Does the collapse of the wave function depend on the observer? Reading various articles on quantum physics paradoxes, I found the following interesting statement:

When a measurement is carried out inside of a closed lab, such a measurement leads to a collapse for inside observers, but it does not lead to a collapse for outside observers.

The quote comes from Jeffrey Bub - Understanding the
Frauchiger-Renner Argument.
I personally think this might be wrong in the case that the outside observer knows that a measure was made at a certain time inside the lab (even if he doesn't know the result of that measure).
I would also appreciate if you could share your thought about.
 A: It's unclear when, or if, wave function collapse happens. What is clear is that everyone agrees in principle on what measurements occur and what their outcomes are.
The only situations I can think of that resemble "observer-dependent measurements" are:

*

*In the many-worlds picture, generally different measurements occur in different worlds (and of course the outcomes are different). However, everyone in a world agrees in principle on all measurements and their outcomes. People inside a sealed lab are in the same world as people outside.


*If you do something that resembles a measurement but is perfectly thermodynamically reversible, then in principle you can undo it. You could imagine that a thermodynamically reversible conscious being (AI running on a quantum computer) makes this sort of quasi-measurement of a quantum system, becomes consciously aware of the result, then reverses it (which necessarily includes erasing its own memory of what it saw), leaving the system in its original unmeasured state. That could be called a measurement, and could be called private to that being.

Edit: I previously said here that I thought Bub's paper was wrong. That argument ignored the fact that the measurement in the $\{\leftarrow,\rightarrow\}$ basis is supposed to be a Heisenberg-picture measurement of the system at an earlier time.
I've now read Frauchiger and Renner's original paper, which seems to be consistent with Bub's. I still think it's wrong, for a more complicated reason, which I wrote up in another answer.
A: When we say that a quantum mechanical object, such as a particle, is subjected to a measurement, we mean that it is interacting in some way with other particles, namely those that form the measuring device. To ascribe some special quality to a measurement, as opposed to any other form of interaction between particles, seems obvious nonsense. Particles interact without any necessity for observation or measuring devices.
Take, for example, the two slits experiment with photons. Imagine the positions of the incident photons being determined by recording the points of contact on a photographic plate. Do you think the marks on the photographic plate would not be there without an 'observer' having been present? No, that is clearly untrue. The localisation of the photon happens when it interacts with one of the molecules that comprises the photo-sensitive coating of the film- ie, when the photon interacts with another quantum object. Observers have nothing to do with the process.
A: Wave collapse is to a large extent a matter of interpretation. In MWI, there is no wave function collapse. Rather, the observer becomes entangled with the state, and the combined system has a component in which the observer sees one result, and other components where the observer sees other results.
In the Copenhagen Interpretation, "observation" doesn't require "seeing" the result in the traditional sense. Rather, it occurs when the thing being measured affects the observer enough for them to become entangled, regardless of whether the observer is aware of how it has affected them. So unless this "closed" system is able to completely isolate the measurement in a quantum mechanical sense, the wavefunction will collapse for the "outside" observer.
In practice, it's impossible, at least at our current level of technology, to isolate more than a tiny number of particles from the rest of the universe. But if we're just doing a thought experiment and imagining that we have isolated a system, then the Copenhagen Interpretation does get a bit funky. The  Schrödinger's cat thought experiment is such an example. According to the Copenhagen Interpretation, there is no collapse of the wave function, and the cat is in a superposition of alive and dead. If we were to put human experimenters in with the cat, those experimenters would be in a quantum superposition of observing the cat as alive and observing it as dead. This is where CI gets problematic, since there seems to be a contradiction between the wavefunction collapsing for the inside observers, but not for the outside.
A: The measurement problem is one of the most relevant open problems of quantum mechanics. What is a measurement? What constitutes an observer and what doesn't? Is the wavefunction a physical object (ontological) or just a mathematical construct that represents our ignorance of the state of a system?
Trying to answer these questions has produced a multitude of interpretations of quantum mechanics.
The Copenhagen interpretation is the most famous. It basically states that small things are quantum, big things are classical, and when a small thing interacts with a big thing there is a measurement and a collapse of the wave function for everyone, while when small things interact with each other the just entangle and evolve unitarily, without any collapse. The problem with this interpretation is that it doesn't say where we should draw the line between big and small.
The Many World interpretations on the other hand treats everything (big and small things) as a quantum system. Everything evolves unitarily, there is never any collapse. The drawback is that this means that you are a quantum system, and so you can be in a superposition. And this is difficult to reconcile with the idea of a "self".
Other interpretations, like quantum Bayesianism advocate that a quantum state is just a representation of the degree of belief a person may have about the outcome of some measurements. The wavefunction is therefore subjective and not an objective physical object. According to quantum Bayesianism, the collapse of the wavefunction is just a Bayesian update of the beliefs of the observer. In this sense, a wavefunction may collapse for me and not for you.
As you can see, the question of the collapse of the wavefunction is far from settled. After a measurement it may collapse for everyone, just for someone or it may never collapse at all. If this seems like speculation to you, and not scientific facts, you are right. As of today, nobody has been able to experimentally distinguish between these (and others) interpretations.
What Frauchiger and Renner are trying to do in their famous paper is to devise a thought experiment that may be able to rule out some of these interpretations, by showing a contradiction between a set of well accepted assumptions.
A: I would suggest that collapse of the wavefunction is a useful approximation, not a mathematical absolute.  Prallax has given a good summary of the positions.  Under this view, a big thing (in the Copenhagen interpretation) is big enough that you will never see superposition effects.  The distinction between big and small is not sharp, it is dependent upon how long you will observe the system.  If you don't observe it for long, improbable events will not (likely) happen and can be ignored.  It agrees with Many Worlds but points out that over the period of observation all the worlds agree on what will happen.  If there are different results with reasonable probability to happen, the wavefunction did not collapse.
There is a classical analog in two body collisions.  If one ball comes in and hits another ball, if there is a wide disparity between the masses of the balls we can ignore the velocity change of the larger ball and ignore the momentum transferred to the large ball.  How big the disparity has to be for this to be a good approximation is dependent on how accurately you are modeling/measuring the system.  Similarly in orbital dynamics, if the satellite is negligible in mass compared to the primary, we assume the primary is fixed and can absorb any amount of momentum.  There is no sharp limit, just the accuracy of the approximation that is acceptable.  Collapse of the wavefunction says that after the interaction (measurement) the state is an eigenstate of the value measured, which means that the measurer is not a quantum object.  Of course the measurer is a quantum object, but the classical approximation may be good enough for the purpose at hand.
A: There is no such thing as wave function collapse. If there were, the Schrödinger equation would be wrong.
Measurement requires a measurement apparatus with multiple orthogonal states. Each of these states is entangled with part of the wave function of the system to be measured. These parts are what you could call collapsed wave functions. They are collapsed with respect to the system without the measurement apparatus.
Physically, adding a measurement apparatus to a physical system alters the sytem in a way that can be called 'collapse'. However there is no such thing as an act of measurement that leads to a change in the wave function let alone cause its collapse.
