Wouldn't it make much more sense to approach a GUT theory using space-entropy, not space-time?

It seems to me that physicists have been scratching their heads ever since Einstein proved that, what they had thought to be the strait-and-constant arrow of time, could actually be made to wobble, curve, and even disappear. Even more troubling, was the small scale, temporal fustercluck realized with the advent of quantum mechanics. In the relativistic universe, where time pes at different rates in different places, suddenly any conceptualization of what the universe looks like "right now" becomes meaningless. Time can speed up or slow down, and these perturbations in time can propagate through space. There are even places in the of the universe (ie a singularity) where temporal direction stops/reverses or who knows what? My point is that, for some reason we seem to be stuck in our umption that time is so intrinsic and fundamental to the geometry of the universe, that after the three spacial dimensions, we regularly use time as 4th. There is only one known phenomenon that is universally and temporally directional: entropy. My intuition tells me that entropy makes more sense to use as a 4th dimensional vector than time; even black holes obey entropy emitting Hawking radiation. I say, time makes a lot more sense if we just let it be a less interesting byproduct of other forces: Temporal gradient is somehow integrally tied up in the flux of light through space (which can later be simplified in terms of entropy) bound by gravity. Isn't that already simpler? What do y'all think? And if you've read this far, you really ought to post an answer regardless the state of your quantum background (pun...dont worry it was bad anyway...), since I really would like to hear what people think.