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Additivity Requirements in Classical and Quantum Probability

Earman, John (2017) Additivity Requirements in Classical and Quantum Probability. [Preprint]

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Abstract

The discussion of different principles of additivity (finite vs. countable vs. complete additivity) for probability functions has been largely focused on the personalist interpretation of probability. Very little attention has been given to additivity principles for physical probabilities. The form of additivity for quantum probabilities is determined by the algebra of observables that characterize a physical system and the type of quantum state that is realizable and preparable for that system. We assess arguments designed to show that only normal quantum states are realizable and preparable and, therefore, quantum probabilities satisfy the principle of complete additivity. We underscore the little remarked fact that unless the dimension of the Hilbert space is incredibly large, complete additivity in ordinary non-relativistic quantum mechanics (but not in relativistic quantum field theory) reduces to countable additivity. We then turn to ways in which knowledge of quantum probabilities may constrain rational credence about quantum events and, thereby, constrain the additivity principle satisfied by rational credence functions.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Earman, Johnjearman@pitt.edu
Keywords: probability, additivity principles, quantum mechanics, Lewis' Principal Principle
Subjects: Specific Sciences > Physics
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Quantum Mechanics
Depositing User: John Earman
Date Deposited: 04 May 2017 22:56
Last Modified: 04 May 2017 22:56
Item ID: 13024
Subjects: Specific Sciences > Physics
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Quantum Mechanics
Date: 4 May 2017
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/13024

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