That's a nice explanation but doesn't it give the impression that if we could find a better way to do that experiment, we could find a way around the problem, when instead it's a fundamental limit on what we can know about a quantum system?
That observational uncertainty increases as the probability of direct interaction decreases (distance, time) strongly supports the hypothesis that observable phenomena are dictated strongly by the presentation and characteristic relationship of the observer to the phenomenon.
We know on the micro scale that all possible states exist simultaneously.
It seems logical, even axiomatic then that on the macro scale the same applies, but that we can only observe the bandwidth of states in which it is possible for us to exist to make the observation.
To claim that this state uncertainty is magically resolved in all cases and coherently for all possible observers into a single set of states seems an extraordinary claim requiring extraordinary evidence.
Post measurement particle is description of our ignorance not a description of reality.
It still evolves according to Schrödinger equation (which degrades to newtonian dynamics for sharp and narrow waves) but for historical reasons we choose to talk about it as it was little billiard ball, not still a wave just sharpened and narrowed down by intraction we call measurement.
The suggestion that if one pushes away something by throwing something else builds on a purely classical intuition and wouldn't require quantum mechanics to explain if this was all we observed. The uncertainty in quantum mechanics is fundamental (to quantum mechanics) and emerges through a different, as yet unknown, mechanism.
> emerges through a different, as yet unknown, mechanism.
In 3Blue1Bron's explanation[1], he shows how the intrinsic uncertainty is an inherent trade-off of trying to measure both position and frequency. A short wave packet only a few wavelengths long correlates with a narrow (precise) range of positions, but also correlates well with a very wide range of frequencies due. A Heisenberg-like uncertainty exists any time you are working with weave packets with length near the wavelength. 3Blue1Brown gives a very good example using Doppler radar.
When I suggest the mechanism is unknown, I mean that Heisenberg uncertainty is a postulate of quantum mechanics. In other words the fundamental reason that quantum mechanics should appeal to wave mechanics isn't really established - we don't really know yet the fundamental objects and interactions that lead to quantum mechanics (despite much effort).
Moreover, similar calculations can be done with other measurements that don't conmute. One that is very important is the spin of a particle in the x, y, and z axis.
Another is the polarization of a photon in directions that are at 45°. For example, most of (all?) the experiments of the EPR paradox are done with polarization instead of position-momentum, because polarization is much easier to measure. https://en.wikipedia.org/wiki/EPR_paradox