|You're trying to put too much into something that isn't in an eigenstate!|
In order to understand these things you have to take Linear Algebra. You take Calculus as a freshman, and then Linear Algebra and Fourier Analysis as a sophomore. At the end of the year Fourier Analysis folds into differential equations. Then, as a junior, it starts getting hard. You take Abstract Algebra and Real Analysis which opens up to Theory and Analysis of a Complex Variable. At that point you're starting to narrow your degree direction..If you're going into physics these elementary math classes are reinforced by applying them. When you take electrical circuits you discover it's intimately linked with differential equations. Pretty soon you discover you can start dry labbing and that's when you can escape going to that smelly old lab.
HUP has to do with epistemology and the theory of measurement. We keep that in mind when we're designing collider experiments but it isn't right in your face , or it's already been compensated for long ago in the evolution of accelerator physics. Why do you need it? If I want to hit a proton beam with an anti proton beam, I only need to align the beams. As I near optimal collision where the two hit head on my detectors give me feedback that the optimal collision position is near. Once i have it tuned then I can prep calorimeters and other collision product receiving devices. I don't need to know if the optimal collision position can't be more finely placed than the parameter space and HUP will allow. It's close enough. Close enough to catch bottom-antibottom pairs, jets, literally the whole parton zoo. Then i'll have per femtobarns of data to analyze and interpret in a way that makes me great.
As you can see, dry labbing leads to greatness. .