The double slit experiment, when applied to single photons traveling one by one through a double slit barrier, proves that there is self interference going on. It also proves that photons manifest themselves as particles, rather than waves, and that the wave-phenomenon that causes the self interference is vastly larger than the photon itself.
The two slits made in the barrier can be far enough apart for us to be seen as separate slits with our naked eye. Photons on the other hand, are far smaller than an electron, which is so small that we have never been able to see it, even with the most powerful microscope. The wave-phenomenon we are talking about is in other words something enormous relative to the photon.
We know that photons manifest themselves as particles by the way they appear on the receiving wall of the setup. Initially, no pattern can be seen. There are only random dots. Each dot represents a single photon, which burns a tiny mark in the light sensitive wall. Gradually, a pattern starts to appear. Certain areas get more hits than other areas. And finally, when we have a thousand dots on the screen, we see a smooth, uniform wave pattern.
All of this can be calculated from present theory which holds that all particles exist as both particle and wave. They can therefore interfere with themselves. But how exactly can this happen without breaking the speed limit of light? Nothing can travel faster than light, yet the wave aspect of photons can cross relatively vast distances, zip through barriers, and come back with the required information to make a change of direction in strict accordance to the dimensions of the double slit setup.
A more common objection to particle-wave duality is that it leads to all sorts of strange effect where things are in more than one place at the same time. This in turn leads to the weird hypothetical case of Schrödinger’s cat, which finds itself neither dead nor alive. One way to get around this problem is to invoke an aether that has the properties of a standing wave. Another way to get around it is to invoke a pilot wave that accompanies all particles. We can also combine these ideas, making the pilot wave a disturbance in the standing wave of the aether. In this way, we separate the wave property of particles from the particles themselves. Things become more definite, and Schrödinger’s cat dies or lives without us needing to check on it.
However, this still leaves us with the faster than light information problem. We still need to explain how a particle that travels at the speed of light can get information about things that are located at a relatively vast distance from itself.
One way to solve this problem is to use a strict particle model in which energetic particles are bigger than less energetic particles. When we combine this with an aether consisting of very low energy photons and neutrinos, we come to the conclusion that particles in the aether can travel in straighter lines than their more energetic counterparts. They can cross bigger distances in a shorter time, because they take fewer turns on their way.
This particular solution yields a pilot wave with attributes similar to a pressure wave in water. A photon traveling through one of two silts can be viewed as a boat, passing through one of two openings to a harbor. The boat is hit by its own waves, coming through both openings as it enters the bay. The smaller the boat, the more affected it is by its own waves, just like red photons are more affected by their pilot waves than blue photons. Red photons produce wider interference patterns than blue photons due to their smaller size.
This demonstrates that a strict particle model solves all the problems related to the double slit experiment. Things stay in a defined state throughout the process, and no information is traveling faster than light.