Is the Uncertainty Principle strictly a consequence of wave-particle duality, or does it arise independently, even in the absence of such duality?*
[sub][sup]*this question could have been placed in this thread on quantum uncertainty, but I was afraid it might be missed there[/sup][/sub]
After reading your post, my principle feeling is uncertainty… and I thought I knew something about Heisenberg!
Show me a universe that doesn’t have wave-particle duality, and I’ll answer that question. Short of that, there’s really no way to know. In the quantum mechanics we know, it’s shown to follow from duality, but then, in our universe, we have duality, so it all works out.
In modern QM it arises as a consequence of the wave nature of particles. More correctly, the quantum field nature of particles. That is, it is not a separate hypothesis, but a result of the mathematical structure of the theory.