“a simple test is to think about what direction gravity is going. if it has a direction there is also a space distortion, because there is no physical direction for time.”
It seems that way in 3 dimensions, but does that hold true in 4 dimensional spacetime? An asteroid that passes into the gravitational field of a star was traveling on a straight line geodesic before it came under the star’s influence and it is still traveling on that same straight line geodesic after it came under the stars’ influence. So where is the “direction” of gravity now?
I didn’t come up with this idea myself, so I may not be doing it proper justice. I actually cribbed it from Einstein, from one of the newspaper articles he wrote where he mentioned that he thought the interpretation of “space” itself being distorted in reality was a mistake, kind of as an offhand comment. Well, if spacetime is only composed of space and time, and the space isn’t being distorted, that would seem to leave time as the only possibility for what is being distorted.