Someone argues: "A dust grain is heavy and macroscopic
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Quantum Mechanics · Quantum dynamics and its formulations
The Structure of Quantum Mechanics, Ch The path integral
Problem
Someone argues: "A dust grain is heavy and macroscopic, so in the sum over paths only the classical straight-line path contributes anything appreciable. The other paths add up with smaller magnitudes and mostly cancel, while the classical path's larger magnitude is what makes it dominate the propagator."
((a)) Explain what is wrong with this claim about the mechanism, independently of any numbers.
((b)) For a dust grain of mass m=1.0×10−9kg observed for a time t=1.0s, use the stationary-phase estimate for the width of the surviving bundle of paths, w=ℏt/m, to compute w, and say why the classical path nonetheless dominates so completely.