Double slit experiment vs interferometry

Question

I'm using radio-interferometric observations from telescopes in my work, and recently I came up with a question which can't solve myself.

We all know about the double slip experiment, where one can either see the interference pattern or measure photons passing through slits - but not both. On the other hand, the way radio interferometers work is by measuring the arriving photons (actually, we don't usually think of them as particles in this case, but it doesn't matter) at receiving antennas separately, and then using this information to get the interference patterns.

Personally I can see clear intuitive correspondence between the slits in the first case and individual antennas in the second - but following the same logic as in the double slit experiment, why can we get the interference pattern at all in radio interferometry?

Answer 1

When two antennae are used in radio interferometry, it is not at all analogous to the two slits in a two-slit optical interferometer. In the former, there are two detectors separated by a distance. In the latter, there are two apertures separated by a distance, with a detector or detector array downstream.

In radio interferometry, if two or more antennae receive a signal from a distant point source, the signal is delayed at one antenna relative to the other antenna. The difference in timing between the received signals, and the distance between the antennae, together provide a basis for calculating the angle from which the signal is arriving. The relative timing can be known with exquisite precision by comparing the phases of the frequency components of the received signals. Even if there are signals arriving from other sources at many different angles, cross-correlation between the composite signals received by the two antennae allows signals from individual sources to be sorted out. In essence, the two signals are interfered with each other (computationally) to do the cross-correlation. Individual radio photons are not detected in radio interferometry.

Usually in the double slit experiment, too, individual photons are not detected. Instead, the averaged relative phase of coincident photons from the two slits is measured at many points in a detection plane (the screen). The relative phase difference results in an amplitude difference via interference. Information that can be derived from the resulting interference pattern, if the slit and screen geometries are known, includes the wavelength of the illumination source, the direction to the illumination source, and the angular width of the illumination source.

So, the same kinds of information can be obtained via a two-slit interferometer or a pair of radio antennas. However, the two systems operate very differently. Similarly, a slide rule and an abacus both can manipulate numbers and produce the same information, but they work by very different principles. Any analogy between the two would be very abstract.

Answer 2

The interference pattern found in the double slit experiment is due to coherent waves physically interfering with each other. Interferometry is when you mathematically superimpose wavefunctions onto eachother.

Answer 3

Finally I found the answer to this exact question in the book "Interferometry and Synthesis in Radio Astronomy" (open-access). Basically it shows that there are inherent noise sources when we do interferometry and so it's impossible to tell (with greater precision than the uncertainty principle allows) which "slit" the photon passed through. The book also gives references to deeper papers.