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Can a Bohmian be a Rovellian for all practical purposes?

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Abstract

The aim of this article is to discuss the preferred basis problem in relational quantum mechanics (RQM). The issue is at the heart of quantum mechanics and we first show that the mathematical formalism of RQM is immune to recent critics concerning consistency. Moreover, we also analyse the notion of interaction in RQM and provide a for all practical purposes reading of RQM comparing it with Bohmian mechanics.

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Notes

  1. ‘The two electrons in the ground state of the helium atom are correlated, but no one would say that each electron “measures” its partner’[8].

  2. The present analysis is motivated by the recent discussion made by Rovelli at the online ‘quantum foundation’ conference: https://www.youtube.com/watch?v=QtU10moL-MI and by private discussions with him concerning RQM and his recent book [2].

  3. We don’t have to suppose that an electron has a mind or consciousness. It is for this reason that I donc accept the Brukner analysis relying on mind states in different basis. For the problem with this concept see the note [12] where it is shown that mind states associated with states of knowledge \(|O_1\rangle\) and \(|O_1\rangle\) have to be orthogonal if the observed subsystem states are: \(\langle S_1|S_2\rangle =0\). In my opinion this conflicts with the postulate ‘DisRS’ of [9].

  4. If it is physical we get something like the spontaneaous collapse theory and if it epistemic we obtain either a version of Wigner’s interpretation involving the mind [17] or a version of QBism involving ‘agents’ [18].

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Acknowledgements

I wish to thank Claudio Calosi for inviting me to participate to this special issue concerning RQM and also Carlo Rovelli for very interesting discussions concerning the physical meaning of RQM. I emphasize that the view presented here concerning RQM is only mine and is not necessarily shared by Calosi or Rovelli.

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  1. Institut NEEL, CNRS and Université Grenoble Alpes, Grenoble, 38000, France

    Aurélien Drezet

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  1. Aurélien Drezet
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Correspondence to Aurélien Drezet.

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After this work was completed a critical analysis of RQM was discussed in [20] and commented by the present author in [21] (see also the reply [22]). I believe that the present analysis of RQM actually constitutes a reply to [20].

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Drezet, A. Can a Bohmian be a Rovellian for all practical purposes?. Found Phys 53, 30 (2023). https://doi.org/10.1007/s10701-023-00670-5

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