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.
Viewed from a very local level (encompassing just a single collision), there’s no arrow of time, because entropy doesn’t change significantly.
Taking a middle-level view (encompassing more balls for a greater span of time), there’s a unique time arrow as you pass from the low-entropy initial configuration to a higher one.
But taking a global view, encompassing all balls for all time, you lose the unique arrow of time again, because you are just as likely to leave low-entropy states as time runs “backwards” as you are when time runs “forwards”.
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.
Oh, okay. Then Drescher has it right:
Viewed from a very local level (encompassing just a single collision), there’s no arrow of time, because entropy doesn’t change significantly.
Taking a middle-level view (encompassing more balls for a greater span of time), there’s a unique time arrow as you pass from the low-entropy initial configuration to a higher one.
But taking a global view, encompassing all balls for all time, you lose the unique arrow of time again, because you are just as likely to leave low-entropy states as time runs “backwards” as you are when time runs “forwards”.