It is commonly taught in introductory QM courses that in order to get to know the position or momentum of a particle, be it by "sending a photon" or similar experiments, the measurement necessarily disturbs the system. What I do not like about these thoughts experiments is that they all assume that the system has some position/momentum value unknown due to some uncertainty (denoted by $\Delta x$ and $\Delta p$). They never consider the case of the system being in a superposition of eigenstates.
Anyway, let's suppose that it's true that in QM a measurement necessarily disturbs the system. I.e. $\Psi$ is necessarily modified between the moment before the measurement and the moment after the measurement. Let's say we make a measurement of a property whose corresponding operator $\hat A$ commutes with the Hamiltonian of the system $\hat H$. Let's say that we're lucky enough to get to know that $\Psi$ "collapsed" into a single non degenerate eigenstate of the operator $\hat A$. We can safely say that before the measurement $\Psi$ was in a superposition of eigenstates of $\hat A$ and that after the measurement it was equal to some eigenstate of $\hat A$, we have perturbed the system. But now if we make another measurement, we know for sure that the result will be exactly the same, because $\hat A$ commutes with $\hat H$. Does this mean that now making any new measurement does not perturb the system anymore? It doesn't make any sense!
I've read from Lubos Motl, John Reenie, Sidney Coleman, David Mermin, London, Zurek, etc. that $\Psi$ is subjective, i.e. it is a representation of the information one knows about the system. Two observers need not to agree on $\Psi$ if they do not have the same information on $\Psi$. It does make sense to me, but then there is something that I do not understand with the description in the previous paragraph. Let's imagine that the description above is from an observer X. An observer Y had made a one measurement before X, that X was unaware of. So Y had perturbed the system and according to the description of Y, $\Psi$ "collapsed" when he made his first measurement. It also means he disturbed the system at that first measurement, not on the ones from X. But from X's viewpoint, it is himself who collapsed his own $\Psi$, and thus perturbed the system in his first measurement. This contradicts Y viewpoint.
While I can buy the fact that $\Psi$ depends on the observer, I find harder to buy the fact of "disturbing the system" is also subjective.
Hmm, after all if "perturbing the system" means that $\Psi$ is changed between the moment before a measurement is performed and the moment after the measurement is performed, and if $\Psi$ is subjective, then it is no wonder that "perturbing the system" is an arbitrary statement. That is quite strange and in sharp contrast with classical mechanics. It would mean that "disturbing the system" is also subjective. I now think that this is the case, i.e. that perturbing the system is not a universal feature, but it is entirely related to the knowledge of each observer and need not a universal agreement on. It is entirely subjective.
I would love some comments, confirmation or infirmation of what I wrote. And if Lubos Motl could write some comment I would be immensely glad.