In the double-slit experiment, when an electron reaches the detector after passing through the holes, it has a certain momentum which we can measure with arbitrary accuracy.
From this data, we can calculate what momentum the electron had when it was passing through the hole.
So we can know the electron's position (as it was inside the hole) with arbitrary accuracy and also simultaneously know its momentum.
Doesn't this violate the uncertainty principle? Where have I gone wrong?
Best Answer
The narrower the slits ($dx$), the broader the expected (measured and/or calculated) distribution of momentum ($dp$) of the photons passing said slits, so the product ($dx.dp$) cannot get arbitrarily small, therefore the Heisenberg principle ($dx dp \geq \hslash$) is respected in the double slit experiment.