Does observing particles in a cloud chamber collapse their wavefunctions?

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eep
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On a recent thread about cloud chambers, a question popped into my head. My knowledge of cloud chambers is that one can see the "path" of certain elementary particles as they pass through the chamber. If, say, we had an electron passing through the chamber, do we have to assume that the wavefunction of the electron is constantly being collapsed to give us this apparent path?
 
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Yes. Each interaction that produces a cloud droplet is a measurement of the electron's position.