dorsal/arxiv
View SchemaOn Reichenbach's common cause principle and Reichenbach's notion of common cause
| Authors | G. Hofer-Szabo, M. Redei, L. E. Szabo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9805066 |
| URL | https://arxiv.org/abs/quant-ph/9805066 |
Abstract
It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbach's definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle.
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"abstract": "It is shown that, given any finite set of pairs of random events in a Boolean\nalgebra which are correlated with respect to a fixed probability measure on the\nalgebra, the algebra can be extended in such a way that the extension contains\nevents that can be regarded as common causes of the correlations in the sense\nof Reichenbach\u0027s definition of common cause. It is shown, further, that, given\nany quantum probability space and any set of commuting events in it which are\ncorrelated with respect to a fixed quantum state, the quantum probability space\ncan be extended in such a way that the extension contains common causes of all\nthe selected correlations, where common cause is again taken in the sense of\nReichenbach\u0027s definition. It is argued that these results very strongly\nrestrict the possible ways of disproving Reichenbach\u0027s Common Cause Principle.",
"arxiv_id": "quant-ph/9805066",
"authors": [
"G. Hofer-Szabo",
"M. Redei",
"L. E. Szabo"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"math.PR"
],
"title": "On Reichenbach\u0027s common cause principle and Reichenbach\u0027s notion of common cause",
"url": "https://arxiv.org/abs/quant-ph/9805066"
},
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