Is the double slit experiment an example of entanglement when it seems as if the photon is going through both slits? Or put another way, is it at this stage when we attempt measurement we see a photon on one side affect the photon on the other side? Do entangled particles have to be made first to show entanglement or is the double slit experiment in itself showing entanglement? Also, what else in nature collapses the wave function?
I'll take a stab at this though my answer may be incomplete / fuzzy:
The double slit experiment demonstrates wave-particle duality, not entanglement. It shows that a "particle" can interfere with itself, demonstrating that it really acts as a wave in this instance.
Entanglement is correlation of measurements of particles (most commonly) that were generated under conditions that require two values to be coordinated because of a conservation law. Which value is taken is random, but the other value will always complement the first measurement like the opposite side of a coin.
The wave function only collapses when "observed." Meaning, unless it has to have a definite value at a moment in time, a value exists as a superposition of potential values (it has more than one value at once). We don't yet know what the "observed" part means on a deeper level.
The double slit experiment actually has nothing to do with entanglement by itself. Photons are generated in processes that are quantum in nature, and their direction that they come out in is subject to some randomness. Photons will then be in a state of superposition with respect to their direction. When a photon goes through the double slit, it goes through both since it's in superposition - one photon has both momentums, corresponding to each slit. The two superposition states of the one photon interfere with each other.
The interesting thing is when two photons go off in different directions and one of them goes through the double slit (call it photon DS for double slit). If DS is in a superposition state, it will go through both slits and interfere with itself, which determines the probability of it being detected on the screen in various places. However, if the other photon is detected in such a way as to measure its momentum, that will "collapse" the wave functions of both photons, thus making a which-way measurement and changing the probability of where DS will be detected.
Here's a longer explanation: