Reality doesn't change in a corner of the world just because you're thinking about it

Most Quantum Mechanics courses try to avoid imposing any kind of interpretation. This makes sense since the interpretation of QM is controversial but the mathematics is not. Unfortunately a little bit of interpretation always sneaks in through the back door. Whether you're being taught the Schroedinger Equation, Feynman path integrals, or QFT, the assumption is always that you can divide reality into That Which Is Under Study and the Rest Of The World... and that the nature of reality in the two parts is entirely different. If it's the Schroedinger Equation being taught That Which Is Under Study is represented by a state vector in a Hilbert Space that evolves with time; with Feynman Path integrals That Which Is Under Study is the set of all legal Feynman diagrams which complete the picture by joining neatly with the diagram for The Rest Of The World; if it's QFT then the nature of reality inside That Which Is Under Study is a single state vector which can be converted into a superposition for each field. In all of these the nature of reality inside That Which Is Under Study is a superposition, and the nature of reality in The Rest Of The World is classical.

Given that the division of reality into the two parts is completely arbitrary it is absurd to claim that the nature of reality inside the box is different to that outside. To do so implies an interpretation that treats human consciousness as having paranormal powers.

If we accept that it is not possible to teach QM without some interpretation leaking in then it's surely better to choose the interpretation at the outset and make it explicit. And I think it should be a starting principle that a valid interpretation cannot allow for reality to have completely different rules inside and outside of arbitrarily drawn spacetime boxes. Given that we cannot rid ourselves of the necessity that the inside of the box is in a superposition let's assume that the outside is too and see where that leads us:

Every legal Feynman diagram for the universe must be physically real (although they don't all carry the same weight).  Let's create a spacetime box (think of it as a shoe box which pops out of thin air and disappears some time later). In a given diagram the outside of the box contains many things. For example it contains your brain weaving a worm-like path through spacetime, for some of which it's trying to guess what's going on inside the box.  But since every universal Feynman diagram is real, a single one describing just the outside of the box can be completed in infinitely many ways by extending it to the inside.  Therefore the brain on the outside must describe the inside as a superposition to be accurate, otherwise it would have to be wrong in most of the completions!

This explains why we need to - mathematically - describe the inside of the box as a superposition whilst describing the outside classically, even though the boundaries were totally arbitrary. It is an illusion resulting from the fact we live in a multiverse.

What about probabilities?

Each completion to the inside of the box carries a weight known as the probability amplitude. To get the overall probability amplitude for the boundary of the box you sum the probability amplitudes of all the possible completions (which may add up to zero since probability amplitudes are complex numbers with phases as well as magnitudes). Let's see why this boundary amplitude is important.

Place the box (which we'll call Box 1) inside another called Box 2 and call the Feynman diagram fragment which connects the two $W$. Let $w$ be the probability amplitude of $W$ and $z_i$ the probability amplitude of the $i$th completion into Box 1. If $\sum z_i = 0$ then $\sum w z_i = 0$ too. But $w z_i$ is just the probability amplitude for the diagram combining $W$ with its $i$th completion into Box 1. This means that if That Which Is Under Study is the contents of Box 2, we can ignore any Feynman diagram that contains a Box 1 boundary with amplitude zero as these add nothing to the amplitude of any Box 2 boundary. I.e. we can treat those Box 1 boundaries as if they never happen!