Double slit experiment (DSE or DSX) is an iconic experiment of quantum mechanics, because it illustrates well quantum delocalization and collapse of wave function phenomena and you can play with it in Java applet herein. While mechanical analogy of DSE exists already, the AWT explanation of DSE experiment is quite easy and it follows exactly the macroscopic experiment.
By AWT vacuum has a foamy structure of Aether density fluctuations and every object is moving through vacuum foam like boat or fish beneath water surface. Such fish creates a typical undulations of water surface - a ripples, which are always perpendicular to the fish motion direction. In quantum physics such undulations are called de-Broglie wave.
At the water surface, the surface waves are increasing a density of density fluctuations, thus leading into formation of turbulence. In vacuum, such shaking increases a density of vacuum foam in direction, by which particle is moving, so that the speed of light remains invariant for such object. From outside perspective we could observe a relativistic contraction of such object. This connection illustrates a close relation of quantum mechanics and relativity:
Note that the deBroglie wave propagates through vacuum by speed of light, it always advances particle location like ripples spreading from swimming duck. While pin-point particle cannot pass through both slits at the single moment apparently, its deBroglie wave can do that without problem under formation formation of typical flabelliform interference patterns.
Because every shaking makes vacuum foam more dense, the vacuum density becomes non-uniformly distributed around particle, when passing through double slit. This affects particle motion accordingly, because by AWT every particle consist of standing wave packet and it propagates along foam branes like wave. All waves are focused by more dense environment, so that path of particle motion prefers the directions of flabelliform patterns. At the case of repeated experiment, the particle traveling through random undulations of vacuum foam follows the wave interference patterns at target. Note, that such interpretation doesn't require mutual interaction of individual particles during experiment - path of particle spreading remains affected by interference even at the case, when only single particle gets involved into experiment.