Earman, John (2017) Additivity Requirements in Classical and Quantum Probability. [Preprint]
|
Text
Forms of Additivity 5.5.17 Laura + Gordon Revision.pdf Download (305kB) | Preview |
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.
| Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |
| Social Networking: |
| Item Type: | Preprint | ||||||
|---|---|---|---|---|---|---|---|
| Creators: |
|
||||||
| 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.pitt.edu/id/eprint/13024 |
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
 |
View Item |
![[feed]](http://philsci-archive.pitt.edu/style/images/feed-icon-32x32.png){kind=icon}