Suppose a crowd of people are passing through a set of turnstiles like you see at a train station. there's two trurnstiles and each person has a wrist device that says left or right according to an atomic decay event. Each person consults his device and selects the turnstile to go through according to what it says. Now suppose you're an experimenter who cannot see the choices the people are making but you can only plot the points where each person crosses a line just beyond the turnstiles. Would you see an interference pattern build up on the line because each person was behaving like a wave and passing through both turnstiles at the same time until their wave function collapses at the measurement line?