Ok, but it's not clear to me that your "energy" is now describing the same thing that is meant in our universe. Suppose everything in Randomverse stood still for a moment, and then the electric coupling constant changed; clearly the potential energy changes. So it does not seem to me that Randomverse has conservation of energy.
Hmmm... yes, totally freely randomly won't work. All right. If I can go classical I can do it.
You have some ensemble of particles and each pair maintains a stack recording a partial history of their interactions, kept in terms of distance of separation (with the bottom of the stack being at infinite separation). Whenever two particles approach each other, they push the force they experienced as they approached onto the pair's stack; the derivative of this force is subject to random fluctuations. When two particles recede, they pop the force off the stack. ...
This is a thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. The previous thread is at close to 500 comments.