I'm trying to understand the Heisenberg Uncertainty Principle, as it relates to experimental measurements, because it's kind of confusing me. We just learned the derivations for it in my QM class -- basically it's two standard deviations multiplied together (corresponding to measurements of incompatible observables). Before I explain what I'm asking, I want to be clear that I'm not trying to understand it from a "philosophical" angle, i.e. Copenhagen interpretation. I'm just trying to understand the aspects of QM as they relate to physical measurements. So the usual soundbite is "The Heisenberg Uncertainty Principle says that the more accurately momentum or position is know, the less accurately the other one may be known". Another favorite is "Even with a perfect measuring device, there is still an inherent uncertainty in knowing both the position and momentum of a particle". These statements are meaningless to me, and they sort of gloss over a good physical explanation. I view them as cop outs -- like saying "Well, I don't really understand HUP, but I'm just going to repeat something everyone else says that sounds fancy and scientific so I still appear as if I know what I'm talking about". Let's consider a hypothetical situation in which humans have perfected particle detectors down to Planck scale. And let's assume these detectors record data to a trillion significant digits. The detector is a big slab of some material, and when a particle hits it, it registers the particle's position on the slab, and the momentum as it strikes. So what exactly does the operator of this detector see on their computer screen? Will it show two numbers, each with a trillion digits, or will the computers just shut off to prevent HUP from being violated? (I kid). In other words, assuming we lived in a universe without HUP, how would the results of an actual high-resolution experiment differ from those with HUP? Thanks if you can shed any light on this!