# Is Bohmian quantum mechanics noncontextual and can it be tested?

Concerning to the different plausible modifications of Quantum Mechanics, we have the so-called Bohmian Quantum Mechanics. It is frequently stated that Bohmian Quantum Mechanics is non-local, but is it non-contextual and so beyond quantum mechanics? Does non-locality of bohmian QM imply necessarily non-contextuality? Note the paper: https://arxiv.org/abs/quant-ph/0406166 remarks that the sense in which Bohmian QM is "contextual" (or non-contextual) depends on your notion of contextuality. So, to what extent is bohmian QM contextual or non-contextual? Furthermore, can the contextuality or non-contextuality of bohmian QM be tested experimentally? How?

## 1 Answer

It is contextual as every theory with hidden variables which complete QM. The Kochen–Specker theorem states that no non-contextual hidden variable model can reproduce the predictions of quantum theory when the dimension of the Hilbert space is three or more. Bohmian Quantum Mechanics refers to the theory of one or more particles with or without spin, so that the Hilbert space of the quantum theory is at least some $L^2(\mathbb R^k)$ that is infinite dimensional.

• No, it is not in the general sense: arxiv.org/abs/quant-ph/0406166 This paper notes that Bohmian Quantum Mechanics is NOT as contextual as another approaches. – riemannium Dec 28 '17 at 23:20
• This also rises the question of how much contextual a theory can be... – riemannium Dec 28 '17 at 23:47
• @Valter Moretti-Why do you write explains between quotation marks? – descheleschilder Dec 29 '17 at 3:16
• @riemannium So, it seems to me that you already have an answer. What I wrote is also G. C. Ghirardi's opinion on this issue as I found in the book "philosophy of physics" (unfortunately in Italian). There, Ghirardi discussed contextuality of Bohm's approach. Personally I am not interested in this question. – Valter Moretti Dec 29 '17 at 7:39
• @descheleschilder Just because I was not sure on the verb to use here. I replaced it for complete without quotation marks. – Valter Moretti Dec 29 '17 at 7:42