It is difficult to discuss quantum physics without getting lost in philosophy. All of science is based on the principle of causality. We use models to better predict future outcomes based on observations of cause and effect. Electrons are a relatively new creation, which most people believe exist in a universe that obeys cause and effect. The photovoltaic effect was one of four of Albert Einstein's famous 1905 papers and was the foundation of quantum theory. The idea that energy was quantized was the most instantly impactful work Einstein produced. During this era the electron was determined to be a point particle: it has no axis to rotate on, it is not a physical thing with dimensions that matter. Every year scientists devized more radical experiments and extended the implications of quantum physics. Einstein and others were unhappy with the results that were amassing, notoriously saying "God does not play dice[!]".
Einstein loathed the results the way that quantum theory was evolving. He was famously an atheist, in the previous quote its safe to assume that "Nature" is an effective substitute for God. The idea that observable pairs like position and momentum can't be observed without uncertainty in the counterpart does not coincide with the idea of a deterministic universe. In an effort to disprove the logical outcomes of the theories that were evolving Einstein and his colleagues Boris Podolsky and Nathan Rosen devised an elaborate thought experiment. The three scientists, in a desire to show the incomplete nature of Quantum Mechanics created the most inexplicable phenomena in nature - quantum entanglement.
By taking two particles (call them A and B), and establishing a "spin singlet", one can create an entangled state. By measuring A and determining it to be an "up" (+1/2) or "down" (-1/2) we know that the other particle must be in the state that adds up to 0. Angular momentum is conserved. Einstein, Podolsky and Rosen thought this must be impossible since the speed of light is the speed limit of the universe! Remember, this is Einstein we're talking about.
https://www.youtube.com/watch?v=qAMoWEwK-4A
Well, it turns out that this is actually what happens! Modern science has accepted quantum entanglement to be a part of our reality. Bell's Theorem arrived and through the use of entanglement, proved that no hidden mechanism existed for predicting the behavior of electrons until they were measured.
https://www.youtube.com/watch?v=zcqZHYo7ONs
This video did a fantastic job about explaining EPR and Bell's Theorem, with the core takeaway that electrons and their wavefunctions make no damn sense. After creating the EPR paradox, Einstein called this "spooky action at a distance". This is when I get to pitch my science fiction idea. An entangled state is predicated on the belief that all observations on wavefunction will collapse the wavefunction. Observation tells us what spin is up and what spin is down and the fun is over.
What if its possible to observe a wavefunction, just to prove that its there and that it hasn't collapsed? As far as I can tell, proving that this possible or impossible has yet to happen. If it is possible, this really screws with the core principle of cause and effect, here's an example as to why:
Take the stalwart experimental actors, Alice and Bob. Alice and Bob work together to create two devices, one containsing entangled particle A and the other B. Each box has our theoretical 'wavefunction detector', that polls at the highest possible frequency to see if the wavefunction has collapsed. If the wavefunction collapses this detector will emit a signal COLLAPSED as soon as physically possible. The box for particle A has a button that reads COLLAPSE, upon clicking the wavefunction is forced to collapse by some intrusive measurement. For the sake of argument lets agree that these devices are not susceptible to errors.
When Alice and Bob create this device, they devise a scheme to get rich quick. Alice is going to put her device near the New York Stock Exchange, while Bob goes to an exchange that is far away, but overlaps in hours with the Exchange, like the London Exchange. At 9am in New York for Alice, 2pm London Time for Bob, they identify the most volatile traded stock. On every hour they pick the most volatile stock, and Alice communicates to Bob that if she presses COLLAPSE, he should short that stock, because it will hit his target short decrease that leads to some small margin of profits. If no collapse happens, they repeat the process on the hour until trading hour overlap closes. After a few days of trying it eventually happens and Bob and Alice short a bunch of stock and make a lot of money before anyone in London could have possibly known that the stock went down in New York.
The ramifications here seem to violate the principle of cause and effect. Bob acted on information that seemed to come before it ever actually happened in his 'light cone'. Viewing it this way violates the principle of cause and effect. But maybe the cause of Alice and Bob's winnings wasn't the act of reacting to the collapse of the wavefunction, but the quantum promise that they made before reacting to the collapse. Cause and effect seems to delve into more philosphical problems than hard science.
That's all I've got, but I think there are plenty of other thought experiments that can make this a pretty wild idea to think about. As an aside, isn't it so damn badass that Einstein created one of his least favorite aspects of science in an effort to disprove the results of Quantum Mechanics? Science is brutally unforgiving in that regard, and I think its so impressive to strengthen theory in an effort to negate it.
I think this is a pretty good explanation for why it's physically impossible to passively observe a wave function and alert when it collapses. Following the Copenhagen interpretation (which is the implicit in most discussions about the 'collapse' of the wave function) any observation or measurement would cause a collapse. So your 'collapse detector' would have to be doing something like observing the wave function on some small interval and reporting back if the wave function it observed was a collapsed wave function. But each time it makes that observation, it would cause a collapse. So it'd basically always return True and give no information about the other entangled particle.
It's also probably worth noting that "the collapse of the wave function" isn't really a well-defined physical phenomenon. There are a small number of physicists like Roger Penrose who are working on theories of the collapse of the wave function and taking the Copenhagen interpretation as literal, physical behavior. He's trying to discover the mechanism of the process of collapse. But as it stands today we don't have any physical evidence that wave functions collapse when 'observed' (and 'observation' here is also really hard to define.) And we don't have any real information about what that would mean.
One school of thought that tries to deal with this is Everetian interpretation of QM (the Many Worlds interpretation) which says that wave functions don't collapse. They just branch. If you're on branch A, you see the result A, if you're on branch B you see the result B. But there's nothing in Schoedinger's equation (which is, so far as we can tell, always right) that says anything about collapsing wave functions. It only describes evolving wave functions. And we don't have any theories whatsoever that 1) describe the collapse of a wave function and 2) make a prediction. So in a sense, the Everetian interpretation is the most parsimonious. We only include concepts which are part of our theories (wave functions) and don't tack on something else after-the-fact (collapse).