As far as I know, exchanges of momentum between colliding systems are permitted, provided they conserve vector momentum. This suggests multiplicity of outcome, since there are an infinite number of exchanges of momentum between, for example, two colliding particles, that will conserve momentum. I happen to quantize basically everything in my model of physics, but it doesn’t matter, because you still get multiplicity of outcome, albeit finite in number. Note that a wave can be thought of as a set of individual, interacting frequencies, that together produce a single composite system. I’m not an expert on the matter, and I’m just starting to look into these things, but I don’t believe there’s any meaningful multiplicity to the outcome of a set of juxtaposed frequencies, and instead, I believe you end up with the same wave every time. This would make perfect sense if the quantity of momentum possessed by a wave is incapable of subdivision, which would either produce an interaction or not, between two individual waves. You could, for example, have wave interference, at offsetting points of two waves, each possessing equal quantity, in opposite directions, when and where they interact, producing a zero height at each such point. As the probability of interaction increases, you’d have an increasingly uniform zero wave.

Interestingly, this suggests the possibility that rules of physics actually have complexity, in the sense that you might have primitive rules for some interactions that impose what is in this case binary quantization (i.e., either it happens or it doesn’t). This is alluded to in Section 1.4 of the first link above, where I discuss the applications of the Kolmogorov Complexity to physical systems.

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