The double-slit experiment demonstrates a key principle of quantum mechanics: wave-particle duality. Particles like electrons and photons can exhibit properties of both particles and waves.
When particles pass through the two slits without observation, they create an interference pattern characteristic of waves. However, when we observe which slit each particle passes through, the interference pattern disappears, and we see a pattern consistent with particles.
This experiment shows that the act of measurement affects the behavior of quantum systems - a fundamental aspect of quantum mechanics that distinguishes it from classical physics.
The double-slit experiment has a rich history stretching back over 200 years, evolving from studies of light to fundamental quantum mechanics.
The experiment has been performed with increasingly larger particles, including atoms and even molecules like buckyballs (C60), demonstrating that wave-particle duality applies not just to elementary particles but to larger quantum objects as well.
The wave-like behavior of particles is described by the wave function (ψ), which evolves according to the Schrödinger equation.
Schrödinger Equation (Time-independent):
-ℏ²/2m ∇²ψ(r) + V(r)ψ(r) = Eψ(r)
For a free particle passing through slits, the wave function after the slits can be approximated as:
ψ(x) = ψ₁(x) + ψ₂(x)
where ψ₁ and ψ₂ are the wave functions from each slit.
The probability density of finding the particle at position x on the screen is:
P(x) = |ψ(x)|² = |ψ₁(x) + ψ₂(x)|² = |ψ₁(x)|² + |ψ₂(x)|² + 2|ψ₁(x)||ψ₂(x)|cos(φ)
where φ is the phase difference between the two paths.
The interference term (2|ψ₁(x)||ψ₂(x)|cos(φ)) is responsible for the interference pattern. When we measure which slit the particle passes through, this term disappears, resulting in P(x) = |ψ₁(x)|² + |ψ₂(x)|², which is just the sum of probabilities from each slit without interference.
The principles demonstrated by the double-slit experiment have far-reaching applications:
Quantum computers leverage superposition and quantum interference to perform calculations that would be infeasible for classical computers. The ability of quantum particles to exist in multiple states simultaneously enables quantum parallelism.
Quantum key distribution (QKD) uses the principles of quantum mechanics to create secure communication channels. The fact that observation disturbs quantum systems makes it possible to detect eavesdropping attempts.
The wave nature of electrons allows for imaging at much higher resolutions than light microscopy, enabling atomic-scale visualization.
Quantum interference effects are used in extremely sensitive sensors for measuring gravity, magnetic fields, and time, with applications in navigation, mineral exploration, and fundamental physics.
Federal agencies are investing in quantum technologies for secure communications, breakthrough computing capabilities, and advanced sensing for defense and intelligence applications. The National Quantum Initiative coordinates quantum research across multiple agencies including DoD, DOE, and NIST.