There are a number of interesting points to add to that "Heisenberg split" idea. First of all, it existed in classical mechanics also, it just never mattered to science. In other words, we never had a way to describe what happens to a system that is not observed, but we never found any evidence that what happens was different, so we simply made the simplifying assumption that it was not. It is perfectly good science to make such simplifying working assumptions, the only difference with quantum mechanics is that the targeted precision of the measurements is so spectacularly higher that we discovered the principle of "non-commuting measurements", which means that if you prepare a system in a state with a known value of some measurable, you might not simultaneously be able to know the value of some other measurable. In that light, we see that "measurement" happens at both ends of a scientific prediction-- it happens when you prepare the experiment, and again when you test the result.

This was unknown in classical physics, where it was thought that objects "carried with them" complete information about everything you could measure, but note that was only pure assumption in classical physics-- we simply did not have precise enough measurements to ever test if it was true. Physics made the simplifying assumption, but it should never have taken that assumption as seriously as it did for centuries (it was "magical thinking" to extrapolate a successful hypothesis to a level of precision that was untested). Ironically, many people see quantum mechanics as having a kind of "magical" quality not present in classical physics, but I argue that QM actually represents jettisoning a magical aspect of classical physics in a regime where it could actually be tested.

The second thing about the "Heisenberg split" I'd like to point out is that measurements applied from one side of the divide to quantum systems on the other side do not have some kind of "coincidental" effect of replacing the uncertainty of the possible outcomes with a particular one. Instead, the act of measurement is expressly set up to accomplish precisely that physical influence. So it's not a byproduct of a measurement that a quantum system goes from a "superposition state" to an "eigenstate" of the measurement-- the measurement is designed to create decoherence between the different eigenstates so that the system will behave as if "one or the other actually happened", which is just how classical systems behave. In short, measurement is the act of coupling quantum systems to classical systems so that they will behave classically and we can apply our standard scientific norms. Ironically, this is exactly the opposite from what many people (not Schrodinger, by the way) think happens when you connect a cat to a quantum system that can be used to kill the cat-- they think this puts the cat into a quantum state, when in fact the whole point of measurement is to get a quantum system to behave classically! If you could really put a cat in a quantum state that way, then measurement no longer serves its purpose, and suddenly we are awash in an ephemeral domain where science's norms fail and we have no idea what we are doing any more. We should only go there kicking and screaming, and so far there just isn't any good reason to.