Two Slits, One Quantum Surprise

Light passing through two slits forms alternating bright and dark bands on a screen.

An experiment you can glimpse on a wall reveals why quantum probabilities do not always add like ordinary odds.

Imagine sending electrons toward a barrier with two narrow openings and watching a screen behind it. Each arrival leaves a single dot, as though a tiny pellet has struck the surface. But as you wait, the dots gather into alternating dense and sparse bands—not simply two piles behind the openings. Even when the electrons travel through the apparatus one at a time, the same pattern gradually emerges.

Where the Darkness Comes From

The double-slit experiment works with light as well as matter. To understand its striped interference pattern, begin with waves: each slit contributes a wave to every point on the screen. Where the contributions arrive in step, they reinforce each other; where they arrive out of step, they can cancel.

The deciding factor is often geometry. A point on the screen lies slightly farther from one slit than the other. That path difference, $Δ L$ , produces a phase difference

Δ ϕ = \frac{2 π Δ L}{λ},

where $λ$ is the wavelength, assuming the contributions start in phase at the slits. As you move across the screen, the path difference changes, producing successive bright and dark bands.

For equal-strength contributions, complete cancellation occurs when

Δ L = (m + \frac{1}{2}) λ, m \in Z .

A half-wavelength difference, for example, makes a peak meet a trough. Unequal contributions cannot cancel completely, leaving a dim band rather than a perfectly dark one.

A Wave of Possibilities, a Dot of Evidence

For individual particles, quantum mechanics describes the two alternatives using probability amplitudes, $ψ_{1}$ and $ψ_{2}$ . When the paths remain indistinguishable, the probability density for detection is

P (x) = ∣ ψ_{1} (x) + ψ_{2} (x) ∣^{2} .

Expanding this gives

P (x) = ∣ ψ_{1} ∣^{2} + ∣ ψ_{2} ∣^{2} + 2 Re (ψ_{1}^{*} ψ_{2}) .

The last term is the interference term: it raises the probability in some places and lowers it in others. Each detection is localized, but many detections reveal the distribution predicted by the wavefunction.

A single arrival makes a dot; many arrivals reveal the interference of possibilities.

If an apparatus reliably records which slit the particle traversed, those alternatives become distinguishable. The interference term disappears, leaving the sum of the separate probabilities. No conscious observer is required: the physical interaction that makes the paths distinguishable is what matters.

Bring the Bands Home

You can demonstrate light interference with a low-power visible laser pointer, a double-slit slide and a white wall or sheet of paper. In a dim room, place the slide in the beam, ideally a few metres from the screen. With suitable alignment, you should see alternating bands.

Cover one slit and the two-slit fringes vanish, although the remaining slit still produces its own diffraction pattern. This home demonstration does not resolve individual photons; that requires specialized equipment.

Keep the beam below eye level, never look into it or aim it at anyone, and avoid reflective surfaces. Do not use a high-power laser.

The apparatus is modest, but its lesson is profound: when alternatives cannot be distinguished, you must add their amplitudes before calculating their probabilities. Sometimes, offering two possible routes makes an arrival less likely than offering one.