I knew the other shoe was bound to drop. There are a number of different ideas about why we see only part of the wave. I'll give you a very brief description of some of the main ones.
1. It may be that the entire wave continues to exist but different portions of it 'decohere' and become quite separate. There would be a version of you in each decoherent part. Each version of you only sees its own part of reality. This is called the Many Worlds interpretation, and it is in some ways the most natural way to read quantum mechanics.
2. There may be a particular value for the coordinates of all things, but guided around in a very strange way by the wave. This is called the Bohm interpretation of quantum mechanics. It is 'non-local', a term which I can explain if you're interested.
3. There may be some as yet not described 'collapse' process, by which most parts of the wave disappear, following a non-linear random equation. This is also severely non-local, and not yet fully formulated. Such ideas are sometimes called 'macro-realist'.
4. There may be some way of denying the existence of the wave except as something which helps predict human observations. various ideas like this are known as 'the Copenhagen interpretation'.
I hope that gets you started.
(published on 06/22/08)