To see the Heisenberg's relations at work, imagine an experiment in which particles emitted by a source pass through a narrow circular slit before impinging on a perpendicular detection plate. If we average over a large ensemble of particles and we look at the spatial distribution of the spots left on the detection plate by the impinging particles, we see that not all the particles are recorded at the point O corresponding to a straight trajectory (see picture); some of the spots are actually found at a distance r from O . If we now repeat the whole experiment by varying the amplitude of the slit, we see that the spatial distribution of the spots is modified correspondingly (red and blue curves).

With the help of the Heisenberg's relation, we can easily interpret these results in terms of the classical concepts of ‘particle' and ‘trajectory' (which, as we argue in the implications, should be used with some caution when dealing with quantum phenomena). Consider for example the case of a narrow slit, and call t the intant at which the particle is expected to pass through the slit. In order to arrive at the detection plate, the particle has to pass through a small hole: its radial coordinate at time t is therefore precisely determined. In other words, the slit acts as a filter which selects only those particles whose radial position lies within a small interval. According to the Heisenberg's relation, for these particles the uncertainty on the transversal velocity (i.e. the components of the velocity vector parallel to the screen) at time t is large. Indeed, the narrower the slit, the larger the transversal velocity can be. Because of its nonzero transversal velocity, each particle deviates from the axis while flying between the slit and the detection plate, and is finally detected on the plate somewhere in a circle whose radius is inversely proportional to the slit amplitude (compare the red curve with the blue one).