The point of this exercise is to suggest a treatment of uncertainty in quantum theory that works for both position-momentum uncertainty and time-energy uncertainty. Elsewhere I have suggested that the former be treated in a (vaguely neo-Kantian) way that makes explicit reference to their relationship to various transformations (such as spatial translations and velocity boosts). Prima facie, this way of proceeding will not work for time and energy because of Pauli’s ‘theorem’, the alleged upshot of which is that there cannot be a time operator. However, recently it has been recognized that there are (at least) two important gaps in Pauli’s proof, and this recognition has led to two very interesting approaches to the representation of time in quantum theory. I will review them and endorse one of them as enabling an account of uncertainty that has more or less the same structure as my preferred account of position-momentum uncertainty.

This talk will be informal, though there are numerous formal results lying just beneath the surface. I will frame the discussion so that those unfamiliar with the technicalia can still appreciate what is going on. On the other hand, I am happy to delve into the technical details to whatever extent desired.