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In any interference experiment, whether it be an unequal arm length interferometer or the classical double slit set up, we have two unequal distances from source (or slits) to screen/detector. Single photon interference in the regime of quantum mechanics is explained by saying that every photon interferes with itself. This generally gives rise to the following misconception that this interference seems impossible since the photon going through the shorter path always gets absorbed at the detector before the one at the longer path makes it.

I have gone through this question which seems to be asking a similar question to this but allow me to explain.

In the double slit exp., is it correct to say that just after the photon is ejected from our source, the wavefunction, which may have a speed greater than the speed of light ** or have no speed at all and is present at all points in space, from the moment the photon was released, has already interfered at the detector before the photon would make it to the detector at velocity $c$ and it's only after time $t = \frac{(Path Length)}{c}$ that we get the measurement/click at the detector?

** I also understand that the wavefunction cannot be attributed a physical meaning but I've seen some sources mentioning about the wavefunction propagating as a spherical wavefront. I'm not sure what to make of this. I find it easier to not even try to visualise the wavefunction at all!

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I guess this paper could be interesting for you:Nature Physics 11, 539–542 (2015) doi:10.1038/nphys3343. There is a physics world article available as well and which you might want to read first.

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