dorsal/arxiv
View SchemaWhat is Probability?
| Authors | Simon Saunders |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412194 |
| URL | https://arxiv.org/abs/quant-ph/0412194 |
| DOI | 10.1007/3-540-26669-0_12 |
Abstract
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, nor the pilot-wave theory, nor stochastic state-reduction theories, give a satisfactory answer to the question of what objective probabilities are in quantum mechanics, or why they should satisfy the Born rule; nor do they give any reason why subjective probabilities should track objective ones. But it is shown that if probability only arises with decoherence, then they must be given by the Born rule. That further, on the Everett interpretation, we have a clear statement of what probabilities are, in terms of purely categorical physical properties; and finally, along lines recently laid out by Deutsch and Wallace, that there is a clear basis in the axioms of decision theory as to why subjective probabilities should track these objective ones. These results hinge critically on the absence of hidden-variables or any other mechanism (such as state-reduction) from the physical interpretation of the theory. The account of probability has traditionally been considered the principal weakness of the Everett interpretation; on the contrary it emerges as one of its principal strengths.
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"abstract": "Probabilities may be subjective or objective; we are concerned with both\nkinds of probability, and the relationship between them. The fundamental theory\nof objective probability is quantum mechanics: it is argued that neither Bohr\u0027s\nCopenhagen interpretation, nor the pilot-wave theory, nor stochastic\nstate-reduction theories, give a satisfactory answer to the question of what\nobjective probabilities are in quantum mechanics, or why they should satisfy\nthe Born rule; nor do they give any reason why subjective probabilities should\ntrack objective ones.\n But it is shown that if probability only arises with decoherence, then they\nmust be given by the Born rule. That further, on the Everett interpretation, we\nhave a clear statement of what probabilities are, in terms of purely\ncategorical physical properties; and finally, along lines recently laid out by\nDeutsch and Wallace, that there is a clear basis in the axioms of decision\ntheory as to why subjective probabilities should track these objective ones.\n These results hinge critically on the absence of hidden-variables or any\nother mechanism (such as state-reduction) from the physical interpretation of\nthe theory.\n The account of probability has traditionally been considered the principal\nweakness of the Everett interpretation; on the contrary it emerges as one of\nits principal strengths.",
"arxiv_id": "quant-ph/0412194",
"authors": [
"Simon Saunders"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/3-540-26669-0_12",
"title": "What is Probability?",
"url": "https://arxiv.org/abs/quant-ph/0412194"
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