Yet it is built upon very simple observations. If light is shone though a pair of slits then the emerging light will illuminate a series of light and dark bands on a screen. That light behaves as a wave is perhaps not too surprising. What is far more challenging to understand is how particles manage the same trick. Fire single atoms through the pair of slits and the pattern formed by their collisions with the screen adds up to the same kind of interference patterns as you see with light.
Waves generate interference patterns because they can pass through the two slits simultaneously.
And the world that emerges from the physicists' efforts is not the one we know. Today, one of the most popular interpretations, and one that has the backing of Nobel prize-winning physicists, is that a multiverse exists in which everything that can happen does happen. Each place is in its own parallel universe. But, you may say, the world we see is just not like that. At least part of the answer seems to be that the quantum mechanical weirdness that allows particles to occupy different states simultaneously is itself wavy.