# Which is more fundamental,''constancy of speed of light'' or ''space-time''? [closed]

My friend asked me,''which is more basic or fundamental? constancy of speed of light which makes space-time behave dynamically OR dynamical behavior of space-time that makes light to travel with constant speed? I think 1st one because space-time is just a human-created model...''?

I answered ,''space-time is more fundamental ,because speed of light is constant only locally,where space-time can be taken as flat ,so constancy of speed of light is a property of space-time ,so space-time is more fundamental(?).''

he replied,''speed of light is always constant ,its only different in different coordinate system''.

So what should be the correct ans?

$$ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2$$
and this is fundamental in the sense that all of special relativity is described by this equation. But it is also fundamental that the parameter $c$ in the equation (which is of course the speed of light) is a constant. So you can't say the geometry is more fundamental than the constancy of the speed of light or vice versa.
I'm not a big fan of science fiction, but the SciFi author Greg Egan in his "Orthogonal" series does a most wonderful job of exploring one such universe, where the manifold is not locally Lorentzian (i.e. all inertial observers measure $c$ to be the same) but Euclidean. The physics in such a universe is very weird indeed, and Egan gives a primer to Orthogonal on his website here where he compares how simple physical principles would change.