PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · The formalism of quantum mechanics
The Structure of Quantum Mechanics, Ch Compatible observables and uncertainty as a theorem
Problem
Find the error in the following argument, offered as a derivation of the position-momentum uncertainty relation: "To locate a particle to precision Δx, one must illuminate it with light of wavelength λ≲Δx (Heisenberg's microscope). Such a photon carries momentum pph=h/λ, and scattering it off the particle transfers a kick of order Δp∼h/λ∼h/Δx. Hence ΔxΔp∼h, which is the uncertainty relation, derived as a consequence of the disturbance caused by the measuring photon. It follows that a particle which is never measured has a perfectly well-defined position and momentum simultaneously, restricted only by our practical inability to measure both without disturbing one of them."