Basically, the article is about what most commonly would be called wave-function collapse. In quantum mechanics, there are two distinct ways a quantum state can evolve: one is the deterministic, unitary Schrödinger evolution, and the other is the indeterministic, nonunitary collapse; it is the latter the article is concerned with, and specifically, whether it is an objective event (and thus, by extension, whether or not the wave function is something ‘real’). Essentially, a collapse occurs when the wave function discontinuously evolves from a superposed state to one single, specific element of that superposition, i.e. when, say, an excited atom, which continuously evolves into a superposition of being decayed and being not-decayed, suddenly attains a definite state of being decayed.

The original idea was that this jump is an objective, non-observer dependent event: the quantum system really and spontaneously undergoes a sudden state change. Today, the tendency is often to just consider the wave function as something akin to a summary of the knowledge we have of a physical system, which is updated by measurement; the wave function collapse then is something akin to the Bayesian updating of a probability distribution.

For a simplified example, consider two boxes, in one of which there is a ball. You might describe this by a probability distribution, say 50% probability of being in box 1, and 50% probability of being in box 2. Now, you might be in a room which is very dimly lit, say there’s just one photon around at any given time. Eventually, the photon is going to scatter of the ball and hit your eye or a suitable detector, thus revealing its location, causing you to change the probability distribution to, say, 100% in box 1, 0% in box 2. Now, what has happened? Under a conventional interpretation of probability, you would say that you have simply *learned* the actual position of the ball – this is the detector-dependent model: had you not detected the photon, you would not have had cause to change the probability distribution. However, you might also try and claim that the probability distribution is something real in some way, and that the ball, prior to the scattering event, actually was not in any of the boxes as such, and that only the scattering has forced it into a definite state in an objective way.

What’s now being claimed is that they can exclude models where the wavefunction is treated in a way (roughly; the actual situation in the quantum realm is a bit more subtle) analogous to the latter case, thus favoring the ‘detector-dependent’ view.