Question

I recently came across an interesting explanation of diffraction through an aperture which does not use Huygens’ construction but instead relies on Heisenberg’s uncertainty principle:

The uncertainty principle states that trying to pin a particle down to a definite position will create uncertainty in its momentum, and vice-versa. Therefore when you are confining a particle to go through a narrow aperture, one is very certain about its position (the aperture is very narrow and hence the particle must have been somewhere in that extremely small gap) So, by Heisenberg’s principle, the particle will now have a crazy momentum… so it can go in any direction.

However, it seems we cannot use the same principle to explain the case where diffraction occurs when light passes around an obstacle. We are not locking the photons in a small position in that case, are we? Keeping the uncertainty principle in mind, diffraction through an aperture makes sense; but in the case of a solid obstacle, my intuition says the wave should just be deflected. Is there a way to relate the uncertainty principle to diffraction around an obstacle?

Besides, given that the uncertainty principle is defined in terms of particles, can it be used to explain diffraction in mechanical waves such as sound which are not composed of photons?

Answer 1

The Heisenberg Uncertainty Principle provides a link between a particle's position and its momentum, implying that a particle passing through a narrow aperture has a highly uncertain momentum, leading to diffraction. Diffractive behavior around an obstacle is more directly explained by wave-particle duality, which applies to both quantum and non-quantum waves, such as sound. Thus, while Heisenberg's principle may not directly explain light diffraction around obstacles, wave-like properties and behaviors are core to both phenomena.

Step-by-step explanation:

The Heisenberg Uncertainty Principle is a fundamental concept in quantum mechanics that relates the uncertainty in a particle's position with the uncertainty in its momentum. In the context of diffraction through an aperture, like a slit, the principle suggests that the more precisely we know the particle’s position, the less we know about its momentum. This implies that as a particle such as a photon or electron passes through a narrow opening, there is a significant uncertainty in its momentum, hence it can spread out or diffract in various directions and not just proceed in a straight line.

When considering diffraction around an obstacle, it is the wave nature of particles, as suggested by de Broglie's wave-particle duality principle, that is more directly responsible for the behavior we see. The waves spread out after encountering an edge or slit, and this behavior is consistent with how waves, in general, behave – be they light waves or mechanical waves like sound. Thus, even if the Heisenberg Uncertainty Principle doesn't directly explain the behavior of light when diffracting around an obstacle, the principle still supports wave-particle duality which is fundamental to such wave phenomena.

Diffractive effects can apply even to sound waves despite their non-quantum nature. While the Heisenberg Uncertainty Principle is primarily used in quantum mechanics, the concept of waves spreading when encountering obstacles is universal and is observed with both light and sound. The wave-like properties that give rise to diffraction patterns do not require the particles to be confined to as small a volume as an aperture directs them, but rather the interference effects can arise from any constraint or boundary in the wave's path.