Why the single slit experiment? Because it shows, more than anything else, the importance of information transfer. Not energy or force transfer, but information. For this discussion it is necessary to define information the way the universe defines it -- not the way we humans define it. Briefly, information is that which causes physical reality to assume the properties we observe. Particles, forces, and fields, all will have their own properties. One type of particle will be different from another type of particle, one kind of force different from another type. It is this phenomenological information that gives  observable reality the various identities we can see and measure. But what is information in this context? Is it something we can actually measure? Is it something solid we can lay our hands on? No. Information of  the basic, fundamental kind I am talking about is a 'quantum' property of the object we are studying. And as already stated, there is no 'reality' to quantum physics - information is as 'real' as the object we are looking at, and applying the word 'real' to a quantum object, such as a single electron, is nonsensical.  From it's very beginnings, the quantum theory and reality have been at odds with each other, and this continues even today. But, if there are roots to making some sense of the world we see around us, and the random, imaginary world quantum physics paints is correct, it must be found at the beginning of the quantum interpretation of things - we have to go back to its roots, and see what we can see. And, the single slit experiment, is just about the most basic, fundamental, and practical place to start.

When we look at the single slit experiment ( I would recommend Feynman's Lectures for anyone really interested in a lucid description that makes sense of the results of experiment, as long as you don't ask why - Feynman was wise enough to stick to results, not conjecture. But I should point out, even he starts with a 'double slit' experiment - you can always cover up one of the slits...), it shows us a glimpse of the shadowy world single particles of matter and energy live in. Common sense gives way to a realm of possibilities that make no sense. Yet, even in this topsy turvy world, there is one thing that we can understand and make use of.  Probability. Quantum mechanics is a physics of statistics. When dealing with a single particle, nothing much can be told about that particle. It is only when you begin to deal with large numbers of particles, order begins to emerge. For example, a Uranium nucleus is unstable. Eventually it will spontaneously break apart, but we can't know when this simple process will happen - because you can't do statistics with a single sample. Now, on the other hand, if you have a very large sample of Uranium atoms, you can begin to get some meaningful information about them:  like for a Uranium-238 atom, the half life is around 4.46 billion years, and the unstable atoms will eventually wind up as stable Lead-206. This is the kind of information quantum physics tells us. But statistics is a fickle thing - we can know that in 4.5 billion years half of your lump of  Uranium  has turned into lead, but we can't know which of the atoms have 'popped off' to make this happen.... you can sit there looking at a single uranium atom, and never know when it will decay. It could be in 10 minutes, or a trillion years. So, for single atoms of uranium, quantum physics is useless. Quantum physics gives almost no information about individual atoms. Yet they manage to do their thing anyway. And Quantum physics is one of our most powerful tools for obtaining information about the natural world.... yes it has its weaknesses. That is why we need to go all the way back to the very beginning, and that is the single slit experiment, and see if there is something there we have missed or misinterpreted. Well, the single slit experiment is all about shooting individual particles through a slit cut in gold foil, or some other aperture. The particle will either hit the material that makes up the slit, or travel on through, and get detected as it hits the sensors aligned all around the slit for just such a joyous occasion. It can't get any simpler than that, for sure. Even the results are simple. The detector records an area where particles make it through. Everywhere else, except for the oddball particle that gets scattered, there is a flat line. In other words, this is a simple experiment that has simple and explainable results -- it is well behaved, and that is *exactly* what we are looking for. However you design it, the results of the experiment, whether the particle makes it through the slit or not, is governed by simple statistics - by putting the particle emitter on a track and moving it, the odds of the particle making it through the slit change. You can control the probability of success or failure. This is information, and we can control it. That information is probability itself. This is why I brought up this ridiculously simple experiment and took so much time  on it -- if  nothing else, it is an example of simple quantum mechanics where we humans are able through simple means, to control the outcome of events by changing the nature of probability itself. This is very important - so important, I am going to write a bit more...