So in terms of actual measurement, how is it possible to actually figure out the value of a quantum particle, that's the thing I really can't figure out.
I am somewhat familiar with the Cauchy Schwartz inequality, I believe it was in relation to vectors, but I am not familiar with the Bandwidth Theorem.
Now I might be getting at this from the wrong angle, but in order to physically measure a particle, disturbing it or not, then you must be able to know exactly where it is. But if you can never know the energy and/or position at any time, how can you actually measure anything at all? Let alone watch it interact with other particles, since they suffer from the same problem (I assume)?
I think one of the hardest things for me to understand as well - somewhat related - is when do these types of effects "blend" into the real world. In other words, when do things obey classical Newtonian mechanics, and when does an object obey quantum mechanics?
A molecule for instance, is not a quantum object to my knowledge, as in it doesn't have the particle/wave duality, but it's made of particles that do. So when does the switch occur so to speak, is there a certain mass or number of particles in a system, that determines how an object behaves? Why don't molecules and atoms all behave like particles and waves?
(Is it obvious I don't have a Ph.d in physics? lol)