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When an image of a distant galaxy is split by a gravitational lens are the photons from the two images capable of displaying interference? This may not be possible in real conditions because of magnetic fields/polarization/intervening matter etc. but in an ideal case it is possible? Is this split image inherently different from a two slit interference experiment?

There is a new observation cited of using correlations in intensity fluctuations of a quasar image split by a gravitational lens to determine the Hubble constant.

https://www.sciencedaily.com/releases/2019/01/190122171325.htm

What are the primary limiting criteria for observing interference with this example of a quasar split by a gravitational lens? Is this a small enough source? Is the time interval too large to create a delay line in one of the images to have interference? Is the correlation length too small?

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  • $\begingroup$ You can do interferometry with radio frequencies. You can even do it with recorded data. $\endgroup$
    – PM 2Ring
    Jan 26, 2019 at 5:01

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There is no interference in this situation. You need coherent light for interference. The distant galaxy is not a source of coherent light. It is an extended source emitting incoherent light.

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Consider a two-slit stellar interferometer. Every point on the star produces a set of fringes, and the width of the star is determined by the blur resulting from superposition of the fringes over the angular width of the star. White-light interference is a well-understood phenomenon.

There can definitely be interference in the light from a distant source, split by an intervening gravitational lens. The question is where you might be able to observe it, and that will depend on the location of the source and the location and size of the gravitational lens.

Here is a good explanation of two-slit stellar interferometry.

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  • $\begingroup$ The photons in the different images may arrive years apart. $\endgroup$ May 21, 2018 at 2:34
  • $\begingroup$ It depends on where you put the detector. Actually, each photon interferes only with itself (to first order). To detect interference, it would be necessary to find a place out in the void where the path lengths for the split parts of the wavefunction are very nearly the same. Actually detecting the interference might be a challenge! $\endgroup$
    – S. McGrew
    May 21, 2018 at 3:35
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I had the same question, and believe that there would in fact be interference. Perhaps it would wash out in the case of a wide-spread source such as a galaxy, but for a distant individual star acting as a point source, I don't see why there wouldn't be interference between the possible paths. I am assuming that the light's spatial coherence exceeds the effective diameter of the gravitational lens, but I do not know if this is valid.

This is a bit different from a double slit, since this situation involves cylindrical symmetry. So the resulting interference pattern might resemble a large Airy disk due to the lens, perhaps with a large Argo spot due to the black hole horizon. Assuming a gravitational lens 1000km wide located 1000 light years away, a basic calculation indicates a fringe spacing on the order of the earth's diameter. So even if my assumptions are correct, I doubt this will be observed any time soon (if ever).

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  • $\begingroup$ By "spatial coherence", do you mean coherence length? Actually the coherence length can be much shorter than the width between the two slits in Young's experiment, or in most other types of interferometers. For there to be interference, all that's needed is for the path lengths to differ by less than the coherence length. $\endgroup$
    – S. McGrew
    May 21, 2018 at 2:01

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