Locally, the physics of collision are time-symmetric; if you observe a movie of a collision between just two balls, you cannot tell if the movie is being played forwards or backwards in time.
However, when you look at a movie of the whole simulation, you can easily identify the direction of time's arrow.
I haven't read Drescher's book, but this sounds like the usual Boltzmann-style attempt to explain the arrow of time by starting in a low-entropy state. When you start with many small balls, all moving at similar (because small) velocities, you are in a low entropy state. As the clock advances, you wander from this highly atypical low-entropy region of configuration space into more typical high-entropy regions. This is what gives you all sorts of time-arrows, such as the tracks left by the big balls.
The problem with using this as a global arrow of time is that, if you run the simulation backwards from the initial low-entropy state, you will again almost surely wander into a high-entropy state. From the point in time when entropy is minimized, both directions in time will look like futures (almost surely).
Imagine that you start with a big 2D box. Assume that all collisions are elastic. In the initial configuration, the box is evenly filled with a bunch of nearly-stationary little balls, and one big ball with large initial velocity. As you run the simulation forwards, you'll see the big ball clear out a path behind itself as it moves through the little balls, just as you said.
But now run the simulation backwards from that same initial configuration. You'll see exactly the same time-arrow-indicating phenomena as the simulation runs backwards. Only now, the time-arrows will be pointing into the past (towards which the simulation is running).
After running the simulation backwards for a while, stop, and rerun the simulation forwards from that time in the past. It will seem uncanny as the balls arrange themselves just so, but something strange had to happen for the balls to end up in the wildly improbable initial configuration with which we began.
Drescher actually deals with this — from an initial configuration, positive or negative movement both work as time arrows; time can be measured as distance in accumulated correlation from that initial state in any particular direction. At zero, moving along the positive or negative direction is equally "forward in time"; but at +42, it isn't.
Related to: lesswrong.com/lw/qp/timeless_physics/
Why do I find myself at this point in
time, configuration space, rather than another point? In other words, why do I have certain expectations rather than others?I don't expect the U.S. presidential elections to have happened but to happen next, where "to happen" and "to have happened" internally marks the sequential order of steps indexed by consecutive timestamps. But why do I find myself to have that particular expectation rather than any other, what is it that does privilege this point?
My question is why I find myself to remember that the particle went left and then right rather than left but not yet right?
Yes, but why does my version experience this point of my branch and not any other point of my branch?
I understand that if this universe was a giant simulation and that if it was to halt and then resume, after some indexical measure of causal steps used by those outside of it, then I wouldn't notice it. Therefore if you remove the notion of an outside world there ceases to be any measure of how many causal steps it took until I continued my relational measure of progression.
But that's not my question. Assume for a moment that my consciousness experience is not a causal continuum but a discrete sequence of causal steps from 1, 2, 3, ... to N where N marks this point. Why do I find myself at N rather than 10 or N+1?