Your example completely breaks the restrictions I gave it. The whole idea of pushing and popping is that going out is exactly the same as the last time they went in.
Oh, I see. The coefficients are only allowed to change randomly if the particles are approaching. I misunderstood your scenario. I do note that this is some immensely complex physics, with a different set of constants for every pair of particles!
Edit to add: Also, since whether two particles are going towards each other or away from each other can depend on the frame of reference, you again lose whatever conservation it is that is associated with invariance under boosts.
If you hold those to be the same, you completely reconstruct our physics and of course there’s no room for randomness.
Right. The original question was, are there any conservation laws you can knock out without losing determinism? It seems conservation of whatever-goes-with-boosts is one of them.
Oh, I see. The coefficients are only allowed to change randomly if the particles are approaching. I misunderstood your scenario. I do note that this is some immensely complex physics, with a different set of constants for every pair of particles!
Edit to add: Also, since whether two particles are going towards each other or away from each other can depend on the frame of reference, you again lose whatever conservation it is that is associated with invariance under boosts.
Right. The original question was, are there any conservation laws you can knock out without losing determinism? It seems conservation of whatever-goes-with-boosts is one of them.