The interference pattern observed in Young's double-slit experiment is not directly explained by Heisenberg's uncertainty principle. The uncertainty principle states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously. It does not directly address the specific phenomenon of interference.
The interference pattern in the double-slit experiment arises from the wave-like nature of particles, such as electrons or photons, which exhibit wave-particle duality. When a beam of particles, like electrons, is sent through two closely spaced slits, each slit acts as a new source of waves. These waves propagate and overlap, leading to constructive and destructive interference at various points on a screen placed behind the slits.
The probability distribution of detecting the particles on the screen is determined by the square of the total amplitude resulting from the superposition of the waves. The interference pattern emerges as a result of this constructive and destructive interference, leading to regions of enhanced and diminished particle detection on the screen.
Heisenberg's uncertainty principle becomes relevant when considering the precise determination of the path of a particle through one of the slits. When we attempt to determine which slit the particle goes through, we introduce additional interactions or measurements that disturb the particle's momentum and, thus, its wave behavior. This disturbance destroys the interference pattern because the particle's wave-like behavior collapses into a specific localized position.
In summary, the interference pattern in the double-slit experiment is a consequence of wave interference resulting from the superposition of wave amplitudes, while Heisenberg's uncertainty principle is related to the limitations of simultaneous precision in measuring certain pairs of properties of a particle.