MathJakob said:
but there seems, for me, to be ambiguity with the word "observe".
Indeed there is in the literature - especially those of the populist bent - the professional literature such as textbooks for serious students (eg Ballentine - QM - A Modern Development) are quite clear though and it is that view I will explain.
QM is a theory about measurements that appear here in the classical commonsense macro world. That world is assumed to have all the usual things such as existing out there regardless of being observed by us, a tree makes a sound in a forest regardless of if anyone is there to hear it - no wideness there at all. Measurements are also taken in a somewhat general sense, and basically measurements are 'marks' in that commonsense macro-world that numbers can be assigned to if desired. In the double slit experiment that would be when the photon, electron or whatever you are using leaves a mark on the photographic plate, a screen that flashes or whatever.
You probably have read about Schrodinger's Cat, and some accounts can confuse again for the same reason - they do not take appropriate care explaining exactly what an observation is - you get the impression its when a conscious observer opens the box - it isn't. The observation is at the particle detector - that's where the essential quantum weirdness occurs. Everything is commonsense and classical from that point - the cat is never in some weird superposition of live and dead - it is alive or dead - period - regardless of if the lid is opened or not.
The real importance of Schrodinger's cat is not what some of the pop-sci press harp on about. Its simply this - how does this classical commonsense world emerge from the quantum world. We have assumed its existence - but really we would like an explanation for it.
A lot of work has been done on that issue and great progress has been made with the understanding of what is called decoherence:
http://en.wikipedia.org/wiki/Quantum_decoherence
'The discontinuous "wave function collapse" postulated in the Copenhagen interpretation to enable the theory to be related to the results of laboratory measurements now can be understood as an aspect of the normal dynamics of quantum mechanics via the decoherence process. Consequently, decoherence is an important part of the modern alternative to the Copenhagen interpretation, based on consistent histories. Decoherence shows how a macroscopic system interacting with a lot of microscopic systems (e.g. collisions with air molecules or photons) moves from being in a pure quantum state—which in general will be a coherent superposition (see Schrödinger's cat)—to being in an incoherent mixture of these states. The weighting of each outcome in the mixture in case of measurement is exactly that which gives the probabilities of the different results of such a measurement.
However, decoherence by itself may not give a complete solution of the measurement problem, since all components of the wave function still exist in a global superposition, which is explicitly acknowledged in the many-worlds interpretation. All decoherence explains, in this view, is why these coherences are no longer available for inspection by local observers. To present a solution to the measurement problem in most
interpretations of quantum mechanics, decoherence must be supplied with some nontrivial interpretational considerations (as for example Wojciech Zurek tends to do in his Existential interpretation). However, according to Everett and DeWitt the many-worlds interpretation can be derived from the formalism alone, in which case no extra interpretational layer is required.'
Einstein once asked Bohr is the Moon there when you are not looking, and in answer to that and similar questions, Bohr said - stop telling God what to do. The jokes on both of them though - we now know the moon is being observed all the time by its environment, and that in fact is how this classical commonsense world emerges.
I hasten to add issues still remain such as the so called factorization problem - and you will find them discussed on this forum, but we certainly know a lot more about the real issues with QM than we did - and its most definitely not the mystical nonsense you sometimes read about in popularizations such as What The Bleep Do We Know Anyway.
If you really want to understand the double slit experiment from the modern view check out Lenny Susskinds lectures on entanglement:
http://theoreticalminimum.com/courses/quantum-entanglement/2006/fall
Decoherence is a form of entanglement and these days it is thought by some, including me, entanglement is really the rock bottom essence of what QM is about:
http://arxiv.org/abs/0911.0695
Thanks
Bill