Is Quantum Mechanics a New Theory of Probability?

Abstract

Some physicists but many philosophers believe that standard Hilbert space quantum mechanics faces a serious measurement problem, whose solution requires a new theory or at least a novel interpretation of standard quantum mechanics. Itamar Pitowsky did not. Instead, he argued in a major paper (Pitowsky, Quantum mechanics as a theory of probability. In: Demopoulos W, Pitowsky I (eds) Physical theory and its interpretation. Springer, Dordrecht, pp 213–240, 2006) that quantum mechanics offers a new theory of probability. In these and other respects his views paralleled those of QBists (quantum Bayesians): but their views on the objectivity of measurement outcomes diverged radically. Indeed, Itamar’s view of quantum probability depended on his subtle treatment of the objectivity of outcomes as events whose collective structure underlay this new theory of probability. I’ve always been puzzled by the thesis that quantum mechanics requires a new theory of probability, as distinct from new ways of calculating probabilities that play the same role as other probabilities in physics and daily life. In this paper I will try to articulate the sources of my puzzlement. I’d like to be able to think of this paper as a dialog between Itamar and me on the nature and application of quantum probabilities. Sadly, that cannot be: by taking his part in the dialog I will inevitably impose my own distant, clouded perspective on his profound and carefully crafted thoughts.