The World According to de Finetti: On de Finetti's Theory of Probability and Its Application to Quantum Mechanics [chapter]

Joseph Berkovitz
2011 Probability in Physics  
Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of probability and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that degrees of belief be coherent, and he argued that the whole of probability theory could be derived from these coherence conditions. De
more » ... interpretation of probability has been highly influential in science. This paper focuses on the application of this interpretation to quantum mechanics. We argue that de Finetti held that the coherence conditions of degrees of belief in events depend on their verifiability. Accordingly, the standard coherence conditions of degrees of belief that are familiar from the literature on subjective probability only apply to degrees of belief in events which could (in principle) be jointly verified; and the coherence conditions of degrees of belief in events that cannot be jointly verified are weaker. While the most obvious explanation of de Finetti's verificationism is the influence of positivism, we argue that it could be motivated by the radical subjectivist and instrumental nature of probability in his interpretation; for as it turns out, in this interpretation it is difficult to make sense of the idea of coherent degrees of belief in, and accordingly probabilities of unverifiable events. We then consider the application of this interpretation to quantum mechanics, concentrating on the Einstein-Podolsky-Rosen experiment and Bell's theorem. Outline 16.1 The background and motivation 16.2 Joint distributions, probabilistic inequalities and Bell's theorem 16.3 De Finetti's theory of probability 16.4 Verifiability, coherence and contextuality 16.5 Coherent degrees of belief for the EPR/Bohm experiment 16.6 De Finetti on the nature of quantum probabilities 16.7 Conclusions +Mailing address: IHPST, Victoria College, Rm 311,
doi:10.1007/978-3-642-21329-8_16 fatcat:zzgfd4hpxnhb5mjv6e6put7sua