The kids and I watched the old Time Machine movie the other night, and it's shortly after the announcement that gravity waves have been really detected at the LIGO thing and it has physics and time rolling around in the back of my head here. But this post is for record keeping more than anything else, don't expect fully formed thoughts or cogent arguments...you'll be lucky if I spell check.
Imagine you're standing on the deck of a cruise ship along with all the chairs and toys and several other people. Now the ship starts to list just a little to port. Some items on that deck, like the bottle of sun tan oil that's on its side, will start to roll toward what is now effectively "downhill." As the ship lists more and more each object and each person will feel the gravitational pull toward the port rail. Some are more stable than others, some are bolted to the deck. What if the "arrow of time" is a little like that? What if, not unlike Einstein's insight that gravity is best understood as the geometry of warped space, that time is also "geometric" in that it reflects the fact that our universe lists toward the future? In such a world then moving toward the future is simply the path of least resistance like a ball rolling downhill.
If that deck on the ship has just a few people on it then a determined man might plant his feet and stand still - fighting the portward pull. If the deck is crowded shoulder to shoulder with people then the downward pressure of all the "uphill" people would make such a choice harder and harder, he'd be carried along with the falling crowd. In that case, the way we try to walk across a river might be a better picture. When the water is slow, or only to our ankles, we find ourselves fully capable of fording it. But as it deepens or goes faster the downhill energy of the river is transferred to us and we get swept away. If the whole universe is heading downstream and the constant collisions of atoms and subatomic particles pushes us with it then it would suggest going with the flow would take less energy than going against it.
How is it that motion in the three normal directions is linked to the speed of time? If I can say that going faster slows time down I can also say that going slower speeds time up. How can motion/speed be linked to time?
What if entropy isn't a result of time but the other way around? What if it is the regular degradation of order that creates the slope of the ships deck?