With the double slit, experiment we show the double nature of light and matter as wave and particle. In particular, the so called "which way" thought experiment illustrate the complementary principle. In my book, this experiment is analyzed putting a series of particles in front of one of the two slit, so when the electron pass through the slit it scatter with the particles, changing the component of the momentum perpendicular to the direction of motion Δpy. Using the uncertainty principle, it's said that the uncertainty on the position of the electron is now Δy<<D with D the distance between the two slits, and consequently, Δpy is so large that the interference pattern is destroyed. But since the uncertainty principle represents an intrinsic property of the electron, independently of the measurement (correct me if I'm wrong), even if I don't alter the state of the electron but can still determine in which slit the electron crosses (I don't know if it's possible), the interference pattern should be destroyed. Doesn't that mean that considering the scattering I should take into consideration the uncertainty principle and the uncertainty due to the scattering?
