Placing this in a comment in case someone else is interested in some other aspect, but I am confused by this time-reversal point. Yes, the equation can go in ei

Placing this in a comment in case someone else is interested in some other aspect, but I am confused by this time-reversal point. Yes, the equation can go in either direction but time itself -- as we understand it -- goes in one direction, basically divided by our memory. So why not just stipulate that the equation is one directional, and there is another (inverse, but otherwise identical) equation for the reverse process?