Why does time only run in one direction?

We all are familiar with the Arrow of Time. Even those who have never studied time as a concept in physics would find it quite strange if one day they found themselves walking backwards on a street, and as they backed past the china shop, they noted that a bull was backing around in it. As the bull backed up, various shards of china would fly from here and there to assemble themselves into complete tea kettles and cups, then bound from the floor back onto the shelves as perfect tea sets and other assorted pottery.

Finally, the china shop now orderly, the bull would emerge from the broken glass of the china shop door, butt-first of course, and as his horns cleared the opening broken shards of glass would fly up from the china shop floor and the sidewalk outside, and assemble themselves into an unbroken pane of glass in the door.

Any of us, no matter what our scientific training, would think we had either gone quite insane, or somehow fallen into a movie running in reverse. Outfielders simply don’t catch a pop-up fly before the batter swings at the ball.

And yet there is nothing about Newtonian mechanics or quantum mechanics that doesn’t work just as well when calculated backwards in time as forwards. If you know the conditions now, you can calculate previous states just as easily as you can future states. So if the laws of physics describe how the world we live in works, why is there an Arrow of Time?