Uncertainty Principal

Fig 1. Single slit scattering set-up and patterns for a wide and a narrow slit.

You no doubt have heard of the Heisenberg uncertainty relationships. These relationships hold for quantum mechanical objects and state the degree to which we can know something about these objects. For example the position-momentum uncertainty relation has the form

where Dx is the uncertainty in the x position and Dp is the uncertainty in the x momentum. Unlike classical mechanics we cannot know the exact position and momentum of a quantum mechanical object at the same time. Measurements of one quantity introduce uncertainties in the value of conjugate quantities, etc. The intuition for this result is grounded in our understanding of wave properties.

Interestingly, light is a quantum mechanical object or objects, photons. Photons may be sent one at a time through a single slit. They are detected on the screen across the room. The slit introduces some uncertainty into the lateral momentum because the slit localizes the photon to some lateral region in space. As the photons fall on the screen at random, they form a pattern, the single slit diffraction pattern. The single slit diffraction pattern first minimum occurs when a Sin(q) = l. The photons coming to the screen must have come through the slit, so Dx = a gives the degree of lateral uncertainty in position. The momentum of the photon is p = h/l according to de Broglie and Einstein. The slit changes the direction and consequently the momentum of the photon. We take the first minimum in the diffraction pattern as a measure of the uncertainty in momentum.

Starting with the relationship for the first minimum in the diffraction pattern and using the relationships introduced above, we arrive at the Heisenberg uncertainty relation---for light.

When you observe diffraction broadening, it is a quantum mechanical observation!