Double-Slit Experiment

One-Sentence Significance

The double-slit experiment shows that coherent alternatives require adding amplitudes before probabilities.

What Was Measured

Particles or waves pass through two openings and are detected on a screen. In quantum versions with electrons, photons, atoms, or molecules, individual detections can be localized while the accumulated distribution shows interference.

If the two alternatives contribute amplitudes $\mathcal A_1$ and $\mathcal A_2$, then

$$\mathcal A = \mathcal A_1+\mathcal A_2, \qquad P = \lvert\mathcal A\rvert^2.$$

Expanding,

$$P = \lvert\mathcal A_1\rvert^2 + \lvert\mathcal A_2\rvert^2 + 2\operatorname{Re} \left( \mathcal A_1^*\mathcal A_2 \right).$$

The final term is the interference term.

What It Showed

When alternatives are coherent and indistinguishable in the relevant physical setup, probabilities do not simply add. The phase relation between amplitudes affects the final detection distribution.

What It Did Not Show By Itself

The experiment does not require human consciousness to collapse anything. Physical which-path records, environmental entanglement, or apparatus changes can suppress interference without a conscious observer.

It also does not say particles are just classical waves. Quantum mechanics combines localized detection events with wave-like amplitude propagation.

Modern Interpretation

The experiment is a clean laboratory version of the amplitude rule. If which-path information is unavailable and coherence is preserved, amplitudes add. If which-path information is available in principle, the interference term is reduced or absent in the corresponding measurement context.

Decoherence explains how uncontrolled environmental records suppress interference in realistic macroscopic settings.

Canonical Links

• Double-Slit Glossary Entry
• Probability Amplitudes
• Born Rule
• Decoherence Preview
• Davisson–Germer Experiment

Common Myths

• The experiment proves particles are ordinary waves.
• Looking with human eyes is the decisive ingredient.
• Interference disappears only when the particle is mechanically disturbed.
• Single-particle detections and interference are contradictory.

Quick Check

When is it correct to add probabilities rather than amplitudes?

Solution

It is correct when the alternatives are distinguishable or incoherent in the relevant physical context. Then the interference term is absent, and the total probability is the sum of the separate probabilities.

References

• C. Jonsson, “Elektroneninterferenzen an mehreren kuenstlich hergestellten Feinspalten,” Zeitschrift fuer Physik 161, 454-474, 1961.
• A. Tonomura et al., “Demonstration of single-electron buildup of an interference pattern,” American Journal of Physics 57, 117-120, 1989.
• R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Volume III, Addison-Wesley, 1965.