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QBism and Relational Quantum Mechanics compared

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Abstract

The subjective Bayesian interpretation of quantum mechanics (QBism) and Rovelli’s relational interpretation of quantum mechanics (RQM) are both notable for embracing the radical idea that measurement outcomes correspond to events whose occurrence (or not) is relative to an observer. Here we provide a detailed study of their similarities and especially their differences.

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Notes

  1. A notable exception being Brukner’s interpretation [33, 34].

  2. In QBism I cannot meaningfully posit that there is another version of ‘me’ who had a different experience; per definition that other person would not be ‘me’.

  3. Rovelli has implied in Ref.[28] and elsewhere that RQM is agnostic to the direction of time. This implies that we may choose the observer’s proper time to increase in either direction, corresponding to different ways of defining the observer’s ‘history’ and ‘future’, hence different ways of defining their perspective and state assignments.

  4. More plausibly, doing so might result in something resembling Healey’s pragmatist interpretation.

  5. QBism does not make any special assumptions about what kinds of things can satisfy these requirements: perhaps machines and other complex arrangements of inanimate matter could qualify. Rather, the question of agency is taken as a pragmatic assumption: so long as it is useful to think of a given entity as choosing actions in order to attain certain ends, then normative rules may be employed in modeling it.

  6. Note that it is possible to interpret probabilities as objective and still conclude that quantum theory is normative. For instance, in Healey’s interpretation probabilities are objective in the sense that there is an objectively ‘best’ quantum state assignment for a given agent. Nevertheless, like in QBism, probabilities are taken to be the agent’s degrees of belief, so the rules of quantum theory are normative in Healey’s account.

  7. Formally, this means the agent holds several ‘generic’ beliefs about how systems respond to measurements, as well as the ‘quantum-specific belief’ that the number of outcomes of a minimal informationally complete measurement of the system is equal to the square of it’s maximum information storage capacity (i.e. its dimension). See [13] for details.

  8. Note that in order to pose the scenario in QBism we must assume that the agents initially agree that they are measuring the same atom using the same practical procedure. There is no conflict here: nothing in QBism forbids agreement; our question is whether there is anything that makes it mandatory.

  9. It would be interesting to investigate whether holding certain beliefs might compel agents to agree in order to avoid being incoherent; but that is a different question than the one we are considering here.

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Acknowledgements

I am grateful to Carlo Rovelli and Andrea Di Biagio for enlightening and cordial correspondence about the differences between RQM and QBism. I also thank Chris Fuchs, Blake Stacey and John DeBrota for feedback on an early draft. This work was supported in part by the John E. Fetzer Memorial Trust.

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  1. QBism group, University of Massachusetts Boston, Boston, MA, USA

    Jacques Pienaar

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Correspondence to Jacques Pienaar.

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Communicated by Carlo Rovelli.

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Pienaar, J. QBism and Relational Quantum Mechanics compared. Found Phys 51, 96 (2021). https://doi.org/10.1007/s10701-021-00501-5

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