First, something is clearly aware of the other slit. We know this because if we block off one slit while the experiment is going on, the diffraction pattern stops and we get the effect of the "one-slit experiment". Second, the pattern obtained through sending sufficient particles through is consistent with the diffraction pattern obtained from a wave with the wavelength consistent with the de Broglie formula pλ = h. The third point is that a single particle is detected as a point. This is important because one detection involved C60 molecules (<PERSON>, M., and 5 others. 1999. Wave–particle duality of C60 molecules. Nature 401: 680-682.) Now, either there is a wave that went through both slits or there is not. Suppose there is no wave, which is effectively what modern QM tends to assert. Either the particle goes through both slits or it does not. Modern QM tends to assert the particle is really a field, and the field "knows" about both slits, and the particle is "realised" as an excitation on observation. 795
Personally, I find that intolerable as an explanation, because how can there be a field of C60 molecules? Similarly, if C60 molecules each go through two slits, they have to break up. How can they reassemble into one molecule, because we know they too are detected as points?
If there is a wave, there is no mystery at all. The wave goes through both slits, the particle through one on a trajectory just as you might expect, and <PERSON>, in his pilot wave theory, predicted the pattern that would be obtained. <PERSON> et al (<PERSON>, S. and 6 others. 2011. Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer Science 332: 1170 – 1173.) carried out a weak detection of photons and found they followed <PERSON>'s prediction precisely. In my opinion, that is fairly strong support for there being a wave.
I should add a warning. I have published an ebook wherein I take the pilot wave but modify it significantly by adding two extra constraints. The first is from <PERSON> - the wave function should become real at the antinode. (That applies to most standard wave functions.) The second is that the wave has to travel the same velocity as the particle to affect it in the two-slit experiment, which now requires the wave to transmit energy, which is what waves generally do anyway. 795