let's define 'a measurement device' as a system which is highly sensitive to the eigenstate of an observable. The sensitivity is quantified let's say by how irreversible and grand the small changes in the eigenstate result in the large scale, classical system's future. A wavefunction collapses when it interacts with such a device.

This seems like a simple and necessary definition, right?

But there's a problem with this interpretation. How do we calculate the 'sensitivity' of a given device, without first knowing when the wavefunction collapses? For example, in the double slit experiment, let's say that the wavefunction collapses into a sharp peak when it passes the slits. Then surely a small change in this eigenfunction will result in large changes in what happens at the screen? If the wavefunction collapses at the slits, then we can draw a midway line at the screen, and effectively use the screen as a which way device. However, since it does not collapse, we know that the screen is therefore not sensitive to the eigenstate of the wavefunction at the slits. Therefore the wavefunction should not collapse at the slits rather than at the screen.

The question is, this is clearly a case of circular logic. How do we know a priori what device will collapse the wavefunction when it passes.

• Can you focus on one clear question? – Norbert Schuch Sep 2 at 18:43
• which part are you saying is circular logic? In the double-slit example, you observe an output that is not compatible with the photons collapsible at the slits, thus you know/observed that it didn't collapse there but rather at the detector at the end. What's circular about this? – glS Sep 4 at 9:35
• i don't even think this question makes sense. just being silly – BIGFATNIH Sep 13 at 23:09