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Uncertainty is definitely not handwaving. I think JP was saying (and apologies if I am wrong) that the simple particle being hit by an energetic particle to determine position - The Heisenberg Microscope - description of uncertainty is handwaving.

The uncertainty principle itself is rigorous.

The uncertainty principle is not just hand waving. If you use electromagnetic radiation (light) to measure the position or velocity of a particle the change in position of momentum coincides with the errors introduced by the interaction with the light quantum. The energy in light quanta can be proved and measured using completely classical physics and requires no weird quantum effects.

Uncertainty is definitely not handwaving. I think JP was saying (and apologies if I am wrong) that the simple particle being hit by an energetic particle to determine position - The Heisenberg Microscope - description of uncertainty is handwaving. The reduction of a quantum mechanical effect to a classical simile is a great way of understanding it, and an extremely good approximation but is incomplete. Uncertainty arises due to the non-commutative nature of important matrices in quantum mechanics (originally the infinite matrices describing momentum and position) - Newtonian/Classical observables commute, but in general the matrices/observables in qm do not commute.