I know the uncertainty principle tells us that we cannot simultaneously measure both the location and momentum of a particle with a high accuracy. The usual example we find in lectures is to imagine a high energy photon used to locate an electron. When the photon hits the electron it will immediately change its momentum, so if we spotted its location to some accuracy, we don't know what was the electron's momentum with the same accuracy.
My question is, can we measure one first, then calculate the other?
Say we know the momentum of the photon before it hits the electron, and say we measured its momentum after the collision as well as the momentum of the electron after the collision, then can we deduce its original momentum before it was hit by the photon?