The double-slit experiment

The double-slit experiment is a standard experiment illustrating the wave-like nature of light, as described by the Maxwell equations.

It becomes a somewhat queer and paradoxical flavor when one tries to interpret it in terms of a particle picture of light composed of photons. However, with the empirical success of quantum electrodynamics (QED) and other quantum field theories, the particle picture, although ominpresent in the language of quantum physicists, has been replaced by a more adequate picture in terms of quantum fields. As Steven Weinberg wrote:

''In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields.''

How is the double-slit experiment interpreted via quantum field?

Photons are localized lumps of energy, wave packets with a reasonably well-defined position and momentum, with an uncertainty consistent with atandard quantum mechanics. Like waves, photons can be very delocalized. Each photon in a laser beam has the same shape as the classical field by which this beam is described.

In a double-slit experiment with visible light the distance between two slits can be macroscopic, e.g. 0.1 millimeter, or something like that. In order to get an interference pattern, the photon lump should be no smaller than this size. The corresponding volume is filled with a time-changing electromagnetic field, the light beam. This macroscopically large (but in a weak beam possibly very faint) lump of electromagnetic energy falls on the double slit and interferes with itself according to Maxwell equations - its shape becomes that of a superposition of two spherical waves and becomes even more delocalized over a quickly growing region. Then this big but distributed lump of energy reaches the photographic plate and blackens a single silver grain. The photon energy that was previously spread up in a macroscopic region now gets released within a group of few atoms.

Naively (according to the old Einstein picture), and figuratively even in actual practice today, this is interpreted as the photon collapsing to a point of essentially microscopic extension at the place where the black silver appeared. However, this alleged collapse is pure fantasy. The photon is absorbed by the detector, and doesn't survive as a localized photon.

The behavior of the photographic plate in the presence of the incident classical electromagnetic field is fully explained by the detector's quantum structure, and indeed, the quantum structure of the photographic plate is essential for the explanation, not a hypothetical particle structure of the electromagnetic field. See Chapter 9 of the quantum optics book by Mandel & Wolf and the discussion in the FAQ entry ''The photoelectric effect''. The macroscopically delocalized energy of the photon's field is absorbed by the entire photographic plate, and then all this absorbed energy gets channeled somehow - in full agreement with the conceptual and mathematical machinery of quantum mechanics - to a single grain of photoemulsion. The e/m field serves as external potential for the entire photographic plate. The probability density of a particular electron to become free and trigger the subsequent chemical reaction is computed by a sophisticated version of Born's rule. It turns out to generate a Poisson process of emitted photoelectrons. The photoelectrons then starts a chemical reaction in the metastable photoemulsion, blackening a grain according to well-understood chemistry. This produces tiny dots whose density is proportional to the incident intensity of the electromagnetic radiation.

This is quite different from the picture Einstein's explanation suggests - where a tiny particle called photon hit this grain, passed all its energy to the grain, and thus initiated a chemical decomposition of the grain, which resulted in its blackening. People (including quantum optics experts) use this picture all the time, but it must be understood in a figurative sense, on the same level as when we talk about that an atom consists of electrons moving around a nucleus. The latter invokes pictures of Bohr's atomic model which contain some truth and intuition, but are very misleading if taken literally. In the same way, Einstein's picture should not be taken literally.

Basically the same alternative between a naive particle picture and a modern quantum field picture arises when electrons are used in the double-slit experiment instead of photons: Just as photons are lumps of energy of the electromagnetic field, reasonably localized in phase space, so electrons are lumps of energy of the electron field, reasonably localized in phase space.

On a personal note: In 1999, I still had a naive picture of photons, colored by discussions in textbooks, papers on the foundations of quantum mechanics, and quantum information experiemnts by Alice and Bob. It was a very eye-opening event when I had the occasion to discuss my half-bred views on photons with the quantum optics experimentalists in Zeilinger's group. shortly after he moved to Vienna. These discussions revealed to me that real-life photons are something very different from what superficial discussions seemed to suggest. My views about what photons are turned by almost 180 degrees.

See also