Which is more fundamental,''constancy of speed of light'' or ''space-time''? 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?
 A: It is an artificial distinction to say one is more fundamental than the other. The geometry of flat spacetime is given by the Minkowski metric:
$$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$
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.
This applies to general relativity as well, because even when spacetime is curved the local spacetime geometry is approximately flat.
A: Which is more fundamental is probably a meaningless question, but you can think of the geometric notion of a manifold (the mathematical abstraction of spacetime) as being more general than Lorentzian manifolds, i.e. ones whose metric is locally like that given in John Rennie's Answer. So one could in principle conceive of universes that were described by non-Lorentzian manifolds or even by more general geometric objects than manifolds, such as varieties. But the constancy of the speed of light encodes what I would call essential symmetries of our particular universe as I discuss in my answers here and here. I would call these are essential symmetries because a universe without them would be radically different from ours: possible lack of causality is one striking possibility. 
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.
