Can you derive the speed of light from fundamental weak force or gravitational constants?
No. In natural units, c and G are usually just taken as 1. And the weak coupling constant is a fundamental parameter of the standard model. c really shouldn’t be thought of in terms of light or electical and magnetic properties of the vacuum. It is the conversion factor between our units of space and time. Form this, you can show that the product of permissivity and permittivity has to be c^2. And any massless particle has to travel at a speed of c. Neutrinos appear to be not quite massless, so they probably travel at speeds just under c. Photons and gravitons are (as best we can tell) massless, so they travel at c.
