How do time and space dilation work together to ensure the constant speed of light?

D H

I prefer to look at it the other way around: Time dilation and length contraction are a necessary consequence of the constancy of the speed of light. Taking time dilation and length contraction as axiomatic is bit too ad hoc for my tastes.

Starting with some very basic concepts of continuity dictates that some speed must be the same to all observers. You get Newtonian mechanics if this universally agreed-upon speed is infinite. You get a Lorentz manifold if this universally agreed-upon speed is finite. Maxwell's equations and multiple experiments indicate that this universally agreed-upon speed is finite and is in fact the speed of light.