Cyan - Here’s how I see it. Your toy world in effect does not move. You’ve defined the law so that everything shifts left. But from the point of view of the objects themselves, there is no motion, because motion is relative (recall that in our own world, motion is relative; every moving object has its own rest frame). Considered from the inside, your world is equivalent to [0,1] where x(t) = x_0. Your world is furthermore mappable one-to-one in a wide variety of ways to intervals. You can map the left half to itself (i.e., [0,.5]) and map the right half to [.5,5000] without changing the rule of x(t) = x_0. In short, it has no intrinsic geometry.
Since it has no intrinsic geometry, there is no question of applying probability to it. Which is okay, because nothing happens in it. The probability of nothing hardly matters.
Cyan - Here’s how I see it. Your toy world in effect does not move. You’ve defined the law so that everything shifts left. But from the point of view of the objects themselves, there is no motion, because motion is relative (recall that in our own world, motion is relative; every moving object has its own rest frame). Considered from the inside, your world is equivalent to [0,1] where x(t) = x_0. Your world is furthermore mappable one-to-one in a wide variety of ways to intervals. You can map the left half to itself (i.e., [0,.5]) and map the right half to [.5,5000] without changing the rule of x(t) = x_0. In short, it has no intrinsic geometry.
Since it has no intrinsic geometry, there is no question of applying probability to it. Which is okay, because nothing happens in it. The probability of nothing hardly matters.