Problem
Imagine an ideal instrument that never disturbs the system being measured. Which obstacles would disappear in classical physics? And why, in quantum physics, would not even this instrument be enough to eliminate indeterminacy?
Solution
In classical physics. With a non-disturbing instrument, all errors due to feedback from the apparatus onto the system would disappear: the thermometer that, on making contact, exchanges heat and alters the temperature it is trying to measure; the voltmeter that draws a small current and changes the potential of the circuit; the probe that deforms the object by pressing on it. An ideal measurement would return the value of the quantity exactly as it is, without altering it: in the classical world this is the limit that one approaches by improving the instruments.
In quantum physics. The Heisenberg indeterminacy would still remain, because it does not arise from the instrument’s disturbance. It is structural: the microscopic state does not simultaneously possess defined values of conjugate quantities (position and momentum). There is no hidden “true” value that a delicate instrument could read without spoiling it: those simultaneous values simply do not exist. So no instrument, however ideal and non-disturbing, could make them emerge together. The classical limit is technical and can in principle be overcome; the quantum one is inherent in the nature of the states.
Links
Topics: Experimental method Skills: Analysis of limiting cases and science-fiction physics