Wavefunction collapse is a generator of knowledge: it is not so much a process that gives us the answers, but is the process by which answers are created. The outcome of that process can’t, in general, be predicted with certainty, but quantum mechanics gives us a method for calculating the probabilities of particular outcomes. That’s all we can ask for.
Everything that seems strange about quantum mechanics comes down to measurement. If we take a look, the quantum system behaves one way. If we don’t, the system does something else. What’s more, different ways of looking can elicit apparently mutually contradictory answers. If we look at a system one way, we see this; but if we look at the same system another way, we see not merely that but not this. The object went through one slit; no, it went through both. How can that be? How can ‘the way nature behaves’ depend on how – or if – we choose to observe it?
[Q]uantum objects present us with a choice of languages, but it’s too easily forgotten that this is precisely what it is: a struggle to formulate the right words, not a description of the reality behind them. Quantum objects are not sometimes particles and sometimes waves, like a football fan changing her team allegiance according to last week’s results. Quantum objects are what they are, and we have no reason to suppose that ‘what they are’ changes in any meaningful way depending on how we try to look at them. Rather, all we can say is that what we measure sometimes looks like what we would expect to see if we were measuring discrete little ball-like entities, while in other experiments it looks like the behaviour expected of waves of the same kind as those of sound travelling in air, or that wrinkle and swell on the sea surface. So the phrase ‘wave–particle duality’ doesn’t really refer to quantum objects at all, but to the interpretation of experiments – which is to say, to our human-scale view of things.
[T]he wavefunction of the electron in [a] box can penetrate into the walls. If the walls aren’t too thick, the wavefunction can actually extend right through them, so that it still has a non-zero value on the outside. What this tells you is that there is a small chance – equal to the amplitude of the wavefunction squared in that part of space – that if you make a measurement of where the electron is, you might find it within the wall, or even outside the wall.
[A]tomic nuclei are pretty hard to peer into. But that’s not the root of the problem. It’s that we simply can’t, for quantum processes, talk about a historical progression of events that led to a given outcome. There’s no story of how it ‘got’ to be that way.
The wavefunction of superposed states doesn’t say anything about what the photon is ‘like’. It is a tool for letting you predict what you will measure. And what you will measure for a superposed state like this is that sometimes the measurement device registers a photon with a vertical polarization, and sometimes with a horizontal one. If the superposed state is described by a wavefunction that has an equal weighting of the vertical and horizontal wavefunctions, then 50% of your measurements will give the result ‘vertical’ and 50% will indicate ‘horizontal’. If you accept Bohr’s rigour/complacency (delete to taste), we don’t need to worry what the superposed state ‘is’ before making a measurement, but can just accept that such a state will sometimes give us one result and sometimes another, with a probability defined by the weightings of the superposed wavefunctions in the Schrödinger equation. It all adds up to a consistent picture.