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I have a little problem understanding Young's slit experiment with single photons :

I have understood for a long time that each photon impact on the screen corresponds to a photon sent by the source, and that, if we don't try to find out by which path the photon has passed, of course, each impact of photon contributes to gradually draw an interference pattern, ok.

My problem comes from the description that is often made in popular science articles :

We are told : "The photon interferes with itself", which amounts to saying that the wave function of a photon has passed through the 2 slits.

The problem is this :

If we move away from the median line between the 2 slits, the distance traveled by the photon from one slit is different from the distance traveled by the photon from the other slit.

I conclude that this (single) photon can't interfere "with itself" since when the complementary part of the photon arrives on the screen, the first part has already produced an impact since it arrives ahead of the complementary part (a single photon can't produce 2 impacts, it's impossible, since there is reduction of the wave function at the first impact).

Necessarily, I tell myself that to have an interference, at different distances, (all over the screeen) it's "different" photons that interfere with each other, because the sending rate of single photons is sufficiently fast. That's right ?

If yes, then I deduce that with a much slower rhythm (we wait for the impact of a photon on the screen to send the next one), the pattern is no longer an interference pattern but a pattern of classical diffraction. That's right ?

This seems consistent with the idea that in this very specific case, by knowing at what "moment" a photon arrives, we can deduce what path it has actually traveled by deducing the distance it has traveled from time (potentially measurable, even if it is not measured) and C. (d=C.t).

How does the mathematical formalism of quantum mechanics manage to predict this phenomenon, predictable but a priori surprising since there is no longer a single ψ wave function, but as many ψ wave functions as photons ?

I guess this process (changing pattern with a very slow rate) doesn't work with electrons because the speed of an electron is fundamentally undetermined before measurement, whereas the speed of a photon in vacuum is always fundamentally determined (C), if I'm not talking nonsense. (?)

Is there a reasoning error somewhere ?

Above all, tell me if I wrote one or more nonsense in my message, it's very important for me

In advance, thank you for your answers.

Cordially,

Marilyn