Uncertainty principle is about shape, not measurement. Unless you mean "how you define the measured aspect of the system" . Position and momentum are Fourier t

Uncertainty principle is about shape, not measurement. Unless you mean "how you define the measured aspect of the system" . Position and momentum are Fourier transforms of each other, and therefore their waveforms cannot both be confined to small range at the same time. It is loosely analogous to the concept that a rectangle of area 1 can never have both side lengths less than 1.