What is the difference between the collapse of the wave function and decoherence?

I'll start off by clarifying this question by addressing the difference between state vector (wave function) reduction and state vector collapse. This will also clarify the complimentity principle.

Think of a state vector as containing possible locations of a photon, and then think of the double-slit experiment. If there is no attempt to gain which-path information, you will get an interference pattern on the detection screen. In this case, the wave function travels through both slits, interfering with itself and affecting the probability distribution of its location.

Now let's say you try to find out which slit the photon "really" went through. I am going to oversimplify, but let's just say there are non-invasive measurements that can be done to do this (using polarization), so the effect on the photon isn't like the typical description of "well if you bounce a particle off it to measure it, then you affect it." And by attempting to find out this information in a non-invasive way, you then find the photon going through one or the other slit and a diffeaction pattern on the detection screen.

So what happened? Most would say that the wave function collapsed, but this is not correct. What happened is that our end observation was now the result of a system that involved another device that gave us information as to which path the photon would follow, thereby restricting possible locations along the photons path. This is decoherence (interaction that limits potential locations), and what occurred was not collapse but state vector reduction. The possible locations were limited but did not collapse to one trajectory through the single slit. It still was a wave (a wave packet) traveling through the single slit. It

**acted** more like a particle, but is still a wave and described by wave equations.

So decoherence is state vector reduction, or restriction on possible locations through interactions. State vector collapse is what you get at the end of the experiment when the photon hits the detection plate. In this case, there is a single position that resulted.

It is important to note that the observation (photon hitting detection plate) creates the history. Now we will have to address what an observation is.