Interference is the superposition of waves, where they either reinforce or cancel each other out. Like ripples on water from two thrown stones: in some places waves meet crest to crest and grow, in others they cancel, and the water is almost still.
History
The wave nature of light was discussed by Robert Hooke and Christian Huygens in the 17th century, but the decisive interference experiment was performed by Thomas Young in 1801. He passed light through two closely spaced holes and obtained alternating bright and dark fringes. Augustin Fresnel developed a mathematical theory of diffraction and interference, leading to acceptance of the wave theory of light. In 1924, Louis de Broglie proposed the hypothesis of wave properties of matter, and soon electron interference was experimentally confirmed. Erwin Schrödinger formulated the wave equation, where interference of wave functions explains the quantum behavior of particles.
How it works
Interference occurs when two or more coherentwaves superimpose in space. The resulting field E = E_1 + E_2 + ..., and the intensity is proportional to the square of the amplitude: I ∝ |E|^2. When adding monochromatic waves of the same frequency with a constant phase difference Δφ, we get I = I_1 + I_2 + 2√(I_1 I_2) cos Δφ. Condition for constructive interference: Δφ = 2πm (maximum); destructive: Δφ = (2m+1)π (minimum). In quantum mechanics, the wave function ψ = ψ_1 + ψ_2 gives probability |ψ|^2 = |ψ_1|^2 + |ψ_2|^2 + 2 Re(ψ_1* ψ_2). The superposition principle guarantees linearity of evolution, and interference manifests even when particles are sent one by one.
Fun fact
Noise-canceling headphones work on interference: they create "anti-noise" that cancels out the sound around you.
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