A Note on Deutsch’s “Quantum Theory of Probability and….pdfVIP

A Note on Deutsch’s “Quantum Theory of Probability and Decisions” Malcolm R. Forster University of Wisconsin-Madison Draft, June 12, 1999 ABSTRACT: David Deutsch has a forthcoming article called “Quantum Theory of Probability and Decisions in which he claims to derive the standard probabilistic interpretation of the wavefunction from non-probabilistic considerations. In this note, I try to develop his argument in a classical context, to see whether the same ideas can generate probabilistic conclusions from non- probabilistic assumptions in a more general way. While my answer is negative, the attempt pinpoints the parts of Deutsch’s quantum mechanical argument that must rely on special features of the formalism (assuming that his proof is correct). 1. No Probabilities In, No Probabilities Out? You cannot derive an ‘ought’ from an ‘is’. And I believe that it was Popper (1959) who once said, in response to those who think that randomness can be defined non- probabilistically, that one cannot derive a probabilistic conclusion from non-probabilistic premises. Yet this is exactly what Deutsch (to appear) claims for quantum mechanical probabilities. Historically in the development of quantum theory, the Schrödinger equation came first, and Born’s probabilistic interpretation of the wave function came later, as an additional postulate. If Deutsch is right, then from a few reasonable axioms, that any rational agent must act as if Born’s postulate is true. More specifically, Deutsch considers each wavefunction, together with a particular experimental setup (formally, a