Put the classical electron-emitting double-slit apparatus in a sealed box. At each slit there's a counter to check whether an electron has passed it or not, so had the apparatus been left in open, we would have observed dots pile after the two slits on the screen with no interference pattern. But now the apparatus is running in the sealed box, and the box is so designed that 1) an outside observer can't know anything inside the box unless he opens it. 2) the box destroys the counters just before you open it, leaving no information of their past recordings. My question is, will you see interference pattern after you open the box? Why or why not?
To quote Feynman:"You do add the amplitudes for the different indistinguishable alternatives inside the experiment... At the end of the process you may say that you 'don't want to look at the photon.' That's your bussiness... Nature does not know what you are looking at, and she behaves the way she's going to behave whether you bother to take down the data or not" Does this comment apply here? But which slit the electrons have passed does seem indistinguishable to an outside observer during or after the experiment.