 Quote by Gokul43201
Illegally taking square roots above and forgetting that we are talking about variances and expectations, is what leads to popular misconceptions about intrinsic uncertainties in single measurements.
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Would you care to elaborate on that? I don't think there is any real problem about what is going to happen if repeated measurements are made under the same conditions. Repeated trials are going to result in a pattern of hits on the screen. The issue is focused on a single particle passing through a single slit being detected one time on a screen. You know the particle made it through the slit, and you know, to a precision determined by the detector, where the particle hit the screen. What do you know about the particle? What have you measured?