general relativity - Two "devil's advocate" questions related to LIGO measurement results interpretation

"If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things."

Rene Descartes

Laymen like me typically refers to Wikipedia for basic definitions ...

"In physics, spacetime is any mathematical model that combines space and time into a single interwoven continuum."

http://en.wikipedia.org/wiki/Spacetime

"Gravitational waves are radiant energy produced in certain gravitational interactions. They are ripples in the curvature of spacetime that propagate as waves, travelling outward from the source."

http://en.wikipedia.org/wiki/Gravitational_wave#Effects_of_passing

and from the same source

"As a gravitational wave passes an observer, that observer will find spacetime distorted by the effects of strain. Distances between objects increase and decrease rhythmically as the wave passes, at a frequency corresponding to that of the wave."

Why it is assumed above that it is particular distance component (in its three dimensional space sense) of the spacetime continuum and not the time component of the spacetime continuum - which is changing under the effect of gravitational wave passage?

Let me push my question's logic further in very non-orthodox and ignorant manner and also ask, playing the role of "devil's advocate" (while risking to be accused in lack of confidence in basic concepts of General Relativity):

why one can not interprete the measurement results during LIGO detection, as a manifest of speed of light variations (versus considering the speed of light being absolutely invariant under any possible circumstances, such as the case of gravitational wave passage)?

Answer

A gravitational wave has a polarization. So when one direction transverse to the wave is expanded, the other direction transverse to the wave is contracted. Thus if you try to explain the expansion and contraction as a naïve consequence of time expansion or of time contraction then you'd have a hard time making that effect cause both an expansion and a contraction in two different directions at the same time and place.

Now I'm sure some people would prefer to have a coordinate speed of light that is different in different directions. But coordinate speeds aren't physical so that's just a model effect not a physical effect. You can do General Relativity and make your predictions without even picking any coordinates, ever. So they aren't part of physical reality, just part of how some people manipulate some mathematical models.

In reality the metric determines the lengths along 4d paths and that tells us how (where and when) clocks tick and how (where and when) tape measures have their marks. Which is what we actually see.