Hi Reuben,

To understand that, you have to first understand how waves can interfere. Think of waves at a beach. The up/down motion of the water is a property of the wave. If you have two waves that hit each other--for example, a motorboat goes by the beach, then the total wave is the addition of the two waves. If both waves happen to be going up at the same point, then the total wave is bigger. If one is going up and the other down, then they cancel each other out and the total wave is small.

The 2 slit experiment uses interference as a way of checking to see if something is acting like a wave. It does this because if you have a wave coming in and you send it through only one slit, you get a pattern given by the wave passing through that one slit. If you open a second slit, you get waves from both slits, which interfere with each other, generating a unique pattern which can only be explained by waves. This might seem obvious in the case of ocean waves, but it was amazingly useful to check if light was a wave. Light waves wiggle too fast for us to see the actual waviness of them, but by setting up two slits, we can actually see the interference pattern that confirms that light is a wave. This was done long before quantum mechanics or particles were even considered.

How does the electron fit in? Quantum mechanics said that electrons should behave like waves, and that these waves told you the probability of finding an electron at a point when you went looking for it. This seemed odd, so people wanted to test it. One way of doing that was to send electrons, one at a time, through two slits. If they did really behave like waves, then the waves should form an interference pattern. Physically this means that when you measure a lot of electrons, the pattern you get looks like the interference pattern of light or water waves coming from two slits. The only way this could happen is if some wave was travelling through both slits and interfering. If each electron only went through one slit or the other slit, this pattern could not show up, since it can only be formed by waves coming from both slits each time an electron passes through.

So the justification for this is experimental--the best explanation for this and other results is that particles are somehow wavy when you get down to a tiny scale.