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Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics

A no-go result on common cause approaches via Hardy relations

Katsuaki Higashi

Published May 11, 2019• 2 citations
Publisher
DOI
10.1016/j.shpsb.2019.04.003

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Hardy presented a famous argument that shows that there exist no hidden variables in quantum mechanics. His argument is called Hardy's paradox. The commentaries and discussions on Hardy's paradox have been ordinarily presented for deterministic hidden variables, and it has not been discussed whether a similar paradox will occurs in probabilistic hidden variables. So, first, I will show that Hardy's argument can also be applied to probabilistic hidden variables. After that, I discuss the common cause of a correlation, which has been actively discussed in the philosophy of science in recent years. That is because requiring the common cause of a quantum correlation is mathematically equivalent to introducing a probabilistic hidden variable to explain the correlation. Some researchers argued that in the non-existence proof of hidden variables, the existence of a common common-cause to multiple correlations is tacitly assumed, however that is unreasonably strong. According to their idea, it is sufficient if there exists a respective common-cause of each correlation. However, it will be revealed that at least as far as Hardy's paradox is concerned, merely weakening the common common-cause requirement to the respective common-cause requirement does not help to construct a local model.
According to a conventional view, there exists no common-cause model of quantum correlations satisfying locality requirements. In fact, Bell's inequality is derived from some locality conditions and the assumption that the common cause exists, and the violation of the inequality has been experimentally verified. On the other hand, some researchers argue that in the derivation of the inequality the existence of a common common-cause for multiple correlations is implicitly assumed and that the assumption is unreasonably strong. According to their idea, what is necessary for explaining the quantum correlation is a common cause for each correlation. However, in this paper, we will show that in almost all entangled states we can not construct a local model that is consistent with quantum mechanical prediction even when we require only the existence of a common cause of each correlation.