Appendix

Realist Propositions and the Axioms of Quantum Mechanics

Realist Propositions (Chapters 2 and 3)

Realist Proposition #1: The Moon is still there when nobody looks at it (or thinks about it). There is such a thing as objective reality.

Realist Proposition #2: If you can spray them, then they are real. Invisible entities such as photons and electrons really do exist.

Realist Proposition #3: The base concepts appearing in scientific theories represent the real properties and behaviours of real physical things. In quantum mechanics, the ‘base concept’ is the wavefunction.

Realist Proposition #4: Scientific theories provide insight and understanding, enabling us to do some things that we might otherwise not have considered or thought possible. This is the ‘active’ proposition. When deciding whether a theory or interpretation is realist or anti-realist, we ask ourselves what it encourages us to do.

The Axioms of Quantum Mechanics (Chapter 4)

Axiom #1: The state of a quantum mechanical system is completely defined by its wavefunction. This is the ‘nothing to see here’ axiom. The wavefunction has everything you need so don’t bother to look for some deeper level of reality that lies beneath it.

Axiom #2: Observables are represented in quantum theory by a specific class of mathematical operators. This is the ‘right set of keys’ axiom. To get at the observables, such as momentum and energy, we need to unlock the box represented by the wavefunction. Different observables require different keys drawn from the right set.

Axiom #3: The average value of an observable is given by the expectation value of its corresponding operator. This is the ‘open the box’ axiom. It is the recipe we use to combine the operators and the wavefunction to calculate the values of the observables.

Axiom #4: The probability that a measurement will yield a particular outcome is derived from the square of the corresponding wavefunction. This is the Born rule, or the ‘What might we get?’ axiom. Applying the Born rule to a superposition doesn’t tell us what we will get from the next measurement.

Axiom #5: In a closed system with no external influences, the wavefunction evolves in time according to the time-dependent Schrödinger equation. This is the ‘how it gets from here to there’ axiom. Note that there’s no place here for the kind of discontinuity we associate with the process of measurement. As von Neumann understood, accepting this axiom forces us to adopt a further (but related) axiom in which we assume that a wavefunction representing a superposition of many measurement possibilities collapses to give a single outcome.