of light in a vacuum is constrained by these constants in the same way as the speed of waves in a string are determined by its properties of tension, density.
Naturally light travels slower in a refractive medium and particles can exceed the speed of light in glass or a semiconductor medium. In an other universe with diff initial conditions light speed may well have a different value.
Last bit..although material particles cannot REACH the speed of light, there is nothing in physics to disallow particles with imaginary mass travelling faster..just as Absolute zero cannot be achieved..but states with negative absolute temperatures can be 'prepared'