With an exam imminent, I’ve had a queue of students outside my door wanting help with their quantum mechanics. This semester, they’ve come across the Schrodinger equation and the wavefunction for the first time and, unsurprisingly, some are struggling to grasp it. "But what IS the wavefunction?", they say. "How do you derive the Schrodinger equation?"
Very good questions. While we use Schrodinger’s equation quite happily to make predictions (and extremely accurate ones at that) about the behaviour of things at small length scales, a physicist won’t be able to give you a decent answer as to why it works. There are hand-wavy explanations about wave-particle duality and energy balance, but the honest answer to the questions "What is the wavefunction?" and "Why does the Schrodinger equation work?" is I don’t know.
They are questions that philosophers have seized upon, and have resulted in many ‘thought’ experiments, such as the famous Schrodinger’s cat, who is neither alive or dead, and the Einstein Podolsky Rosen ‘paradox’. How does the wavefunction correspond to reality?
In the May Physics World magazine (unfortunately not accessible free online), a great article from Jon Cartwright explores some of the thinking and possibilities for ‘untangling’ the ‘uncertainty’ in all this (puns intended). What are the possibilities for interpreting the wavefunction? Four are listed, broadly along the lines below.
1. Quantum mechanics just happens to be descriptive of the real world, but it’s not a real thing in itself. Reality happens only when we look at something. It’s a recipe for making predictions. (This is part of the ‘Copenhagen Interpretation’ of quantum mechanics – from Niels Bohr and others). For a physicist, there’s something deeply disturbing about this interpretation since it is not a realist theory – reality only exists when we are observing it. The problem is that it has worked really well.
2. Quantum mechanics does describe reality, but the wavefunction is just describes probabilities of finding answers. There’s something deeper underlying it. (Einstein’s view).
3. Quantum mechanics and the wavefunction are both real things, but that’s not the entirety of reality.
4. Quantum mechanics and the wavefunction are both real, and that’s all there is folks.
The first two situations are considered ‘epistimic’ interpretations, since they are concerned with knowledge of things. The second two are considered ‘ontic’ interpretations, since they are concerned with reality. (See my rant about social science for more about reality). The key question is "Are wavefunctions real?" Are they things in their own right, or are they simply descriptive?
The article explains that there’s mounting evidence for the ontic case. The Pusey, Barrett and Rudolph theorem (something I won’t try to elucidate here) says that the only way for quantum mechanics to be epistemic if for it to be wrong. And given that it appears to be right in all its experimental predictions, it looks as if we may have to abandon the epistemic view. So the wavefunction may well be real (hooray!), and both Einstein and Niels Bohr are wrong. In one way, that will make most physicists happy (reality is back), but one has to ask now what sort of reality is it? Given that option 4 includes Hugh Everett’s ‘many worlds’ interpretation of quantum mechanics, in which every possible outcome is played out in an array of parallel universes (great for science fiction writers but freaky for everyone else – I’ve always thought this viewpoint as laughable) there might be some more discomfort to come.
Though it might be reassuring for my students to know that out there somewhere is a universe in which they have straight ‘A+’ grades in their exams.