Simon Saunders (University of Oxford): ‘Quantum mechanics and intrinsic probability’

This is a Bristol-London-Oxford-Cambridge (BLOC) Philosophy of Physics event.

Abstract: I examine the concept of interval or imprecise probability as applied to any admissible ensemble of microstates, in which the probability of a projector P in an ensemble is bounded by the frequency of +1 eigenstates (lower bound) and 0 eigenstates (upper bound). Given a Hilbert space H and quantum state |psi>, an admissible ensemble is defined  by (any) equi-amplitude decomposition of the state (so the ensembles are necessarily finite). It is a simple matter to see that all such interval probabilities for fixed |psi>, H, and P are mutually consistent, and that in the limit of large ensembles, they approximate the Born-rule quantity <psi|P|psi>.

This account of probability is synchronic, so independent of the dynamics, and independent of the basis, and of whether any experiment is performed, or any evaluation by any agent. So it plausibly counts as ‘intrinsic’. I also consider its implications for the Everett interpretation, and its connection to Gibbs’ analysis of probability, which it closely follows.