The essential indefiniteness of quantum mechanics {Heisenberg)

The origin of quantum mechanics was an attempt to break away from the usual kinematical and mechanical concepts and in their place to substitute relations between concrete numbers given by experiment.

The position of an electron

The position of an electron relative to a given system of axes must be measurable by experiment if the term is to have a meaning in quantum mechanics. We illuminate the electron and observe it through a microscope; the accuracy with which the position can be observed is given by the wave-length of the light used. If we use a y ray microscope, we should get the most exact result physically possible. But these y rays produce a Compton effect on the electron, so that at the instant when the position is determined the momentum of the electron is suddenly changed. This change of momentum is all the greater the shorter the wave-length of the light used, i.e. the more accurate the determination of position is.

Thus at the moment when the position of the electron is known, its momentum can only be known to an order equal to this discontinuous change. Hence the more exactly a coordinate q is determined, the less exactly can its momentum p be found; and conversely.